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 e^iφ 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!!!!!!

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.

Did you have a college in mind for your undergraduate studies?  

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.

Did you do research while earning your undergraduate degree?  

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.

What’s your least favorite part of your job?

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.

Do you love your job?

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!!

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, .

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.

Before I arrived in Los Angeles, I thought I might need to hit the brakes a bit with some of the radical physics theories I’d encountered during my preliminary research. After all, these were scientists I was meeting: people who “engage in a systematic activity to acquire knowledge that describes and predicts the natural world”, according to Wikipedia. It turns out I wasn’t hardly as far-out as they were.

I could recount numerous anecdotes that exemplify my encounter with the frighteningly intelligent and vivid imagination of the people at LIGO with whom I had the great pleasure of working – Prof. Rana X. Adhikari, Maria Okounkova, Eric Quintero, Maximiliano Isi, Sarah Gossan, and Jameson Graef Rollins – but in the end it all boils down to a parable about fish.

Rana’s version, which he recounted to me on our first meeting, goes as follows: “There are these two young fish swimming along, and a scientist approaches the aquarium and proclaims, “We’ve finally discovered the true nature of water!” And the two young fish swim on for a bit, and then eventually one of them looks over at the other and goes, “What the hell is water?”” In David Foster Wallace’s more famous version, the scientist is not a scientist but an old fish, who greets them saying, “Morning, boys. How’s the water?”

The difference is not circumstantial. Foster Wallace’s version is an argument against “unconsciousness, the default setting, the rat race, the constant gnawing sense of having had, and lost, some infinite thing” – personified by the young fish – and an urgent call for awareness – personified by the old fish. But in Rana’s version, the matter is more hard-won: as long as they are fish, they haven’t the faintest apprehension of the very concept of water: even a wise old fish would fail to notice. In this adaptation, gaining awareness of that which is “so real and essential, so hidden in plain sight all around us, all the time” as Foster Wallace describes it, demands much more than just an effort in mindfulness. It demands imagining the unimaginable.

Albert Einstein once said that “Imagination is more important than knowledge. For knowledge is limited to all we now know and understand, while imagination embraces the entire world, and all there ever will be to know and understand.” But the question remains of how far our imagination can reach, and where the radius ends for us in “what there ever will be to know and understand”, versus that which happens to be. My earlier remark about LIGO scientists’ being far-out does not at all refer to a speculative disposition, which would characterise amateur anything-goes, and does go over-the-edge pseudo-science. Rather, it refers to the high level of creativity that is demanded of physicists today, and to the untiring curiosity that drives them to expand the limits of that radius, despite all odds.

The possibility of imagination has become an increasingly animating thought within my currently ongoing project:

As an independent curator of contemporary art, I travelled to Caltech for a 6-week period of research, towards developing an exhibition that will invite the public to engage with some of the highly challenging implications around the concept of time in physics. In it, I identify LIGO’s breakthrough detection of gravitational waves as an unparalleled incentive by which to acquire – in broad cultural terms – a new sense of time that departs from the old and now wholly inadequate one. After LIGO’s announcement proved that time fluctuation not only happens, but that it happened here, to us, on a precise date and time, it is finally possible for a broader public to relate, however abstract some of the concepts from the field of physics may remain. More simply put: we can finally sense that the water is moving.[1]

One century after Einstein’s Theory of General Relativity, most people continue to hold a highly impoverished idea of the nature of time, despite it being perhaps the most fundamental element of our existence. For 100 years there was no blame or shame in this. Because within all possible changes to the three main components of the universe – space, time & energy – the fluctuation of time was always the only one that escaped our sensorial capacities, existing exclusively in our minds, and finding its fullest expression in mathematical language. If you don’t speak mathematics, time fluctuation remains impossible to grasp, and painful to imagine.

But on February 11th, 2016, this situation changed dramatically.

On this date, a televised announcement told the world of the first-ever sensory detection of time-fluctuation, made with the aid of the most sensitive machine ever to be built by mankind. Finally, we have sensorial access to variations in all components of the universe as we know it. What is more, we observe the non-static passage of time through sound, thereby connecting it to the most affective of our senses.

Of course, LIGO’s detection is limited to time fluctuation and doesn’t yet make other mind-bending behaviours of time observable. But this is only circumstantial. The key point is that we can take this initial leap, and that it loosens our feet from the cramp of Newtonian fixity. Once in this state, gambolling over to ideas about zero time tunnelling, non-causality, or the future determining the present, for instance, is far more plausible, and no longer painful but rather seductive, at least, perhaps, for the playful at heart.

Taking a slight off-road (to be re-routed in a moment): there is a common misconception about children’s allegedly free-spirited creativity. Watching someone aged between around 4 and 15 draw a figure will demonstrate quite clearly just how taut they really are, and that they apply strict schemes that follow reality as they see and learn to see it. Bodies consistently have eyes, mouths, noses, heads, rumps and limbs, correctly placed and in increasingly realistic colours. Ask them to depart from these conventions – “draw one eye on his forehead”, “make her face green” – like masters such as Pablo Picasso and Henri Matisse have done – and they’ll likely become very upset (young adolescents being particularly conservative, reaching the point of panic when challenged to shed consensus).

This is not to compare the lay public (including myself) to children, but to suggest that there’s no inborn capacity – the unaffected, ‘genius’ naïveté that the modernist movements of Primitivism, Art Brut and Outsider Art exalted – for developing a creativity that is of substance. Arriving at a consequential idea, in both art and physics, entails a great deal of acumen and is far from gratuitous, however whimsical the moment in which it sometimes appears. And it’s also to suggest that there’s a necessary process of acquaintance – the knowledge of something through experience – in taking a cognitive leap away from the seemingly obvious nature of reality. If there’s some truth in this, then LIGO’s expansion of our sensorial access to the fluctuation of time, together with artistic approaches that lift the remaining questions and ambiguities of spacetime onto a relational, experiential plane, lay fertile ground on which to begin to foster a new sense of time – on a broad cultural level – however slowly it unfolds.

The first iteration of this project will be an exhibition, to take place in Berlin, in July 2017. It will feature existing and newly commissioned works by established and upcoming artists from Los Angeles and Berlin, working in sound, installation and video, to stage a series of immersive environments that invite the viewers’ bodily interaction.

Though the full selection cannot be disclosed just yet, I would like here to provide a glimpse of two works-in-progress by artist-duo Evelina Domnitch & Dmitry Gelfand, whom I invited to Los Angeles to collaborate in my research with LIGO, and whose contribution has been of great value to the project.

For more details on the exhibition, please stay tuned, and be warmly welcome to visit Berlin in July!

Text & images: courtesy of the artists.

ORBIHEDRON | 2017

A dark vortex in the middle of a water-filled basin emits prismatic bursts of rotating light. Akin to a radiant ergosphere surrounding a spinning black hole, Orbihedron evokes the relativistic as well as quantum interpretation of gravity – the reconciliation of which is essential for unravelling black hole behaviour and the origins of the cosmos. Descending into the eye of the vortex, a white laser beam reaches an impassible singularity that casts a whirling circular shadow on the basin’s floor. The singularity lies at the bottom of a dimple on the water’s surface, the crown of the vortex, which acts as a concave lens focussing the laser beam along the horizon of the “black hole” shadow. Light is seemingly swallowed by the black hole in accordance with general relativity, yet leaks out as quantum theory predicts.

ER = EPR | 2017

Two co-rotating vortices, joined together via a slender vortical bridge, lethargically drift through a body of water. Light hitting the water’s surface transforms the vortex pair into a dynamic lens, projecting two entangled black holes encircled by shimmering halos. As soon as the “wormhole” link between the black holes rips apart, the vortices immediately dissipate, analogously to the collapse of a wave function. Connecting distant black holes or two sides of the same black hole, might wormholes be an example of cosmic-scale quantum entanglement? This mind-bending conjecture of Juan Maldacena and Leonard Susskind can be traced back to two iconoclastic papers from 1935. Previously thought to be unrelated (both by their authors and numerous generations of readers), one article, the legendary EPR (penned by Einstein, Podolsky and Rosen) engendered the concept of quantum entanglement or “spooky action at a distance”; and the second text theorised Einstein-Rosen (ER) bridges, later known as wormholes. Although the widely read EPR paper has led to the second quantum revolution, currently paving the way to quantum simulation and computation, ER has enjoyed very little readership. By equating ER to EPR, the formerly irreconcilable paradigms of physics have the potential to converge: the phenomenon of gravity is imagined in a quantum mechanical context. The theory further implies, according to Maldacena, that the undivided, “reliable structure of space-time is due to the ghostly features of entanglement”.

[1] I am here extending our capacity to sense to that of the technology itself, which indeed measured the warping of spacetime. However, in interpreting gravitational waves from a human frame of reference (moving nowhere near the speed of light at which gravitational waves travel), they would seem to be spatial. In fact, the elongation of space (a longer wavelength) directly implies that time slows down (a longer wave-period), so that the two are indistinguishable.

Isabel de Sena

For decades, understanding the origin of high temperature superconductivity has been regarded as the Holy Grail by physicists in the condensed matter community. The importance of high temperature superconductivity resides not only in its technological promises, but also in the dazzling number of exotic phases and elementary excitations it puts on display for physicists. These myriad phases and excitations give physicists new dimensions and building bricks for understanding and exploiting the world of collective phenomena. The pseudogap, charge-density-wave, nematic and spin liquid phases, for examples, are a few exotica that are found in cuprate high temperature superconductors. Understanding these phases is important for understanding the mechanism behind high temperature superconductivity, but they are also interesting in and of themselves.

The charge-density-wave (CDW) phase in the cuprates – a spontaneous emergence of a periodic modulation of charge density in real space – has particularly garnered a lot of attention. It emerges upon the destruction of the parent antiferromagnetic Mott insulating phase with doping and it appears to directly compete with superconductivity. Whether or not these features are generic, or maybe even necessary, for high temperature superconductivty is an important question. Unfortunately, currently there exists no other comparable high temperature superconducting materials family that enables such questions to be answered.

Recently, the iridates have emerged as a possible analog to the cuprates. The single layer variant Sr₂IrO₄, for example, exhibits signatures of both a pseudogap phase and a high temperature superconducting phase. However, with an increasing parallel being drawn between the iridates and the cuprates in terms of their electronic phases, CDW has so far eluded detection in any iridate, calling into question the validity of this comparison. Rather than studying the single layer variant, we decided to look at the bilayer iridate Sr₃Ir₂O₇ in which a clear Mott insulator to metal transition has been reported with doping.

While CDW has been observed in many materials, what made it elusive in cuprates for many years is its spatially short-ranged (it extends only a few lattice spacings long) and often temporally short-ranged (it blinks in and out of existence quickly) nature. To get a good view of this order, experimentalists had to literally pin it down using external influences like magnetic fields or chemical dopants to suppress the temporal fluctuations and then use very sensitive diffraction or scanning tunneling based probes to observe them.

But rather than looking in real space for signatures of the CDW order, an alternative approach is to look for them in the time domain. Works by the Gedik group at MIT and the Orenstein group at U.C. Berkeley have shown that one can use ultrafast time-resolved optical reflectivity to “listen” for the tone of a CDW to infer its presence in the cuprates. In these experiments, one impulsively excites a coherent mode of the CDW using a femtosecond laser pulse, much like one would excite the vibrational mode of a tuning fork by impulsively banging it. One then stroboscopically looks for these CDW oscillations via temporally periodic modulations in its optical reflectivity, much like one would listen for the tone produced by the tuning fork. If you manage to hear the tone of the CDW, then you have established its existence!

We applied a similar approach to Sr₃Ir₂O₇ and its doped versions [hear our experiment]. To our delight, the ringing of a CDW mode sounded immediately upon doping across its Mott insulator to metal transition, implying that the electronic liquid born from the doped Mott insulator is unstable to CDW formation, very similar to the case in cuprates. Also like the case of cuprates, this charge-density-wave is of a special nature: it is either very short-ranged, or temporally fluctuating. Whether or not there is a superconducting phase that competes with the CDW in Sr₃Ir₂O₇ remains to be seen. If so, the phenomenology of the cuprates may really be quite generic. If not, the interesting question of why not is worth pursuing. And who knows, maybe the fact that we have a system that can be controllably tuned between the antiferromagnetic order and the CDW order may find use in technology some day.

Few settings foster equanimity like Canada’s Banff International Research Station (BIRS). Mountains tower above the center, softened by pines. Mornings have a crispness that would turn air fresheners evergreen with envy. The sky looks designed for a laundry-detergent label.

Doesn’t it?

One day into my visit, equilibrium shattered my equanimity.

I was participating in the conference “Beyond i.i.d. in information theory.” What “beyond i.i.d.” means is explained in these articles.  I was to present about resource theories for thermodynamics. Resource theories are simple models developed in quantum information theory. The original thermodynamic resource theory modeled systems that exchange energy and information.

Imagine a quantum computer built from tiny, cold, quantum circuits. An air particle might bounce off the circuit. The bounce can slow the particle down, transferring energy from particle to circuit. The bounce can entangle the particle with the circuit, transferring quantum information from computer to particle.

Suppose that particles bounced off the computer for ages. The computer would thermalize, or reach equilibrium: The computer’s energy would flatline. The computer would reach a state called the canonical ensemble. The canonical ensemble looks like this:  .

Joe Renes and I had extended these resource theories. Thermodynamic systems can exchange quantities other than energy and information. Imagine white-bean soup cooling on a stovetop. Gas condenses on the pot’s walls, and liquid evaporates. The soup exchanges not only heat, but also particles, with its environment. Imagine letting the soup cool for ages. It would thermalize to the grand canonical ensemble, . Joe and I had modeled systems that exchange diverse thermodynamic observables.^*

What if, fellow beyond-i.i.d.-er Jonathan Oppenheim asked, those observables didn’t commute with each other?

Mathematical objects called operators represent observables. Let represent a system’s energy, and let represent the number of particles in the system. The operators fail to commute if multiplying them in one order differs from multiplying them in the opposite order: .

Suppose that our quantum circuit has observables represented by noncommuting operators and . The circuit cannot have a well-defined energy and a well-defined particle number simultaneously. Physicists call this inability the Uncertainty Principle. Uncertainty and noncommutation infuse quantum mechanics as a Cashmere Glow^TM infuses a Downy fabric softener.

Quantum uncertainty and noncommutation.

I glowed at Jonathan: All the coolness in Canada couldn’t have pleased me more than finding someone interested in that question.^** Suppose that a quantum system exchanges observables and with the environment. Suppose that and don’t commute, like components and of quantum angular momentum. Would the system thermalize? Would the thermal state have the form ? Could we model the system with a resource theory?

Jonathan proposed that we chat.

The chat sucked in beyond-i.i.d.-ers Philippe Faist and Andreas Winter. We debated strategies while walking to dinner. We exchanged results on the conference building’s veranda. We huddled over a breakfast table after colleagues had pushed their chairs back. Information flowed from chalkboard to notebook; energy flowed in the form of coffee; food particles flowed onto the floor as we brushed crumbs from our notebooks.

Exchanges of energy and particles.

The idea morphed and split. It crystallized months later. We characterized, in three ways, the thermal state of a quantum system that exchanges noncommuting observables with its environment.

First, we generalized the microcanonical ensemble. The microcanonical ensemble is the thermal state of an isolated system. An isolated system exchanges no observables with any other system. The quantum computer and the air molecules can form an isolated system. So can the white-bean soup and its kitchen. Our quantum system and its environment form an isolated system. But they cannot necessarily occupy a microcanonical ensemble, thanks to noncommutation.

We generalized the microcanonical ensemble. The generalization involves approximation, unlikely measurement outcomes, and error tolerances. The microcanonical ensemble has a simple definition—sharp and clean as Banff air. We relaxed the definition to accommodate noncommutation. If the microcanonical ensemble resembles laundry detergent, our generalization resembles fabric softener.

Suppose that our system and its environment occupy this approximate microcanonical ensemble. Tracing out (mathematically ignoring) the environment yields the system’s thermal state. The thermal state basically has the form we expected, .

This exponential state, we argued, follows also from time evolution. The white-bean soup equilibrates upon exchanging heat and particles with the kitchen air for ages. Our quantum system can exchange observables with its environment for ages. The system equilibrates, we argued, to the state . The argument relies on a quantum-information tool called canonical typicality.

Third, we defined a resource theory for thermodynamic exchanges of noncommuting observables. In a thermodynamic resource theory, the thermal states are the worthless states: From a thermal state, one can’t extract energy usable to lift a weight or to power a laptop. The worthless states, we showed, have the form of .

Three path lead to the form of the thermal state of a quantum system that exchanges noncommuting observables with its environment. We published the results this summer.

Not only was Team Banff spilling coffee over . So were teams at Imperial College London and the University of Bristol. Our conclusions overlap, suggesting that everyone calculated correctly. Our methodologies differ, generating openings for exploration. The mountain passes between our peaks call out for mapping.

So does the path to physical reality. Do these thermal states form in labs? Could they? Cold atoms offer promise for realizations. In addition to experiments and simulations, master equations merit study. Dynamical typicality, Team Banff argued, suggests that results from equilibration. Master equations model equilibration. Does some Davies-type master equation have as its fixed point? Email me if you have leads!

Experimentalists, can you realize the thermal state whose charges don’t commute?

A photo of Banff could illustrate Merriam-Webster’s entry for “equanimity.” Banff equanimity deepened our understanding of quantum equilibrium. But we wouldn’t have understood quantum equilibrium if questions hadn’t shattered our tranquility. Give me the disequilibrium of recognizing problems, I pray, and the equilibrium to solve them.

^*By “observable,” I mean “property that you can measure.”

^**Teams at Imperial College London and Bristol asked that question, too. More pleasing than three times the coolness in Canada!