# Life among the experimentalists

I used to catch lizards—brown anoles, as I learned to call them later—as a child. They were colored as their name suggests, were about as long as one of my hands, and resented my attention. But they frequented our back porch, and I had a butterfly net. So I’d catch lizards, with my brother or a friend, and watch them. They had throats that occasionally puffed out, exposing red skin, and tails that detached and wriggled of their own accord, to distract predators.

Some theorists might appreciate butterfly nets, I imagine, for catching experimentalists. Some of us theorists will end a paper or a talk with “…and these predictions are experimentally accessible.” A pause will follow the paper’s release or the talk, in hopes that a reader or an audience member will take up the challenge. Usually, none does, and the writer or speaker retires to the Great Deck Chair of Theory on the Back Patio of Science.

So I was startled when an anole, metaphorically speaking, volunteered a superconducting qubit for an experiment I’d proposed.

The experimentalist is one of the few people I can compare to a reptile without fear that he’ll take umbrage: Kater Murch, an associate professor of physics at Washington University in St. Louis. The most evocative description of Kater that I can offer appeared in an earlier blog post: “Kater exudes the soberness of a tenured professor but the irreverence of a Californian who wears his hair slightly long and who tattooed his wedding band on.”

Kater expressed interest in an uncertainty relation I’d proved with theory collaborators. According to some of the most famous uncertainty relations, a quantum particle can’t have a well-defined position and a well-defined momentum simultaneously. Measuring the position disturbs the momentum; any later momentum measurement outputs a completely random, or uncertain, number. We measure uncertainties with entropies: The greater an entropy, the greater our uncertainty. We can cast uncertainty relations in terms of entropies.

I’d proved, with collaborators, an entropic uncertainty relation that describes chaos in many-particle quantum systems. Other collaborators and I had shown that weak measurements, which don’t disturb a quantum system much, characterize chaos. So you can check our uncertainty relation using weak measurements—as well as strong measurements, which do disturb quantum systems much. One can simplify our uncertainty relation—eliminate the chaos from the problem and even eliminate most of the particles. An entropic uncertainty relation for weak and strong measurements results.

Kater specializes in weak measurements, so he resolved to test our uncertainty relation. Physical Review Letters published the paper about our collaboration this month. Quantum measurements can not only create uncertainty, the paper shows, but also reduce it: Kater and his PhD student Jonathan Monroe used light to measure a superconducting qubit, a tiny circuit in which current can flow forever. The qubit had properties analogous to position and momentum (the spin’s z– and x-components). If the atom started with a well-defined “position” (the z-component) and the “momentum” (the x-component) was measured, the outcome was highly random; the total uncertainty about the two measurements was large. But if the atom started with a well-defined “position” (z-component) and another property (the spin’s y-component) was measured before the “momentum” (the x-component) was measured strongly, the total uncertainty was lower. The extra measurement was designed not to disturb the atom much. But the nudge prodded the atom enough, rendering the later “momentum” measurement (the x measurement) more predictable. So not only can quantum measurements create uncertainty, but gentle quantum measurements can also reduce it.

I didn’t learn only physics from our experiment. When I’d catch a lizard, I’d tip it into a tank whose lid contained a magnifying lens, and I’d watch the lizard. I didn’t trap Kater and Jonathan under a magnifying glass, but I did observe their ways. Here’s what I learned about the species experimentalus quanticus.

1) They can run experiments remotely when a pandemic shuts down campus: A year ago, when universities closed and cities locked down, I feared that our project would grind to a halt. But Jonathan twiddled knobs and read dials via his computer, and Kater popped into the lab for the occasional fixer-upper. Jonathan even continued his experiment from another state, upon moving to Texas to join his parents. And here we theorists boast of being able to do our science almost anywhere.

2) They speak with one less layer of abstraction than I: We often discussed, for instance, the thing used to measure the qubit. I’d call the thing “the detector.” Jonathan would call it “the cavity mode,” referring to the light that interacts with the qubit, which sits in a box, or cavity. I’d say “poh-tay-toe”; they’d say “poh-tah-toe”; but I’m glad we didn’t call the whole thing off.

3) Experiments take longer than expected—even if you expect them to take longer than estimated: Kater and I hatched the plan for this project during June 2018. The experiment would take a few months, Kater estimated. It terminated last summer.

4) How they explain their data: Usually in terms of decoherence, the qubit’s leaking of quantum information into its environment. For instance, to check that the setup worked properly, Jonathan ran a simple test that ended with a measurement. (Experts: He prepared a $\sigma_z$ eigenstate, performed a Hadamard gate, and measured $\sigma_z$.) The measurement should have had a 50% chance of yielding $+1$ and a 50% chance of yield $-1$. But the $-1$ outcome dominated the trials. Why? Decoherence pushed the qubit toward toward $-1$. (Amplitude damping dominated the noise.)

5) Seeing one’s theoretical proposal turn into an experiment feels satisfying: Due to point (3), among other considerations, experiments aren’t cheap. The lab’s willingness to invest in the idea I’d developed with other theorists was heartening. Furthermore, the experiment pushed us to uncover more theory—for example, how tight the uncertainty bound could grow.

After getting to know an anole, I’d release it into our backyard and bid it adieu.1 So has Kater moved on to experimenting with topology, and Jonathan has progressed toward graduation. But more visitors are wriggling in the Butterfly Net of Theory-Experiment Collaboration. Stay tuned.

1Except for the anole I accidentally killed, by keeping it in the tank for too long. But let’s not talk about that.

# May you go from weakness to weakness

I used to eat lunch at the foundations-of-quantum-theory table.

I was a Masters student at the Perimeter Institute for Theoretical Physics, where I undertook a research project during the spring term. The project squatted on the border between quantum information theory and quantum foundations, where my two mentors worked. Quantum foundations concerns how quantum physics differs from classical physics; which alternatives to quantum physics could govern our world but don’t; and those questions, such as about Schrödinger’s cat, that fascinate us when we first encounter quantum theory, that many advisors warn probably won’t land us jobs if we study them, and that most physicists argue about only over a beer in the evening.

I don’t drink beer, so I had to talk foundations over sandwiches around noon.

One of us would dream up what appeared to be a perpetual-motion machine; then the rest of us would figure out why it couldn’t exist. Satisfied that the second law of thermodynamics still reigned, we’d decamp for coffee. (Perpetual-motion machines belong to the foundations of thermodynamics, rather than the foundations of quantum theory, but we didn’t discriminate.) I felt, at that lunch table, an emotion blessed to a student finding her footing in research, outside her country of origin: belonging.

The quantum-foundations lunch table came to mind last month, when I learned that Britain’s Institute of Physics had selected me to receive its International Quantum Technology Emerging Researcher Award. I was very grateful for the designation, but I was incredulous: Me? Technology? But I began grad school at the quantum-foundations lunch table. Foundations is to technology as the philosophy of economics is to dragging a plow across a wheat field, at least stereotypically.

Worse, I drag plows from wheat field to barley field to oat field. I’m an interdisciplinarian who never belongs in the room I’ve joined. Among quantum information theorists, I’m the thermodynamicist, or that theorist who works with experimentalists; among experimentalists, I’m the theorist; among condensed-matter physicists, I’m the quantum information theorist; among high-energy physicists, I’m the quantum information theorist or the atomic-molecular-and-optical (AMO) physicist; and, among quantum thermodynamicists, I do condensed matter, AMO, high energy, and biophysics. I usually know less than everyone else in the room about the topic under discussion. An interdisciplinarian can leverage other fields’ tools to answer a given field’s questions and can discover questions. But she may sound, to those in any one room, as though she were born yesterday. As Kermit the Frog said,

Grateful as I am, I’d rather not dwell on why the Institute of Physics chose my file; anyone interested can read the citation or watch the thank-you speech. But the decision turned out to involve foundations and interdisciplinarity. So I’m dedicating this article to two sources of inspiration: an organization that’s blossomed by crossing fields and an individual who’s driven technology by studying fundamentals.

Britain’s Institute for Physics has a counterpart in the American Physical Society. The latter has divisions, each dedicated to some subfield of physics. If you belong to the society and share an interest in one of those subfields, you can join that division, attend its conferences, and receive its newsletters. I learned about Division of Soft Matter from this article, which I wish I could quote almost in full. This division’s members study “a staggering variety of materials from the everyday to the exotic, including polymers such as plastics, rubbers, textiles, and biological materials like nucleic acids and proteins; colloids, a suspension of solid particles such as fogs, smokes, foams, gels, and emulsions; liquid crystals like those found in electronic displays; [ . . . ] and granular materials.” Members belong to physics, chemistry, biology, engineering, and geochemistry.

Despite, or perhaps because of, its interdisciplinarity, the division has thrived. The group grew from a protodivision (a “topical group,” in the society’s terminology) to a division in five years—at “an unprecedented pace.” Intellectual diversity has complemented sociological diversity: The division “ranks among the top [American Physical Society] units in terms of female membership.” The division’s chair observes a close partnership between theory and experiment in what he calls “a vibrant young field.”

And some division members study oobleck. Wouldn’t you like to have an excuse to say “oobleck” every day?

The second source of inspiration lives, like the Institute of Physics, in Britain. David Deutsch belongs at the quantum-foundations table more than I. A theoretical physicist at Oxford, David cofounded the field of quantum computing. He explained why to me in a fusion of poetry and the pedestrian: He was “fixing the roof” of quantum theory. As a graduate student, David wanted to understand quantum foundations—what happens during a measurement—but concluded that quantum theory has too many holes. The roof was leaking through those holes, so he determined to fix them. He studied how information transformed during quantum processes, married quantum theory with computer science, and formalized what quantum computers could and couldn’t accomplish. Which—years down the road, fused with others’ contributions—galvanized experimentalists to harness ions and atoms, improve lasers and refrigerators, and build quantum computers and quantum cryptography networks.

David is a theorist and arguably a philosopher. But he’d have swept the Institute of Physics’s playing field, could he have qualified as an “emerging researcher” this autumn (David began designing quantum algorithms during the 1980s).

I returned to the Perimeter Institute during the spring term of 2019. I ate lunch at the quantum-foundations table, and I felt that I still belonged. I feel so still. But I’ve eaten lunch at other tables by now, and I feel that I belong at them, too. I’m grateful if the habit has been useful.

Congratulations to Hannes Bernien, who won the institute’s International Quantum Technology Young Scientist Award, and to the “highly commended” candidates, whom you can find here!

# Quantum steampunk invades Scientific American

London, at an hour that made Rosalind glad she’d nicked her brother’s black cloak instead of wearing her scarlet one. The factory alongside her had quit belching smoke for the night, but it would start again soon. A noise caused her to draw back against the brick wall. Glancing up, she gasped. An oblong hulk was drifting across the sky. The darkness obscured the details, but she didn’t need to see; a brass-colored lock would be painted across the side. Mellator had launched his dirigible.

A variation on the paragraph above began the article that I sent to Scientific American last year. Clara Moskowitz, an editor, asked which novel I’d quoted the paragraph from. I’d made the text up, I confessed.

Most of my publications, which wind up in physics journals, don’t read like novels. But I couldn’t resist when Clara invited me to write a feature about quantum steampunk, the confluence of quantum information and thermodynamics. Quantum Frontiers regulars will anticipate paragraphs two and three of the article:

Welcome to steampunk. This genre has expanded across literature, art and film over the past several decades. Its stories tend to take place near nascent factories and in grimy cities, in Industrial Age England and the Wild West—in real-life settings where technologies were burgeoning. Yet steampunk characters extend these inventions into futuristic technologies, including automata and time machines. The juxtaposition of old and new creates an atmosphere of romanticism and adventure. Little wonder that steampunk fans buy top hats and petticoats, adorn themselves in brass and glass, and flock to steampunk conventions.

These fans dream the adventure. But physicists today who work at the intersection of three fields—quantum physics, information theory and thermodynamics—live it. Just as steampunk blends science-fiction technology with Victorian style, a modern field of physics that I call “quantum steampunk” unites 21st-century technology with 19th-century scientific principles.

The Scientific American graphics team dazzled me. For years, I’ve been hankering to work with artists on visualizing quantum steampunk. I had an opportunity after describing an example of quantum steampunk in the article. The example consists of a quantum many-body engine that I designed with members Christopher White, Sarang Gopalakrishnan, and Gil Refael of Caltech’s Institute for Quantum Information and Matter. Our engine is a many-particle system ratcheted between two phases accessible to quantum matter, analogous to liquid and solid. The engine can be realized with, e.g., ultracold atoms or trapped ions. Lasers would trap and control the particles. Clara, the artists, and I drew the engine, traded comments, and revised the figure tens of times. In early drafts, the lasers resembled the sketches in atomic physicists’ Powerpoints. Before the final draft, the lasers transformed into brass-and-glass beauties. They evoke the scientific instruments crafted through the early 1900s, before chunky gray aesthetics dulled labs.

Scientific American published the feature this month; you can read it in print or, here, online. Many thanks to Clara for the invitation, for shepherding the article into print, and for her enthusiasm. To repurpose the end of the article, “You’re reading about this confluence of old and new on Quantum Frontiers. But you might as well be holding a novel by H. G. Wells or Jules Verne.”

Figures courtesy of the Scientific American graphics team.

# Achieving superlubricity with graphene

Sometimes, experimental results spark enormous curiosity inspiring a myriad of questions and ideas for further experimentation. In 2004, Geim and Novoselov, from The University of Manchester, isolated a single layer of graphene from bulk graphite with the “Scotch Tape Method” for which they were awarded the 2010 Nobel Prize in Physics.  This one experimental result has branched out countless times serving as a source of inspiration in as many different fields.  We are now in the midst of an array of branching-out in graphene research, and one of those branches gaining attention is ultra low friction observed between graphene and other surface materials.

Much has been learned about graphene in the past 15 years through an immense amount of research, most of which, in non-mechanical realms (e.g., electron transport measurements, thermal conductivity, pseudo magnetic fields in strain engineering).  However, superlubricity, a mechanical phenomenon, has become the focus among many research groups. Mechanical measurements have famously shown graphene’s tensile strength to be hundreds of times that of the strongest steel, indisputably placing it atop the list of construction materials best for a superhero suit.  Superlubricity is a tribological property of graphene and is, arguably, as equally impressive as graphene’s tensile strength.

Tribology is the study of interacting surfaces during relative motion including sources of friction and methods for its reduction.  It’s not a recent discovery that coating a surface with graphite (many layers of graphene) can lower friction between two sliding surfaces.  Current research studies the precise mechanisms and surfaces for which to minimize friction with single or several layers of graphene.

Research published in Nature Materials in 2018 measures friction between surfaces under constant load and velocity. The experiment includes two groups; one consisting of two graphene surfaces (homogeneous junction), and another consisting of graphene and hexagonal boron nitride (heterogeneous junction).   The research group measures friction using Atomic Force Microscopy (AFM).  The hexagonal boron nitride (or graphene for a homogeneous junction) is fixed to the stage of the AFM while the graphene slides atop.  Loads are held constant at 20 𝜇N and sliding velocity constant at 200 nm/s. Ultra low friction is observed for homogeneous junctions when the underlying crystalline lattice structures of the surfaces are at a relative angle of 30 degrees.  However, this ultra low friction state is very unstable and upon sliding, the surfaces rotate towards a locked-in lattice alignment. Friction varies with respect to the relative angle between the two surface’s crystalline lattice structures. Minimum (ultra low) friction occurs at a relative angle of 30 degrees reaching a maximum when locked-in lattice alignment is realized upon sliding. While in a state of lattice alignment, shearing is rendered impossible with the experimental setup due to the relatively large amount of friction.

Friction varies with respect to the relative angle of the crystalline lattice structures and is, therefore, anisotropic.  For example, the fact it takes less force to split wood when an axe blade is applied parallel to its grains than when applied perpendicularly illustrates the anisotropic nature of wood, as the force to split wood is dependent upon the direction along which the force is applied.  Frictional anisotropy is greater in homogeneous junctions because the tendency to orient into a stuck, maximum friction alignment, is greater than with heterojunctions.  In fact, heterogeneous junctions experience frictional anisotropy three orders of magnitude less than homogeneous junctions. Heterogenous junctions display much less frictional anisotropy due to a lattice misalignment when the angle between the lattice vectors is at a minimum.  In other words, the graphene and hBN crystalline lattice structures are never parallel because the materials differ, therefore, never experience the impact of lattice alignment as do homogenous junctions. Hence, heterogeneous junctions do not become stuck in a high friction state that characterizes homogeneous ones, and experience ultra low friction during sliding at all relative crystalline lattice structure angles.

Presumably, to increase applicability, upscaling to much larger loads will be necessary. A large scale cost effective method to dramatically reduce friction would undoubtedly have an enormous impact on a great number of industries.  Cost efficiency is a key component to the realization of graphene’s potential impact, not only as it applies to superlubricity, but in all areas of application.  As access to large amounts of affordable graphene increases, so will experiments in fabricating devices exploiting the extraordinary characteristics which have placed graphene and graphene based materials on the front lines of material research the past couple decades.

# A Roman in a Modern Court

Yesterday I spent some time wondering how to explain the modern economy to an ancient Roman brought forward from the first millennium BCE. For now I’ll assume language isn’t a barrier, but not much more. Here’s my rough take:

“There have been five really important things that were discovered since when you left and now.

First, every living thing has a tiny blueprint inside it. We learned how to rewrite those, and now we can make crops that resist pests, grow healthy, and take minimal effort to cultivate. The same tool also let us make creatures that manufacture medicine, as well as animals different from anything that existed before. Food became cheap because of this.

Second, we learned that hot air and steam expand. This means you can burn oil or coal and use that to push air around, which in turn can push against solid objects. With this we’ve made vehicles that can go the span of the Empire from Rome to Londinium and back in hours rather than weeks. Similar mechanisms can be used to work farms, forge metal, and so on. Manufactured goods became cheap as a result.

Third, we discovered an invisible fluid that lives in metals. It flows unimaginably quickly and with minimal force through even very narrow channels, so by pushing on it in one city it may be made to move almost instantly in another. That lets you work with energy as a kind of commodity, rather than something that hooks up and is generated specifically for each device.

Fourth, we found that this fluid can be pushed around by light, including a kind human eyes can’t see. This lets a device make light in one place and push on the fluid in a different device with no metal in between. Communication became fast, cheap, and easy.

Finally, and this one takes some explaining, our machines can make decisions. Imagine you had a channel for water with a fork. You can insert a blade to control which route the water takes. If you attach that blade to a lever you can change the direction of the flow. If you dip that lever in another channel of water, then what flows in one channel can set which way another channel goes. It turns out that that’s all you need to make simple decisions like “If water is in this channel, flow down that other one.”, which can then be turned into useful statements like “Put water in this channel if you’re attacked. It’ll redirect the other channel and release boiling oil.” With enough of these water switches you can do really complicated things like tracking money, searching for patterns, predicting the weather, and so on. While water is hard to work with, you can make these channels and switches almost perfect for the invisible fluid, and you can make them tiny, vastly smaller than the width of a hair. A device that fits in your hand might have more switches than there are grains in a cubic meter of sand. The number of switches we’ve made so far outnumbers all the grains of sand on Earth, and we’re just getting started.”

# The math of multiboundary wormholes

Xi Dong, Alex Maloney, Henry Maxfield and I recently posted a paper to the arXiv with the title: Phase Transitions in 3D Gravity and Fractal Dimension. In other words, we’ll get about ten readers per year for the next few decades. Despite the heady title, there’s deep geometrical beauty underlying this work. In this post I want to outline the origin story and motivation behind this paper.

There are two different branches to the origin story. The first was my personal motivation and the second is related to how I came into contact with my collaborators (who began working on the same project but with different motivation, namely to explain a phase transition described in this paper by Belin, Keller and Zadeh.)

During the first year of my PhD at Caltech I was working in the mathematics department and I had a few brief but highly influential interactions with Nikolai Makarov while I was trying to find a PhD advisor. His previous student, Stanislav Smirnov, had recently won a Fields Medal for his work studying Schramm-Loewner evolution (SLE) and I was captivated by the beauty of these objects.

SLE example from Scott Sheffield’s webpage. SLEs are the fractal curves that form at the interface of many models undergoing phase transitions in 2D, such as the boundary between up and down spins in a 2D magnet (Ising model.)

One afternoon, I went to Professor Makarov’s office for a meeting and while he took a brief phone call I noticed a book on his shelf called Indra’s Pearls, which had a mesmerizing image on its cover. I asked Professor Makarov about it and he spent 30 minutes explaining some of the key results (which I didn’t understand at the time.) When we finished that part of our conversation Professor Makarov described this area of math as “math for the future, ahead of the tools we have right now” and he offered for me to borrow his copy. With a description like that I was hooked. I spent the next six months devouring this book which provided a small toehold as I tried to grok the relevant mathematics literature. This year or so of being obsessed with Kleinian groups (the underlying objects in Indra’s Pearls) comes back into the story soon. I also want to mention that during that meeting with Professor Makarov I was exposed to two other ideas that have driven my research as I moved from mathematics to physics: quasiconformal mappings and the simultaneous uniformization theorem, both of which will play heavy roles in the next paper I release.  In other words, it was a pretty important 90 minutes of my life.

Google image search for “Indra’s Pearls”. The math underlying Indra’s Pearls sits at the intersection of hyperbolic geometry, complex analysis and dynamical systems. Mathematicians oftentimes call this field the study of “Kleinian groups”. Most of these figures were obtained by starting with a small number of Mobius transformations (usually two or three) and then finding the fixed points for all possible combinations of the initial transformations and their inverses. Indra’s Pearls was written by David Mumford, Caroline Series and David Wright. I couldn’t recommend it more highly.

My life path then hit a discontinuity when I was recruited to work on a DARPA project, which led to taking an 18 month leave of absence from Caltech. It’s an understatement to say that being deployed in Afghanistan led to extreme introspection. While “down range” I had moments of clarity where I knew life was too short to work on anything other than ones’ deepest passions. Before math, the thing that got me into science was a childhood obsession with space and black holes. I knew that when I returned to Caltech I wanted to work on quantum gravity with John Preskill. I sent him an e-mail from Afghanistan and luckily he was willing to take me on as a student. But as a student in the mathematics department, I knew it would be tricky to find a project that involved all of: black holes (my interest), quantum information (John’s primary interest at the time) and mathematics (so I could get the degree.)

I returned to Caltech in May of 2012 which was only two months before the Firewall Paradox was introduced by Almheiri, Marolf, Polchinski and Sully. It was obvious that this was where most of the action would be for the next few years so I spent a great deal of time (years) trying to get sharp enough in the underlying concepts to be able to make comments of my own on the matter. Black holes are probably the closest things we have in Nature to the proverbial bottomless pit, which is an apt metaphor for thinking about the Firewall Paradox. After two years I was stuck. I still wasn’t close to confident enough with AdS/CFT to understand a majority of the promising developments. And then at exactly the right moment, in the summer of 2014, Preskill tipped my hat to a paper titled Multiboundary Wormholes and Holographic Entanglement by Balasubramanian, Hayden, Maloney, Marolf and Ross. It was immediately obvious to me that the tools of Indra’s Pearls (Kleinian groups) provided exactly the right language to study these “multiboundary wormholes.” But despite knowing a bridge could be built between these fields, I still didn’t have the requisite physics mastery (AdS/CFT) to build it confidently.

Before mentioning how I met my collaborators and describing the work we did together, let me first describe the worlds that we bridged together.

3D Gravity and Universality

As the media has sensationalized to death, one of the most outstanding questions in modern physics is to discover and then understand a theory of quantum gravity.  As a quick aside, Quantum gravity is just a placeholder name for such a theory. I used italics because physicists have already discovered candidate theories, such as string theory and loop quantum gravity (I’m not trying to get into politics, just trying to demonstrate that there are multiple candidate theories). But understanding these theories — carrying out all of the relevant computations to confirm that they are consistent with Nature and then doing experiments to verify their novel predictions — is still beyond our ability. Surprisingly, without knowing the specific theory of quantum gravity that guides Nature’s hand, we’re still able to say a number of universal things that must be true for any theory of quantum gravity. The most prominent example being the holographic principle which comes from the entropy of black holes being proportional to the surface area encapsulated by the black hole’s horizon (a naive guess says the entropy should be proportional to the volume of the black hole; such as the entropy of a glass of water.) Universal statements such as this serve as guideposts and consistency checks as we try to understand quantum gravity.

It’s exceedingly rare to find universal statements that are true in physically realistic models of quantum gravity. The holographic principle is one such example but it pretty much stands alone in its power and applicability. By physically realistic I mean: 3+1-dimensional and with the curvature of the universe being either flat or very mildly positively curved.  However, we can make additional simplifying assumptions where it’s easier to find universal properties. For example, we can reduce the number of spatial dimensions so that we’re considering 2+1-dimensional quantum gravity (3D gravity). Or we can investigate spacetimes that are negatively curved (anti-de Sitter space) as in the AdS/CFT correspondence. Or we can do BOTH! As in the paper that we just posted. The hope is that what’s learned in these limited situations will back-propagate insights towards reality.

The motivation for going to 2+1-dimensions is that gravity (general relativity) is much simpler here. This is explained eloquently in section II of Steve Carlip’s notes here. In 2+1-dimensions, there are no “local”/”gauge” degrees of freedom. This makes thinking about quantum aspects of these spacetimes much simpler.

The standard motivation for considering negatively curved spacetimes is that it puts us in the domain of AdS/CFT, which is the best understood model of quantum gravity. However, it’s worth pointing out that our results don’t rely on AdS/CFT. We consider negatively curved spacetimes (negatively curved Lorentzian manifolds) because they’re related to what mathematicians call hyperbolic manifolds (negatively curved Euclidean manifolds), and mathematicians know a great deal about these objects. It’s just a helpful coincidence that because we’re working with negatively curved manifolds we then get to unpack our statements in AdS/CFT.

Multiboundary wormholes

Finding solutions to Einstein’s equations of general relativity is a notoriously hard problem. Some of the more famous examples include: Minkowski space, de-Sitter space, anti-de Sitter space and Schwarzschild’s solution (which describes perfectly symmetrical and static black holes.) However, there’s a trick! Einstein’s equations only depend on the local curvature of spacetime while being insensitive to global topology (the number of boundaries and holes and such.) If M is a solution of Einstein’s equations and $\Gamma$ is a discrete subgroup of the isometry group of $M$, then the quotient space $M/\Gamma$ will also be a spacetime that solves Einstein’s equations! Here’s an example for intuition. Start with 2+1-dimensional Minkowski space, which is just a stack of flat planes indexed by time. One example of a “discrete subgroup of the isometry group” is the cyclic group generated by a single translation, say the translation along the x-axis by ten meters. Minkowski space quotiented by this group will also be a solution of Einstein’s equations, given as a stack of 10m diameter cylinders indexed by time.

Start with 2+1-dimensional Minkowski space which is just a stack of flat planes index by time. Think of the planes on the left hand side as being infinite. To “quotient” by a translation means to glue the green lines together which leaves a cylinder for every time slice. The figure on the right shows this cylinder universe which is also a solution to Einstein’s equations.

D+1-dimensional Anti-de Sitter space ($AdS_{d+1}$) is the maximally symmetric d+1-dimensional Lorentzian manifold with negative curvature. Our paper is about 3D gravity in negatively curved spacetimes so our starting point is $AdS_3$ which can be thought of as a stack of Poincare disks (or hyperbolic sheets) with the time dimension telling you which disk (sheet) you’re on. The isometry group of $AdS_3$ is a group called $SO(2,2)$ which in turn is isomorphic to the group $SL(2, R) \times SL(2, R)$. The group $SL(2,R) \times SL(2,R)$ isn’t a very common group but a single copy of $SL(2,R)$ is a very well-studied group. Discrete subgroups of it are called Fuchsian groups. Every element in the group should be thought of as a 2×2 matrix which corresponds to a Mobius transformation of the complex plane. The quotients that we obtain from these Fuchsian groups, or the larger isometry group yield a rich infinite family of new spacetimes, which are called multiboundary wormholes. Multiboundary wormholes have risen in importance over the last few years as powerful toy models when trying to understand how entanglement is dispersed near black holes (Ryu-Takayanagi conjecture) and for how the holographic dictionary works in terms of mapping operators in the boundary CFT to fields in the bulk (entanglement wedge reconstruction.)

Three dimensional AdS can be thought of as a stack of hyperboloids indexed by time. It’s convenient to use the Poincare disk model for the hyperboloids so that the entire spacetime can be pictured in a compact way. Despite how things appear, all of the triangles have the same “area”.

I now want to work through a few examples.

BTZ black hole: this is the simplest possible example. It’s obtained by quotienting $AdS_3$ by a cyclic group $\langle A \rangle$, generated by a single matrix $A \in SL(2,R)$ which for example could take the form $A = \begin{pmatrix} e^{\lambda} & 0 \\ 0 & e^{-\lambda} \end{pmatrix}$. The matrix A acts by fractional linear transformation on the complex plane, so in this case the point $z \in \mathbb{C}$ gets mapped to $z\mapsto (e^{\lambda}z + 0)/(0z + e^{-\lambda}) = e^{2\lambda} z$. In this case

Start with $AdS_3$ as a stack of hyperbolic half planes indexed by time. A quotient by A means that each hyperbolic half plane gets quotiented. Quotienting a constant time slice by the map $z \mapsto e^{2\lambda}z$ gives a surface that’s topologically a cylinder. Using the picture above this means you glue together the solid black curves. The green and red segments become two boundary regions. We call it the BTZ black hole because when you add “time” it becomes impossible to send a signal from the green boundary to the red boundary, or vica versa. The dotted line acts as an event horizon.

Three boundary wormhole:

There are many parameterizations that we can choose to obtain the three boundary wormhole. I’ll only show schematically how the gluings go. A nice reference with the details is this paper by Henry Maxfield.

This is a picture of a constant time slice of $AdS_3$ quotiented by the A and B above. Each time slice is given as a copy of the hyperbolic half plane with the black arcs and green arcs glued together (by the maps A and B). These gluings yield a pair of pants surface. Each of the boundary regions are causally disconnected from the others. The dotted lines are black hole horizons that illustrate where the causal disconnection happens.

Torus wormhole:

It’s simpler to write down generators for the torus wormhole; but following along with the gluings is more complicated. To obtain the three boundary wormhole we quotient $AdS_3$ by the free group $\langle A, B \rangle$ where $A = \begin{pmatrix} e^{\lambda} & 0 \\ 0 & e^{-\lambda} \end{pmatrix}$ and $B = \begin{pmatrix} \cosh \lambda & \sinh \lambda \\ \sinh \lambda & \cosh \lambda \end{pmatrix}$. (Note that this is only one choice of generators, and a highly symmetrical one at that.)

This is a picture of a constant time slice of $AdS_3$ quotiented by the A and B above. Each time slice is given as a copy of the hyperbolic half plane with the black arcs and green arcs glued together (by the maps A and B). These gluings yield what’s called the “torus wormhole”. Topologically it’s just a donut with a hole cut out. However, there’s a causal structure when you add time to the mix where the dotted lines act as a black hole horizon, so that a message sent from behind the horizon will never reach the boundary.

Lorentzian to Euclidean spacetimes

So far we have been talking about negatively curved Lorentzian manifolds. These are manifolds that have a notion of both “time” and “space.” The technical definition involves differential geometry and it is related to the signature of the metric. On the other hand, mathematicians know a great deal about negatively curved Euclidean manifolds. Euclidean manifolds only have a notion of “space” (so no time-like directions.) Given a multiboundary wormhole, which by definition, is a quotient of $AdS_3/\Gamma$ where $\Gamma$ is a discrete subgroup of Isom($AdS_3$), there’s a procedure to analytically continue this to a Euclidean hyperbolic manifold of the form $H^3/ \Gamma_E$ where $H^3$ is three dimensional hyperbolic space and $\Gamma_E$ is a discrete subgroup of the isometry group of $H^3$, which is $PSL(2, \mathbb{C})$. This analytic continuation procedure is well understood for time-symmetric spacetimes but it’s subtle for spacetimes that don’t have time-reversal symmetry. A discussion of this subtlety will be the topic of my next paper. To keep this blog post at a reasonable level of technical detail I’m going to need you to take it on a leap of faith that to every Lorentzian 3-manifold multiboundary wormhole there’s an associated Euclidean hyperbolic 3-manifold. Basically you need to believe that given a discrete subgroup $\Gamma$ of $SL(2, R) \times SL(2, R)$ there’s a procedure to obtain a discrete subgroup $\Gamma_E$ of $PSL(2, \mathbb{C})$. Discrete subgroups of $PSL(2, \mathbb{C})$ are called Kleinian groups and quotients of $H^3$ by groups of this form yield hyperbolic 3-manifolds. These Euclidean manifolds obtained by analytic continuation arise when studying the thermodynamics of these spacetimes or also when studying correlation functions; there’s a sense in which they’re physical.

TLDR: you start with a 2+1-d Lorentzian 3-manifold obtained as a quotient $AdS_3/\Gamma$ and analytic continuation gives a Euclidean 3-manifold obtained as a quotient $H^3/\Gamma_E$ where $H^3$ is 3-dimensional hyperbolic space and $\Gamma_E$ is a discrete subgroup of $PSL(2,\mathbb{C})$ (Kleinian group.)

Limit sets:

Every Kleinian group $\Gamma_E = \langle A_1, \dots, A_g \rangle \subset PSL(2, \mathbb{C})$ has a fractal that’s naturally associated with it. The fractal is obtained by finding the fixed points of every possible combination of generators and their inverses. Moreover, there’s a beautiful theorem of Patterson, Sullivan, Bishop and Jones that says the smallest eigenvalue $\lambda_0$ of the spectrum of the Laplacian on the quotient Euclidean spacetime $H^3 / \Gamma_E$ is related to the Hausdorff dimension of this fractal (call it $D$) by the formula $\lambda_0 = D(2-D)$. This smallest eigenvalue controls a number of the quantities of interest for this spacetime but calculating it directly is usually intractable. However, McMullen proposed an algorithm to calculate the Hausdorff dimension of the relevant fractals so we can get at the spectrum efficiently, albeit indirectly.

This is a screen grab of Figure 2 from our paper. These are two examples of fractals that emerge when studying these spacetimes. Both of these particular fractals have a 3-fold symmetry. They have this symmetry because these particular spacetimes came from looking at something called “n=3 Renyi entropies”. The number q indexes a one complex dimensional family of spacetimes that have this 3-fold symmetry. These Kleinian groups each have two generators that are described in section 2.3 of our paper.

What we did

Our primary result is a generalization of the Hawking-Page phase transition for multiboundary wormholes. To understand the thermodynamics (from a 3d quantum gravity perspective) one starts with a fixed boundary Riemann surface and then looks at the contributions to the partition function from each of the ways to fill in the boundary (each of which is a hyperbolic 3-manifold). We showed that the expected dominant contributions, which are given by handlebodies, are unstable when the kinetic operator $(\nabla^2 - m^2)$ is negative, which happens whenever the Hausdorff dimension of the limit set of $\Gamma_E$ is greater than the lightest scalar field living in the bulk. One has to go pretty far down the quantum gravity rabbit hole (black hole) to understand why this is an interesting research direction to pursue, but at least anyone can appreciate the pretty pictures!

# Majorana update

If you are, by any chance, following progress in the field of Majorana bound states, then you are for sure super excited about ample Majorana results arriving this Fall. On the other hand, if you just heard about these elusive states recently, it is time for an update. For physicists working in the field, this Fall was perhaps the most exciting time since the first experimental reports from 2012. In the last few weeks there was not only one, but at least three interesting manuscripts reporting new insightful data which may finally provide a definitive experimental verification of the existence of these states in condensed matter systems.

But before I dive into these new results, let me give a brief history on the topic of  Majorana states and their experimental observation. The story starts with the young talented physicist Ettore Majorana, who hypothesized back in 1937 the existence of fermionic particles which were their own antiparticles. These hypothetical particles, now called Majorana fermions, were proposed in the context of elementary particle physics, but never observed. Some 60 years later, in the early 2000s, theoretical work emerged showing that Majorana fermionic states can exist as the quasiparticle excitations in certain low-dimensional superconducting systems (not a real particle as originally proposed, but otherwise having the exact same properties). Since then theorists have proposed half a dozen possible ways to realize Majorana modes using readily available materials such as superconductors, semiconductors, magnets, as well as topological insulators (for curious readers, I recommend manuscripts [1, 2, 3] for an overview of the different proposed methods to realize Majorana states in the lab).

The most fascinating thing about Majorana states is that they belong to the class of anyons, which means that they behave neither as bosons nor as fermions upon exchange. For example, if you have two identical fermionic (or bosonic) states and you exchange their positions, the quantum mechanical function describing the two states will acquire a phase factor of -1 (or +1). Anyons, on the other hand, can have an arbitrary phase factor eiφ upon exchange. For this reason, they are considered to be a starting point for topological quantum computation. If you want to learn more about anyons, check out the video below featuring IQIM’s Gil Refael and Jason Alicea.

Back in 2012, a group in Delft (led by Prof. Leo Kouwenhoven) announced the observation of zero-energy states in a nanoscale device consisting of a semiconductor nanowire coupled to a superconductor. These states behaved very similarly to the Majoranas that were previously predicted to occur in this system. The key word here is ‘similar’, since the behavior of these modes was not fully consistent with the theoretical predictions. Namely, the electrical conductance carried through the observed zero energy states was only about ~5% of the expected perfect transmission value for Majoranas. This part of the data was very puzzling, and immediately cast some doubts throughout the community. The physicists were quickly divided into what I will call enthusiasts (believers that these initial results indeed originated from Majorana states) and skeptics (who were pointing out that effects, other than Majoranas, can result in similarly looking zero energy peaks). And thus a great debate started.

In the coming years, experimentalists tried to observe zero energy features in improved devices, track how these features evolve with external parameters, such as gate voltages, length of the wires, etc., or focus on completely different platforms for hosting Majorana states, such as magnetic flux vortices in topological superconductors and magnetic atomic chains placed on a superconducting surface.  However, these results were not enough to convince skeptics that the observed states indeed originated from the Majoranas and not some other yet-to-be-discovered phenomenon. And so, the debate continued. With each generation of the experiments some of the alternative proposed scenarios were ruled out, but the final verification was still missing.

Fast forward to the events of this Fall and the exciting recent results. The manuscript I would like to invite you to read was just posted on ArXiv a couple of weeks ago. The main result is the observation of the perfectly quantized 2e2/h conductance at zero energy, the long sought signature of the Majorana states. This quantization implies that in this latest generation of semiconducting-superconducting devices zero-energy states exhibit perfect electron-hole symmetry and thus allow for perfect Andreev reflection. These remarkable results may finally end the debate and convince most of the skeptics out there.

###### Figure 1. (a,b) Comparison between devices and measurements from 2012 and 2017. (a) In 2012 a device made by combining a superconductor (Niobium Titanium Nitride alloy) and Indium Antimonide nanowire resulted in the first signature of zero energy states but the conductance peak was only about 0.1 x e2/h. Adapted from Mourik et al. Science 2012. (b) Similar device from 2017 made by carefully depositing superconducting Aluminum on Indium Arsenide. The fully developed 2e2/h conductance peak was observed. Adapted from Zhang et. al. ArXiv 2017. (c) Schematics of the Andreev reflection through the Normal (N)/Superconductor (S) interface. (d,e) Alternative view of the Andreev reflection process as a tunneling through a double barrier without and with Majorana modes (shown in yellow).

To fully appreciate these results, it is useful to quickly review the physics of Andreev reflection (Fig. 1c-e) that occurs at the interface between a normal region with a superconductor [4]. As the electron (blue) in the normal region enters a superconductor and pulls an additional electron with it to form a Copper pair, an extra hole (red) is left behind (Fig. 1(c)). You can also think about this process as the transmission through two leads, one connecting the superconductor to the electrons and the other to the holes (Fig. 1d). This allows us to view this problem as a transmission through the double barrier that is generally low. In the presence of a Majorana state, however, there is a resonant level at zero energy which is coupled with the same amplitude with both electrons and holes. This in turn results in the resonant Andreev reflection with a perfect quantization of 2e2/h (Fig. 1e). Note that, even in the configuration without Majorana modes, perfect quantization is possible but highly unlikely as it requires very careful tuning of the barrier potential (the authors did show that their quantization is robust against tuning the voltages on the gates, ruling out this possibility).

Going back to the experiments, you may wonder what made this breakthrough possible? It seems to be the combination of various factors, including using epitaxially grown  superconductors and more sophisticated fabrication methods. As often happens in experimental physics, this milestone did not come from one ingenious idea, but rather from numerous technical improvements obtained by several generations of hard-working grad students and postdocs.

If you are up for more Majorana reading, you can find two more recent eye-catching manuscripts here and here. Note that the list of interesting recent Majorana papers is a mere selection by the author and not complete by any means. A few months ago, my IQIM colleagues wrote a nice blog entry about topological qubits arriving in 2018. Although this may sound overly optimistic, the recent results suggest that the field is definitely taking off. While there are certainly many challenges to be solved, we may see the next generation of experiments designed to probe control over the Majorana states quite soon. Stay tuned for more!!!!!!

# A Few Words With Caltech Research Scientist, David Boyd

Twenty years ago, David Boyd began his career at Caltech as a Postdoctoral Scholar with Dave Goodwin, and since 2012 has held the position of Research Scientist in the Division of Physics, Mathematics and Astronomy.  A 20 year career at Caltech is in itself a significant achievement considering Caltech’s flair for amassing the very best scientists from around the world.  Throughout Boyd’s career he has secured 7 patents, and most recently discovered a revolutionary single-step method for growing graphene.  The method allows for unprecedented continuity in graphene growth essential to significantly scaling-up production capacity.  Boyd worked with a number of great scientists at the outset of his career.  Notably, he gained a passion for science from Professor Thomas Wdowiak (Mars’ Wdowiak Ridge is named in his honor) at the University of Alabama at Birmingham as an undergraduate, and worked as David Goodwin’s (best known for developing methods for growing thin film high-purity diamonds) postdoc at Caltech.  Currently, Boyd is formulating a way to apply Goodwin’s reaction modeling code to graphene.  Considering Boyd’s accomplishments and extensive scientific knowledge, I feel fortunate to have been afforded the opportunity to work in his lab the past six summers. I have learned much from Boyd, but I still have more questions (not all scientific), so I requested an interview and he graciously accepted.

On the day of the interview, I meet Boyd at his office on campus at Caltech.  We walk a ways down a sunlit hallway and out to a balcony through two glass doors.  There’s a slight breeze in the air, a smell of nearby roses, and the temperature is perfect.  It’s a picturesque day in Pasadena.  We sit at a table and I ask my first question.

How many patents do you own?

I have seven patents.  The graphene patent was really hard to get, but we got it.  We just got it executed in China, so they are allowed to use it.  This is particularly exciting because of all the manufacturing in China.  The patent system has changed a bit, so it’s getting harder and harder.  You can come up with the idea, but if disparate components have already been patented, then you can’t get the patent for combining them in a unique way.  The invention has to provide a result that is unexpected or not obvious, and the patent for growing graphene with a one step process was just that.  The one step process refers to cleaning the copper substrate and growing graphene under the same chemistry in a continuous manner.  What used to be a two step process can be done in one.

You don’t have to anneal the substrate to 1000 degrees before growing.

Exactly.  Annealing the copper first and then growing doesn’t allow for a nice continuous process.  Removing the annealing step means the graphene is growing in an environment with significantly lower temperatures, which is important for CMOS or computer chip manufacturing.

Which patents do you hold most dear?

Usually in the research areas that are really cutting edge.  I have three patents in plasmonics, and that was a fun area 10 years ago.  It was a new area and we were doing something really exciting.  When you patent something, an application may never be realized, sometimes they get used and sometimes they don’t.  The graphene patent has already been licensed, so we’ve received quite a bit of traction.  As far as commercial success, the graphene has been much more successful than the other ones, but plasmonics were a lot of fun.  Water desalinization may be one application, and now there is a whole field of plasmonic chemistry.  A company has not yet licensed it, so it may have been too far ahead of its time for application anytime soon.

When did you realize you wanted to be a scientist?

I liked Physics in high school, and then I had a great mentor in college, Thomas Wdowiak.  Wdowiak showed me how to work in the lab.  Science is one of those things where an initial spark of interest drives you into action.  I became hooked, because of my love for science, the challenge it offers, and the simple fact I have fun with it.  I feel it’s very important to get into the lab and start learning science as early as possible in your education.

Were you identified as a gifted student?

I don’t think that’s a good marker.  I went to a private school early on, but no, I don’t think I was good at what they were looking for, no I wasn’t.  It comes down to what you want to do.  If you want to do something and you’re motivated to do it, you’ll find ways to make it happen.  If you want to code, you start coding, and that’s how you get good at it.  If you want to play music and have a passion for it, at first it may be your parents saying you have to go practice, but in the end it’s the passion that drives everything else.

Did you like high school?

I went to high school in Alabama and I had a good Physics teacher.  It was not the most academic of places, and if you were into academics the big thing there was to go to medical school.  I just hated memorizing things so I didn’t go that route.

Were AP classes offered at your high school, and if so, were you an AP student?

Yeah, I did take AP classes.  My high school only had AP English and AP Math, but it was just coming onboard at that time.  I took AP English because I liked the challenge and I love reading.

Were you involved in any extracurricular activities in school?

I earned the rank of Eagle Scout in the Boy Scouts.  I also raced bicycles in high school, and I was a several time state champion.  I finished high school (in America) and wanted to be a professional cyclist.  So, I got involved in the American Field Service (AFS), and did an extra year of high school in Italy as an exchange student where I ended up racing with some of the best cyclists in the world all through Italy.  It was a fantastic experience.

No, I didn’t have a school in mind.  I had thought about the medical school path, so I considered taking pre-med courses at the local college, University of Alabama at Birmingham (UAB), because they have a good medical school.  Then UAB called me and said I earned an academic scholarship.  My father advised me that it would be a good idea to go there since it’s paid for.  I could take pre-med courses and then go to medical school afterwards if I wanted.  Well, I was in an honors program at the university and met an astronomer by the name Thomas Wdowiak.  I definitely learned from him how to be a scientist.  He also gave me a passion for being a scientist.  So, after working with Wdowiak for a while, I decided I didn’t want to go to medical school, I wanted to study Physics.  They just named a ridge on Mars after him, Wdowiak Ridge.  He was a very smart guy, and a great experimentalist who really grew my interest in science… he was great.

Yes, Wdowiak had me in the lab working all the time.  We were doing real stuff in the lab.  I did a lot of undergraduate research in Astronomy, and the whole point was to get in the lab and work on science.  Because I worked with Wdowiak I had one or two papers published by the time I graduated.  Wdowiak taught me how to do science.   And that’s the thing, you have to want to do science, have a lab or a place to practice, and then start working.

So, he was professor and experimentalist.

He was a very hands-on lab guy.  I was in the lab breaking things and fixing things. Astronomers are fun to work with.  He was an experimental astronomer who taught me, among other things, spectroscopy, vacuum technology, and much about the history of science.  In fact, it was Professor Wdowiak who told me about Millikan’s famous “Machine Shop in a Vacuum” experiment that inspired the graphene discovery… it all comes back to Caltech!

Name another scientist, other than Wdowiak, who has influenced you.

Richard Feynman also had a big influence on me.  I did not know him, but I love his books.

Were you focused solely on academics in college, or did you have a social life as well?

I was part of a concert committee that brought bands to the college.  We had some great bands like R.E.M. and the Red Hot Chili Peppers play, and I would work as a stagehand and a roadie for the shows.

So, you weren’t doing keg stands at fraternity parties?

No, it wasn’t like that.  I liked to go out and socialize, but no keg stands.  Though, I have had friends that were very successful that did do keg stands.

You’re always having to raise funds for salaries, equipment, and supplies.  It can be difficult, but once you get the funding it is a relief for the moment.  As a scientist, your focus isn’t always on just the science.

What are your responsibilities related to generating revenue for the university?

I raise funds for my projects via grants.  Part of the money goes to Caltech as overhead to pay for the facilities, lab space, and to keep the lights on.

What do you wish you could do more of in your job?

Less raising money.  I like working in the lab, which is fun.  Now that I have worked out the technique to grow graphene, I’m looking for applications.  I’m searching for the next impactful thing, and then I’ll figure out the necessary steps that need to be taken to get there.

Is there an aspect of your job that you believe would surprise people?

You have to be entrepreneurial, you have to sell your ideas to raise money for these projects.  You have to go with what’s hot in research.  There are certain things that get funded and things that don’t.

There may be some things you’re interested in, but other people aren’t, so there’s no funding.

Yeah, there may not be a need, therefore, no funding.  Right now, graphene is a big thing, because there are many applications and problems to be solved.  For example, diamonds were huge back in the ‘80’s.  But once they solved all the problems, research cooled off and industrial application took over.

Is there something else you’d really rather be researching, or are the trending ideas right now in line with your interests?

There is nothing else I’d rather be researching.  I’m in a good place right now.  We’re trying to commercialize the graphene research.  You try to do research projects that are complementary to one another.  For example, there’s a project underway, where graphene is being used for hydrogen storage in cars, that really interests me.  I do like the graphene work, it’s exciting, we’ll see where that goes.

What are the two most important personality traits essential to being a good scientist?

Creativity.  You have to think outside the box.  Perseverance.  I’m always reading and trying to understand something better.  Curiosity is, of course, a huge part of it as well. You gotta be obsessive too, I guess.  That’s more than two, sorry.

What does it take for someone to become a scientist?

You must have the desire to be a scientist, otherwise you’ll go be a stockbroker or something else.  It’s more of a passion thing, your personality.  You do have to have an aptitude for it though.  If you’re getting D’s in math, physics is probably not the place for you.  There’s an old joke, the medical student in physics class asks the professor, “Why do we have to take physics?  We’ll never use it.”  The Physics professor answers, “Physics saves lives, because it keeps idiots out of medical school.”  If you like science, but you’re not so good at math, then look at less quantitative areas of science where math is not as essential.  Computational physics and experimental physics will require you to be very good at math.  It takes a different temperament, a different set of skills.  Same curiosity, same drive and intelligence, but different temperament.

Do you ever doubt your own abilities?  Do you have insecurities about not being smart enough?

Sure, but there’s always going to be someone out there smarter.  Although, you really don’t want to ask yourself these types of questions.  If you do, you’re looking down the wrong end of the telescope.  Everyone has their doubts, but you need to listen to the feedback from the universe.  If you’re doing something for a long time and not getting results, then that’s telling you something.  Like I said, you must have a passion for what you’re doing.  If people are in doubt they should read biographies of scientists and explore their mindset to discover if science seems to be a good fit for them.  For a lot of people, it’s not the most fun job, it’s not the most social job, and certainly not the most glamorous type of job.  Some people need more social interaction, researchers are usually a little more introverted.  Again, it really depends on the person’s temperament. There are some very brilliant people in business, and it’s definitely not the case that only the brilliant people in a society go into science.  It doesn’t mean you can’t be doing amazing things just because you’re not in a scientific field.  If you like science and building things, then follow that path.  It’s also important not to force yourself to study something you don’t enjoy.

Scientists are often thought to work with giant math problems that are far above the intellectual capabilities of mere mortals.  Have you ever been in a particular situation where the lack of a solution to a math problem was impeding progress in the lab?  If so, what was the problem and did you discover the solution?

I’m attempting to model the process of graphene growth, so I’m facing this situation right now.  That’s why I have this book here.  I’m trying to adapt Professor Dave Goodwin’s Cantera reactor modeling code to model the reaction kinetics in graphene (Goodwin originally developed and wrote the modeling software called Cantera).  Dave was a big pioneer in diamond and he died almost 5 years ago here in Pasadena.  He developed a reaction modeling code for diamond, and I’m trying to apply that to graphene.  So, yeah, it’s a big math problem that I’ve been spending weeks on trying to figure out.  It’s not that I’m worried about the algebra or the coding, it’s trying to figure things out conceptually.

I do, I’ve done it for awhile, it’s fun, and I really enjoy it.  When it works, it’s great. Discovering stuff is fun and possesses a great sense of satisfaction.  But it’s not always that way, it can be very frustrating.  Like any good love affair, it has its peaks and valleys.  Sometimes you hate it, but that’s part of the relationship, it’s like… aaarrgghh!!

# Teacher Research at Caltech

The Yeh Lab group’s research activities at Caltech have been instrumental in studying semiconductors and making two-dimensional materials such as graphene, as highlighted on a BBC Horizons show.

An emerging sub-field of semiconductor and two-dimensional research is that of Transition metal dichalcogenide (TDMC) monolayers. In particular, a monolayer of Tungsten disulfide, a TDMC, is believed to exhibit interesting semiconductor properties when exposed to circularly polarized light. My role in the Yeh Lab, as a visiting high school Physics Teacher intern,  for the Summer of 2017 has been to help research and set up a vacuum chamber to study Tungsten disulfide samples under circularly polarized light.

What makes semiconductors unique is that conductivity can be controlled by doping or changes in temperature. Higher temperatures or doping can bridge the energy gap between the valence and conduction bands; in other words, electrons can start moving from one side of the material to the other. Like graphene, Tungsten disulfide has a hexagonal, symmetric crystal structure. Monolayers of transition metal dichalcogenides in such a honeycomb structure have two valleys of energy. One valley can interact with another valley. Circularly polarized light is used to populate one valley versus another. This gives a degree of control over the population of electrons by polarized light.

The Yeh Lab Group prides itself on making in-house the materials and devices needed for research. For example, in order to study high temperature superconductors, the Yeh Group designed and built their own scanning tunneling microscope. When they began researching graphene, instead of buying vast quantities of graphene, they pioneered new ways of fabricating it. This research topic has been no different: Wei-hsiang Lin, a Caltech graduate student, has been busy fabricating Tungsten disulfide samples via chemical vapor deposition (CVD) using Tungsten oxide and sulfur powder.

Wei-hsiang Lin’s area for using PLD to form the TDMC samples

The first portion of my assignment was spent learning more about vacuum chambers and researching what to order to confine our sample into the chamber. One must determine how the electronic feeds should be attached, how many are necessary, which vacuum pump will be used, how many flanges and gaskets of each size must be purchased in order to prepare the vacuum chamber.

There were also a number of flanges and parts already in the lab that needed to be examined for possible use. After triple checking the details the order was set with Kurt J. Lesker. Following a sufficient amount of anti-seize lubricant and numerous nuts, washers, and bolts, we assembled the vacuum chamber that will hold the TDMC sample.

The original vacuum chamber

Fun in the lab

The prepped vacuum chamber

The second part of my assignment was spent researching how to set up the optics for our experiment and ordering the necessary equipment. Once the experiment is up and running we will be using a milliWatt broad spectrum light source that is directed into a monochromator to narrow down the light to specific wavelengths for testing. Ultimately we will be evaluating the giant wavelength range of 300 nm through 1800 nm. Following the monochromator, light will be refocused by a planoconvex lens. Next, light will pass through a linear polarizer and then a circular polarizer (quarter wave plate). Lastly, the light will be refocused by a biconvex lens into the vacuum chamber and onto a 1 mm by 1 mm area of the sample.

Soon, we are excited to verify how tungsten disulfide responds to circularly polarized light.  Does our sample resonate at the exact same wavelengths as the first labs found? Why or why not?  What other unique properties are observed?  How can they be explained?  How is the Hall Effect observed?  What does this mean for the possible applications of semiconductors? How can the transfer of information from one valley to another be used in advanced electronics for communication?  Then, similar exciting experimentation will take place with graphene under circularly polarized light.

I love the sharp contrast of the high-energy, adolescent classroom to the quiet, calm of the lab.  I am grateful for getting to learn a different and new-to-me area of Physics during the summer.  Yes, I remember studying polarization and semiconductors in high school and as an undergraduate.  But it is completely different to set up an experiment from scratch, to be a part of groundbreaking research in these areas.  And it is just fun to get to work with your hands and build research equipment at a world leading research university.  Sometimes Science teachers can get bogged down with all the paperwork and meetings.  I am grateful to have had this fabulous opportunity during the summer to work on applied Science and to be re-energized in my love for Physics.  I look forward to meeting my new batch of students in a few short weeks to share my curiosity and joy for learning how the world works with them.

# Two Views of the Eclipse

I am sure many of us are thinking about the eclipse.

It all starts with how far are we going to drive in order to see totality. My family and I are currently in Colorado, so we are relatively close to the path of darkness in Wyoming. I thought about trying to book a hotel room. But if you’d like to see the dusk in Lusk, here is what you get:

Let us just say that I became quite acquainted with small-town WY and any-ville NE before giving up. Driving in the same day for 10 hours with my two children, ages 4 and 5, was not an option. So I will have to be content with 90% coverage.

90% coverage sounds like it is good enough… But when you think about the sun and its output, you realize that it won’t actually be very dark. The sun gives out about 1kW of light and heat per square meter. 90% of that still leaves us with 100W per meter squared. Imagine a room lit by a square array of 100W incandescent bulbs at one meter apart from each other. Not so dark. Luckily, we have really dark eclipse glasses.

All things considered, it is a huge coincidence that the moon is just about the right size and distance from the earth to block the sun exactly, $\frac{\mbox{sun radius}}{\mbox{sun-Earth distance}}=\frac{0.7\cdot 10^6 km}{150\cdot 10^6 km}\approx \frac{\mbox{luna radius}}{\mbox{luna-Earth distance}}=\frac{1.7\cdot 10^3 km}{385\cdot 10^3 km}$.

On a more personal note, another coincidence of a lesser cosmic meaning is that my wife, Jocelyn Holland, a professor of comparative literature at UCSB and Caltech, has also done research on eclipses. She has recently published an essay that shows how, for nineteenth-century observers, and astronomers in particular, the unique darkness associated with the eclipse during totality shook their subjective experience of time. Readers might want to share their own personal experiences at the end of this blog so that we can see how a twenty-first century perspective compares.

As for Jocelyn’s paper, here is a redacted ‘poetry for scientists’ excerpt from it.

Eclipses are well-known objects of scientific study but it is just as true that, throughout history, they have been perceived as the most supernatural of events, permitting superstition and fear to intrude. As a result, eclipses have frequently been used across cultures, in particular, by the community of scientists and scholars, as an index of “enlightenment.” Astronomers in the nineteenth century – an epoch that witnessed several mathematical advances in the calculation of solar and lunar eclipses, as exemplified in the work of Friedrich Bessel – looked back at prior centuries with scorn, mocking the irrational fears of times past. The German astronomer Ludwig August Busch, in text published shortly before a total eclipse in 1851, points out with some smugness that scarcely 200 years before then, in Germany, “the majority of the population threw itself upon its knees in desperation during a total eclipse,” and that the composure with which the next eclipse will be greeted is “the most certain proof how only science is able to conquer prejudices and superstition which prior centuries have gone through.”

Two solar eclipses were witnessed by Europeans in the mid-nineteenth century, on July 8th, 1842 and July 28th, 1851, when the first photographic image of an eclipse was made by Julius Berkowski (see below).

What Berkowski’s daguerreotype cannot convey, however, is a particular perception shared by both professional astronomers and amateur observers of these eclipses: that the darkness of the eclipse’s totality is unlike any darkness they had experienced before. As it turns out, this perception posed a challenge to their self-proclaimed enlightenment.

There was already a historical record in place describing the strange darkness of a total eclipse. As another nineteenth-century astronomer, Jacob Lehmann, phrased it, “How is it now to be explained, namely what several observers report during the eclipse of 1706, that the darkness at the time of the total occultation of the sun compares neither to night nor to dusk, but rather is of a particular kind. What is this particular kind?” The strange darkness of the eclipse presents a problem that one can state quite simply in temporal terms: it corresponds to no prior experience of natural light or time of day.

It might strike us as odd that August Ludwig Busch, the same astronomer who derided the superstition of prior generations, writes the following with reference to eclipses past, and in anticipation of the eclipse of 1851:

You will all remember the inexplicable melancholic frame of mind which one already experiences during large if not even total eclipses, when all objects appear in a dull, unusual light, there lies namely in the sight of great plains and far-spread drifts, upon which trees and rocks, although still illuminated by sunlight, still seem to cast no shadow, such a thing which causes mourning, that one is involuntarily overcome by horror. This feeling should occur more intensely in people when, during the total eclipse, a very peculiar darkness arrives which can be named neither night nor dusk.

August Ludwig Busch.

One can say that the perceived relationship between the quality of light and time of day is based on expectations that are so innate as to be taken as infallible until experience teaches otherwise. It is natural for us to use the available light in the sky as the basis for a measure of time when no time-keeping piece is on hand. The cyclical predictability of a steady increase and decrease in available light during the course of the day, however, in addition to all the nuances of how the midday light differs from dawn and twilight, is less than helpful in the rare event of an eclipse. The quality of light does not correspond to any experience of lived time. As a consequence, not only August Ludwig Busch, but also numerous other observers, attributed it to death, as if for lack of an alternative.

For all their claims of rationality, nineteenth-century observers were troubled by this darkness that conformed to no experienced time of day. It signaled to them, among other things, that time and light are out of joint. In short, as natural and as it may be, a full solar eclipse has, historically, posed a real challenge: not to the predictability of mechanical time-keeping, but rather to a very human experience of time.