Reading the sub(linear) text

Physicists are not known for finesse. “Even if it cost us our funding,” I’ve heard a physicist declare, “we’d tell you what we think.” Little wonder I irked the porter who directed me toward central Cambridge.

The University of Cambridge consists of colleges as the US consists of states. Each college has a porter’s lodge, where visitors check in and students beg for help after locking their keys in their rooms. And where physicists ask for directions.

Last March, I ducked inside a porter’s lodge that bustled with deliveries. The woman behind the high wooden desk volunteered to help me, but I asked too many questions. By my fifth, her pointing at a map had devolved to jabbing.

Read the subtext, I told myself. Leave.

Or so I would have told myself, if not for that afternoon.

That afternoon, I’d visited Cambridge’s CMS, which merits every letter in “Centre for Mathematical Sciences.” Home to Isaac Newton’s intellectual offspring, the CMS consists of eight soaring, glass-walled, blue-topped pavilions. Their majesty walloped me as I turned off the road toward the gatehouse. So did the congratulatory letter from Queen Elizabeth II that decorated the route to the restroom.

I visited Nilanjana Datta, an affiliated lecturer of Cambridge’s Faculty of Mathematics, and her student, Felix Leditzky. Nilanjana and Felix specialize in entropies and one-shot information theory. Entropies quantify uncertainties and efficiencies. Imagine compressing many copies of a message into the smallest possible number of bits (units of memory). How few bits can you use per copy? That number, we call the optimal compression rate. It shrinks as the number of copies compressed grows. As the number of copies approaches infinity, that compression rate drops toward a number called the message’s Shannon entropy. If the message is quantum, the compression rate approaches the von Neumann entropy.

Good luck squeezing infinitely many copies of a message onto a hard drive. How efficiently can we compress fewer copies? According to one-shot information theory, the answer involves entropies other than Shannon’s and von Neumann’s. In addition to describing data compression, entropies describe the charging of batteriesthe concentration of entanglementthe encrypting of messages, and other information-processing tasks.

Speaking of compressing messages: Suppose one-shot information theory posted status updates on Facebook. Suppose that that panel on your Facebook page’s right-hand side showed news weightier than celebrity marriages. The news feed might read, “TRENDING: One-shot information theory: Second-order asymptotics.”

Second-order asymptotics, I learned at the CMS, concerns how the optimal compression rate decays as the number of copies compressed grows. Imagine compressing a billion copies of a quantum message ρ. The number of bits needed about equals a billion times the von Neumann entropy HvN(ρ). Since a billion is less than infinity, 1,000,000,000 HvN(ρ) bits won’t suffice. Can we estimate the compression rate more precisely?

The question reminds me of gas stations’ hidden pennies. The last time I passed a station’s billboard, some number like $3.65 caught my eye. Each gallon cost about$3.65, just as each copy of ρ costs about HvN(ρ) bits. But a 9/10, writ small, followed the $3.65. If I’d budgeted$3.65 per gallon, I couldn’t have filled my tank. If you budget HvN(ρ) bits per copy of ρ, you can’t compress all your copies.

Suppose some station’s owner hatches a plan to promote business. If you buy one gallon, you pay $3.654. The more you purchase, the more the final digit drops from four. By cataloguing receipts, you calculate how a tank’s cost varies with the number of gallons, n. The cost equals$3.65 × n to a first approximation. To a second approximation, the cost might equal $3.65 × n + an, wherein a represents some number of cents. Compute a, and you’ll have computed the gas’s second-order asymptotics. Nilanjana and Felix computed a’s associated with data compression and other quantum tasks. Second-order asymptotics met information theory when Strassen combined them in nonquantum problems. These problems developed under attention from Hayashi, Han, Polyanski, Poor, Verdu, and others. Tomamichel and Hayashi, as well as Li, introduced quantumness. In the total-cost expression,$3.65 × n depends on n directly, or “linearly.” The second term depends on √n. As the number of gallons grows, so does √n, but √n grows more slowly than n. The second term is called “sublinear.”

Which is the word that rose to mind in the porter’s lodge. I told myself, Read the sublinear text.

Little wonder I irked the porter. At least—thanks to quantum information, my mistake, and facial expressions’ contagiousness—she smiled.

With thanks to Nilanjana Datta and Felix Leditzky for explanations and references; to Nilanjana, Felix, and Cambridge’s Centre for Mathematical Sciences for their hospitality; and to porters everywhere for providing directions.

“Feveral kinds of hairy mouldy fpots”

The book had a sheepskin cover, and mold was growing on the sheepskin. Robert Hooke, a pioneering microbiologist, slid the cover under one of the world’s first microscopes. Mold, he discovered, consists of “nothing elfe but feveral kinds of fmall and varioufly figur’d Mufhroms.” He described the Mufhroms in his treatise Micrographia, a 1665 copy of which I found in “Beautiful Science.” An exhibition at San Marino’s Huntington Library, “Beautiful Science” showcases the physics of rainbows, the stars that enthralled Galileo, and the world visible through microscopes.

Beautiful science of yesterday: An illustration, from Hooke’s Micrographia, of the mold.

“[T]hrough a good Microfcope,” Hooke wrote, the sheepskin’s spots appeared “to be a very pretty fhap’d Vegetative body.”

How like a scientist, to think mold pretty. How like quantum noise, I thought, Hooke’s mold sounds.

Quantum noise hampers systems that transmit and detect light. To phone a friend or send an email—“Happy birthday, Sarah!” or “Quantum Frontiers has released an article”—we encode our message in light. The light traverses a fiber, buried in the ground, then hits a detector. The detector channels the light’s energy into a current, a stream of electrons that flows down a wire. The variations in the current’s strength is translated into Sarah’s birthday wish.

If noise doesn’t corrupt the signal. From encoding “Happy birthday,” the light and electrons might come to encode “Hsappi birthdeay.” Quantum noise arises because light consists of packets of energy, called “photons.” The sender can’t control how many photons hit the detector.

To send the letter H, we send about 108 photons.* Imagine sending fifty H’s. When we send the first, our signal might contain 108- 153 photons; when we send the second, 108 + 2,083; when we send the third, 108 – 6; and so on. Receiving different numbers of photons, the detector generates different amounts of current. Different amounts of current can translate into different symbols. From H, our message can morph into G.

This spring, I studied quantum noise under the guidance of IQIM faculty member Kerry Vahala. I learned to model quantum noise, to quantify it, when to worry about it, and when not. From quantum noise, we branched into Johnson noise (caused by interactions between the wire and its hot environment); amplified-spontaneous-emission, or ASE, noise (caused by photons belched by ions in the fiber); beat noise (ASE noise breeds with the light we sent, spawning new noise); and excess noise (the “miscellaneous” folder in the filing cabinet of noise types).

Beautiful science of today: A microreso-nator—a tiny pendulum-like device— studied by the Vahala group.

Noise, I learned, has structure. It exhibits patterns. It has personalities. I relished studying those patterns as I relish sending birthday greetings while battling noise. Noise types, I see as a string of pearls unearthed in a junkyard. I see them as “pretty fhap[es]” in Hooke’s treatise. I see them—to pay a greater compliment—as “hairy mouldy fpots.”

*Optical-communications ballpark estimates:

• Optical power: 1 mW = 10-3 J/s
• Photon frequency: 200 THz = 2 × 1014 Hz
• Photon energy: h𝜈 = (6.626 × 10-34 J . s)(2 × 1014 Hz) = 10-19 J
• Bit rate: 1 GB = 109 bits/s
• Number of bits per H: 10
• Number of photons per H: (1 photon / 10-19 J) (10-3 J/s)(1 s / 109 bits)(10 bits / 1 H) = 108

An excerpt from this post was published today on Verso, the blog of the Huntington Library, Art Collection, and Botanical Gardens.

With thanks to Bassam Helou, Dan Lewis, Matt Stevens, and Kerry Vahala for feedback. With thanks to the Huntington Library (including Catherine Wehrey) and the Vahala group for the Micrographia image and the microresonator image, respectively.

The return of the superconducting high school teacher

Last summer, I was blessed with the opportunity to learn about the basics of high temperature superconductors in the Yeh Group under the tutelage of visiting Professor Feng. We formed superconducting samples using a process known as Pulse Laser Deposition. We began testing the properties of the samples using X-Ray Diffraction, AC Susceptibility, and SQUIDs (superconducting quantum interference devices). I brought my new-found knowledge of these laboratory techniques and processes back into the classroom during this past school year. I was able to answer questions about the formation, research, and applications of superconductors that I had been unable to address prior to this valuable experience.

This summer I returned to the IQIM Summer Research Institute to continue my exploration of superconductors and gain even deeper research experience. This time around I have accompanied Caltech second year graduate student Kyle Chen in testing samples using the Scanning Tunneling Microscope (STM), some of which I helped form using Pulse Laser Deposition with Professor Feng last summer. I have always been curious about how we can have atomic resolution. This has been my big chance to have hands-on experience working with STM that makes it possible!

The Scanning Tunneling Microscope was invented by the late Heinrich Rohrer and Gerd Binnig at IBM Research in Zurich, Switzerland in 1981. STM is able to scan the surface contours of substances using a sharp conductive tip. The electron tunneling current through the tip of the microscope is exponentially dependent on the distance (few Angstroms) to the substance surface. The changing currents at different locations can then be compiled to produce three dimensional images of the topography of the surface on the nano-scale. Or conversely the distance can be measured while the current is held constant. STM has a much higher resolution of images and avoids the problems of diffraction and spherical aberration from lenses. This level of control and precision through STM has enabled scientists to use tools with nanometer precision, allowing scientists even to manipulate atoms and their bonds. STM has been instrumental in forming the field of nanotechnology and the modern study of DNA, semiconductors, graphene, topological insulators, and much more! Just five years after building their first STM, Rohrer and Binning’s work rightfully earned them the 1986 Nobel Prize in Physics.

Descending into the Sloan basement, Kyle and I work to prepare and scan several high temperature superconducting (HTSC) Calcium Doped YBCO $(\rm Y_{1-x} Ca_x Ba_2 Cu_3 O_{7-\delta})$ samples in order better to understand the pairing mechanism that causes Cooper Pairs for superconductivity. In regular metals, the pairing mechanism via phonon lattice vibrations is fairly well understood by physicists. Meanwhile, the pairing mechanism for HTSC is still a mystery. We are also investigating how this pairing changes with doping, as well as how the magnetic field is channeled up vortices within HTSC.

One of our first tasks is to make probe tips for STM. Adding Calcium Chloride to de-ionized water, we are preparing a liquid conductive path to begin the chemical etching of the probe tip. Using a 10V battery, a wire bent into a ring is connected to the battery and placed in the Calcium Chloride solution. Then a thin platinum iridium wire, also connected to the voltage source, is placed at the center of the conductive ring. The circuit is complete and a current of about half an Ampere is used to erode uniformly the outer surface of the platinum iridium wire, forming a sharp tip. We examine the tip under a traditional microscope to scrutinize our work. Ideally, the tip is only one atom thick! If not, we are charged with re-etching until we reach a more suitable straight, uniform, sharp tip.   As we work to prepare the platinum iridium tips, a stoic picture of Neils Bohr looks down at our work with the appropriate adjacent quotation, ” When it comes to atoms, language can be used only as in poetry.  The poet, too, is not nearly so concerned with describing facts as with creating images. ”  After making two or three nearly perfect tips, we clean and store them in the tip case and proceed to the next step of preparation.

We are now ready to clean the sample to be tested. Bromine etching removes any oxidation or impurities that have formed on our sample, leaving a top bromine film layer. We remove the bromine-residue layer with ethanol and then plunge further into the (sub)basement to load the sample into the STM casing before oxidation begins again. The STM in the Yeh Lab was built by Professor Nai-Chang Yeh and her students eleven years ago. There are multiple layers of vacuum chambers and separate dewars, each with its own meticulous series of steps to prepare for STM testing. At the center is a long, central STM tube. Surrounding this is a large cylindrical dewar. On the perimeter is an exterior large vacuum chamber.

First we must load the newly etched YBCO sample and tip into the central STM tube. The inner tube currently lays across a work bench beneath desk lamps. We must transfer the tiny tip from the tip case to just above the sample. While loading the tip with an equally minuscule flathead screwdriver, it became quite clear to me that I could never be a surgeon! The superconducting sample is secured in place with a small cover plate and screw. A series of electronic tests for resistance and capacitance must be conducted to confirm that there are no shorts in the numerous circuits. Next we must vacuum pump the inner cylindrical tube holding the sample, tip, and circuitry until the pressure is $10^{-4}$ Bar. Then we “bake” the inner chamber, using a heater to expel any other gas, while the vacuum pump continues until we reach approximately $10^{-5}$ Bar. The heater is turned off and the vacuum continues to pump until we reach $10^{-6}$ Bar. This entire vacuum process takes approximately 15 hours…

During this span of time, I have the opportunity to observe the dark, cold STM room. The door, walls and ceiling are covered with black rubber and spongy padding to absorb vibration. The STM room is in the lowest level basement for the same reason. The vibration from human steps near the testing generates noise in the data, so every precaution is made to minimize noise. Giant cement blocks lay across the STM metal box to increase inertia and decrease noise. I ask Kyle what he usually does with this “down” time. We discuss the importance of reading equipment manuals to grasp a better understanding of the myriad of tools in the lab. He says he needs to continue reading the papers published by the Yeh Lab Group. In knowing what questions your research group has previously answered, one has a better understanding of the history and the direction of current work.

The next day, the vacuum-pumped inner chamber is loaded to the center of the STM dewar. We flush the surrounding chambers with nitrogen gas to extricate any moisture or impurities that may have entered since our last testing. Next we can set up the equipment for a liquid nitrogen transfer which lasts approximately 2 hours, depending on the transfer rate. As the liquid nitrogen is added to the system, we meticulously monitor the temperature of the STM system. It must reach 80 Kelvin before we again test the electronics. Eventually it is time to add the liquid helium. Since liquid helium is quite expensive, additional precautions are taken to ensure maximum efficiency for helium use. It is beautiful to watch the moisture in the air deposit in frost along the tubing connecting the nitrogen and helium tanks to the STM dewar. The stillness of the quiet basement as we wait for the transfer is calming. Again, we carefully monitor the temperature drop as it eventually reaches 4.2 Kelvin. For this research, STM must be cooled to this temperature because we must drop below the critical temperature of the sample in order to observe superconductivity. The lower the temperature, the more of the superconducting component manifests itself. Hence the spectrum will have higher resolution. Liquid nitrogen is first added because it can carry over 90% of the heat away due to its higher mass. Nitrogen is also significantly cheaper than liquid helium. The liquid helium is added later, because it is even cooler than liquid nitrogen.

After adding additional layers of rubber padding on top of the closed STM, we can move over to the computer that controls the STM tip. It takes approximately one hour for the tip to be slowly lowered within range for a tunneling current. Kyle examines the data from the approach to the surface. If all seems normal, we can begin the actual scan of the sample!
An important part of the lab work is trouble shooting. I have listed the ideal order of steps, but as with life, things do not always proceed as expected. I have grown in awe of the perseverance and ingenuity required for daily troubleshooting. The need to be meticulous in order to avoid error is astonishing. I love that some common household items can be a valuable tool in the lab. For example, copper scrubbers used in the kitchen serve as a simple conducting path around the inner STM chamber. Floss can be used to tie down the most delicate thin wires. I certainly have grown in my immense respect for the patience and brilliance required in real research.

I find irony in the quiet simplicity of recording and analyzing data, the stillness of carefully transferring liquid helium juxtaposed to the immense complexity and importance of this groundbreaking research. I appreciate the moments of simple quiet in the STM room, the fast paced group meetings where everyone chimes in on their progress, or the boisterous collaborative brainstorming to troubleshoot a new problem. The summer weeks in the Sloan basement have been a welcome retreat from the exciting, transformative, and exhausting year in the classroom. I am grateful for the opportunity to learn more about superconductors, quantum tunneling, vacuum pumps, sonicators, lab safety, and more. While I will not be bromine etching, chemically forming STM tips, or doing liquid helium transfers come September, I have a new-found love for the process of research that I will radiate to my students.

High School Physics Teacher Embedded on A Quest to Squash Quantum Noise

Date: 8/22/2013

Location: Caltech Cryo Lab, West Bridge:

Hello: I am Steve Maloney, a Physics and Chemistry teacher intern from Duarte High School, sponsored by IQIM (Institute for Quantum Information and Matter), doing whatever I can to be of assistance to Dr. Nicolas Smith-Lefebvre. Upon meeting him in mid-June I soon learned that our mission for the length of my visit was to assist him in determining with a greater degree of certainty the linear expansion coefficient of silicon in and around 125 K. (See below)

Fig. 1: Silicon cavity.

The temperature of 125 K is of special interest to operators of LIGO (Laser Interferometer Gravitational Wave Observatory), because that is one of two temperatures where the thermal expansion coefficient, $\alpha$, of silicon is equal to zero. A zero linear expansion coefficient is of special interest to LIGO researchers because a small change in temperature inside the cryostat, (see Fig. 2, below) will not result in a significant change in length for the silicon cavity shown in Fig. 1.

Fig. 2: Inside the Cryostat

Scientists working at LIGO need to know with great precision the length of the resonance cavity, because as gravitational waves pass through the cavity, they simultaneously compress the length of the cavity and stretch in a direction perpendicular to the shortening (warp). The arrival of a gravity wave produces a signal in the Fabry-Perot Interferometer, shown in Fig. 3, below.

Fig. 3: LIGO set-up with Fabry-Perot cavity.

Because the interferometer is sensitive to changes in length of as little as 1X10-15 m, sources of noise must be reduced to an absolute minimum. This brings us back to establishing the Thermal Coefficient of Linear Expansion, $\alpha$. Knowing the value of $\alpha$ to a greater certainty will provide LIGO researchers the mathematical tools to better correct for small changes in temperature for the cavity, thus reducing the noise, therefore increasing the sensitivity of the Gravity Wave Detector.

So Where Do I Fit In?

In the Cryo-Lab on Thursday, July 11 2013, Nicolas Smith-Lefebvre, with my assistance, fed a radio frequency of 160.13 Mhz by means of a frequency-to-voltage transducer. The frequency fed into the transducer was changed by a fixed amount, and the change in voltage was noted. The hz / volt constant obtained was 253.9 hz / mvolt.

Nicolas then locked the east-west cryo-cavities so that the beat signal was approximately 0 (zero) volts.  See the plot, below:

We then sent a 3.16 second pulse (approximated) of a 3.6 mWatt, 532 nm laser, (green) onto the surface of a mirror that reflects in the infrared, but absorbs in visible wavelengths. (Note top graph) I manufactured the electrical power interface for the laser by modifying the casing of a BIC disposable pen. The mirror was situated at the aperture of a silicon spacer.

The goal of the experiment was to determine the absorbance of the silicon mirror of the 532 nm laser.

Assuming we know the quantity of energy pulsed into the mirror:

3.6 mWatt * 3.16 s = .011376 joules,

the change in length of the cavity was determined by: Change in f/f1550nm = change in L/ L0

The change in volts (.025) gave us a change in f of 6.3475 x 103 hz.

With L0 having a value of 10 cm, that means change in L was 3.2794 x 10-10cm.

The specific heat capacity of Si is 700j/k*kg.

Coefficient of linear expansion for Si = 2.6 x 10 -6/K.

To calculate increase in temperature we need to obtain the change in L.

If 2.6 x 10 -6/C  x 10 cm x DT = DL = 3.2794 x 10-10 cm, then DT must be 1.2613 x 10 -5 K.

If DT = 1.2613 x 10-5 K , then Q must equal .41 kg x 700 j/kg Kx1.2613 x 10-5 K = 3.6 x10-3 j,

Q/Epulse=  3.6 x 10-3j / 1.1376 x 10-2j = .316 absorbance.

In other words, the silicon cavity reflected about 68% of the light that struck it.

What have I come away with from this experience?

What struck me first and foremost during this summer internship in the Cryo-Lab was the importance of future knowledge workers of having certain key skills. Among them:

Proficiency in Language

Proficiency in Math

Proficiency in Science

Proficiency in Coding

I will share my insights with my local school district and I intend to capitalize on the connections I made during my experience at Caltech.

Acknowledgements:

I would like to thank the Duarte Unified School District for giving me a leave of absence, Rana Adhikari for, yet again, finding space for me in spite of my general ineptitude regarding General Relativity, Spyridon Michalakis (Spiros) for inviting me back and letting me participate in cutting-edge science, and most of all I would like to thank Nicolas Smith-Lefebvre (softball savant),  and David Yeaton-Massey (D-Mass), for their patience, generosity, and mentoring.

Tsar Nikita and His Scientists

Once upon a time, a Russian tsar named Nikita had forty daughters:

Every one from top to toe
Was a captivating creature,
Perfect—but for one lost feature.

So wrote Alexander Pushkin, the 19th-century Shakespeare who revolutionized Russian literature. In a rhyme, Pushkin imagined forty princesses born without “that bit” “[b]etween their legs.” A courier scours the countryside for a witch who can help. By summoning the devil in the woods, she conjures what the princesses lack into a casket. The tsar parcels out the casket’s contents, and everyone rejoices.

“[N]onsense,” Pushkin calls the tale in its penultimate line. A “joke.”

The joke has, nearly two centuries later, become reality. Researchers have grown vaginas in a lab and implanted them into teenage girls. Thanks to a genetic defect, the girls suffered from Mayer-Rokitansky-Küster-Hauser (MRKH) syndrome: Their vaginas and uteruses had failed to grow to maturity or at all. A team at Wake Forest and in Mexico City took samples of the girls’ cells, grew more cells, and combined their harvest with vagina-shaped scaffolds. Early in the 2000s, surgeons implanted the artificial organs into the girls. The patients, the researchers reported in the journal The Lancet last week, function normally.

I don’t usually write about reproductive machinery. But the implants’ resonance with “Tsar Nikita” floored me. Scientists have implanted much of Pushkin’s plot into labs. The sexually deficient girls, the craftsperson, the replacement organs—all appear in “Tsar Nikita” as in The Lancet. In poetry as in science fiction, we read the future.

Though threads of Pushkin’s plot survive, society’s view of the specialist has progressed. “Deep [in] the dark woods” lives Pushkin’s witch. Upon summoning the devil, she locks her cure in a casket. Today’s vagina-implanters star in headlines. The Wall Street Journal highlighted the implants in its front section. Unless the patients’ health degrades, the researchers will likely list last week’s paper high on their CVs and websites.

Much as Dr. Atlántida Raya-Rivera, the paper’s lead author, differs from Pushkin’s witch, the visage of Pushkin’s magic wears the nose and eyebrows of science. When tsars or millenials need medical help, they seek knowledge-keepers: specialists, a fringe of society. Before summoning the devil, the witch “[l]ocked her door . . . Three days passed.” I hide away to calculate and study (though days alone might render me more like the protagonist in another Russian story, Chekhov’s “The Bet”). Just as the witch “stocked up coal,” some students stockpile Red Bull before hitting the library. Some habits, like the archetype of the wise woman, refuse to die.

From a Russian rhyme, the bones of “Tsar Nikita” have evolved into cutting-edge science. Pushkin and the implants highlight how attitudes toward knowledge have changed, offering a lens onto science in culture and onto science culture. No wonder readers call Pushkin “timeless.”

But what would he have rhymed with “Mayer-Rokitansky-Küster-Hauser”?

“Tsar Nikita” has many nuances—messages about censorship, for example—that I didn’t discuss. To the intrigued, I recommend The Queen of Spades: And selected works, translated by Anthony Briggs and published by Pushkin Press.

Summer of Science: Caltech InnoWorks 2013

The following post is a collaboration between visiting undergraduates Evan Giarta from Stanford University and Joy Hui from Harvard University. As mentors for the 2013 Caltech InnoWorks Academy, Evan and Joy agreed to share their experience with the audience of this blog.

All throughout modern history, science and mathematics have been the foundation for engineering new, world-advancing technologies. From the wheel and sailboat to the automobile and jumbo jet, the fields of science, technology, engineering and math (STEM) have helped our world and its people move faster, farther, and forward. Now, more than ever, products that were unimaginable a century ago are used every day in households and businesses all over the earth, products made possible by generations of scientists, mathematicians, engineers and technologists.

There is, however, some troublesome news regarding the state of our nation’s math and science education. For the past few years, education and news reports have ranked the United States behind other developed countries in science and mathematics. In fact, the proportion of students that score in the most advanced levels of math and science in the United States is significantly lower than that of several other nations. This reality brings to light a stark concern: If proficiency in science and math is necessary for the engineering of novel technologies and breakthrough discoveries, but is something the next generation will lack, what will become of the production industry, our economy, and global security? While the answer to this question might range from complete and utter chaos to little or no effect, it seems reasonable to try and avoid finding out. Rather, we–the community of collective scientists, technologists, engineers, mathematicians–should seek to solve this problem: What can we do to restore the integrity and substance of the educational system, especially in science and math?

In early August of 2013, the Caltech InnoWorks chapter hosted its second annual summer camp, and Joy and I (Evan) were privileged to be invited as program mentors. As people on the inside, we got a first hand look at how the organization prepares and runs the week-long event and what the students themselves experience in the hands-on, interactive and collaborative one-of-a-kind opportunity that is InnoWorks.

Since Joy and I kept a diary of each day’s activities, we thought you may like to see what our middle-schoolers experienced during that week. Here is a play-by-play of the first few days from Joy’s perspective.

Monday, August 5, 2013 was the first day of our camp! Before I go on with talking about the cool things we did that day, I’d like to introduce my team. The self-titled YOLOSWAG consisted of Michael, Chase, Evan, Phaelan and myself. Michael was the oldest, and a little shy at first, but he definitely started talking when he got comfortable. Chase was respectful and polite, and we hit it off immediately. Evan loved science and had lots of questions and knew a TON. Phaelan was the only other girl on the team, but she was very nice and friendly to the other students, and eager to help with anything she could. We all seem different, right? But wait, here’s the best part: we were all die-hard Percy Jackson (property of Rick Riordan) fans! We were definitely the best team.

Anyway, back to the actual stuff we did. One of the first things we saw was a cloud demo, essentially the creation of a cloud in a fish tank, with lots of dry ice and water. The demonstrator, Rob Usiskin, stuck a lot of dry ice in the (empty) fish tank, and poured some water into the tank, which caused the water to turn into a fog, which turns out to be the exact form of a cloud! Add a bubble maker, a question of whether bubbles will float or sink on the cloud, and a room full of InnoWorks campers (about 40 of them), and you will get an hour of general excitement. See the pictures for yourself! (The bubbles, float, by the way, even when the cloud is invisible!)

Following the demonstration, we made Soap Boats. We were apparently supposed to cut index cards into the shape of boats, and dab a little bit of soap on the bottom of the boat, and set the boat in the water. These “Soap Boats” were supposed to be propelled forward by the soap’s ability to decrease the surface tension of the water it touched. Ours, appropriately named “Titanic,” however, simply sat in the water until the water soaked through, and the Titanic sank for the second time in history. Many other teams’ boats fared about the same, but we certainly had a blast designing and naming our Soap Boat!

The last activity of the day was a secret message decoded with bio-luminescence. Each team was given a vial of dried up ostracods, which are sea creatures found glowing in the darkness of the deep sea. Then, each team crushed the ostracods and mixed the resulting powder with water to catalyze the bio-luminescence. Every mentor had written a secret message on a slip of paper, folded it, and handed it to their teams to decipher in the dark (Mine said: YOLOSWAG for the win). The convenient cleaning closet provided said darkness–Spiros, our faculty mentor, suggested that it might also provide passage to Narnia. I don’t think we lost any of our students that day, so no Narnia-traveling was done; by students. Nevertheless, it was a fun-filled and action-packed day, and a great start to an eventful week.

Tuesday was full of fun, hands-on activities. After a short lesson on the effects of air resistance and gravity on free-falling objects, we demonstrated the concept with a thin sheet of paper and a large textbook. As expected, when placed side by side and dropped, air resistance caused the sheet of paper to hit the ground much later than the textbook. But when the sheet of paper was placed directly above the textbook, to the shock of students, both items fell at the exact same rate. Though thorough in their knowledge of physical laws, the connection between their conceptual understanding and real life application had yet to be established. And as a result, when asked to explain what happened and why, the best answer one could muster was simply, “SCIENCE!”.

Following an exercise consisting of blow dryers and floating ping pong balls, the kids received a brief tutorial on how tornadoes are formed by air moving through high and low pressure regions and gusts of vertically rising winds. Due to the forces it is producing and acting upon, the tornado would then be able to more or less sustain itself. To explore this concept further, students constructed water tornado machines by taping two soda bottles together at their openings. Laughter and wetness ensued. Some groups added small trinkets in their tornado machine to observed the water tornado’s effect on “debris”. One team in particular inserted duct tape sharks, and aptly renamed themselves as Sharknado.

In the afternoon, the campers were presented a lesson on the transportation of sailboats and aircraft. Contrary to what most people intuit, the fastest way to control a boat is not to flow in the direction of the wind, but to place the sail at the heading which produces a net force, which can be explained by Bernoulli’s Principle. It states that faster moving fluid has less pressure than slower moving fluid, therefore producing a force from the slower moving side to the faster moving side. Though in sailing this force is initially barely noticeable, over time it creates a large impulse to move the craft at considerable speeds. The same principle can also explain the way a plane takes flight.

With the importance of good design in mind, students were tasked with prototyping the fastest water-bottle boat. Given a solar panel, electric motor, various propellers, empty bottle, tape, and other construction essentials, kids started with basic designs, then diversified in order to gain an edge against other teams. Some teams boasted two-bottle designs, and others used one, each type having trade-offs in speed and stability. Few implemented style upgrades with graphics and colors, and even fewer leveraged performance modifications with ballast and crude control systems. But with a tough deadline to meet, not all boats met their intended specifications. Nonetheless, the races commenced and each team’s innovation was tested in the torrents of Caltech’s Beckman Fountain. Some failed, but those that survived were rewarded accordingly.

By the end of the second day, many of the campers’ initial shyness had been replaced with conversation and budding new friendships. Lunch hour and break times allowed time for kids and mentors alike to hang out and enjoy themselves in California’s summer sun in-between discovering the applications of science and math to engineering, medicine, and technology. These moments of discovery, no matter how rare, are the reasons why we do what we do as we continue our research, studies, and work to improve the world we live in.

Guns versus butter in quantum information

From my college’s computer-science club, I received a T-shirt that reads:

while(not_dead){

sleep--;

time--;

awesome++;

}

/*There’s a reason we can’t hang out with you…*/

The message is written in Java, a programming language. Even if you’ve never programmed, you likely catch the drift: CS majors are the bees’ knees because, at the expense of sleep and social lives, they code. I disagree with part of said drift: CS majors hung out with me despite being awesome.

The rest of the drift—you have to give some to get some—synopsizes the physics I encountered this fall. To understand tradeoffs, you needn’t study QI. But what trades off with what, according to QI, can surprise us.

The T-shirt haunted me at the University of Nottingham, where researchers are blending QI with Einstein’s theory of relativity. Relativity describes accelerations, gravity, and space-time’s curvature. In other sources, you can read about physicists’ attempts to unify relativity and quantum mechanics, the Romeo and Tybalt of modern physics, into a theory of quantum gravity. In this article, relativity tangos with quantum mechanics in relativistic quantum information (RQI). If I move my quantum computer, RQIers ask, how do I change its information processing? How does space-time’s curvature affect computation? How can motion affect measurements?

Nottingham researchers kindly tolerating a seminar by me

For example, acceleration entangles particles. Decades ago, physicists learned that acceleration creates particles. Say you’re gazing into a vacuum—not empty space, but nearly empty space, the lowest-energy system that can exist. Zooming away on a rocket, I accelerate relative to you. From my perspective, more particles than you think—and higher-energy particles—surround us.

Have I created matter? Have I violated the Principle of Conservation of Energy (and Mass)? I created particles in a sense, but at the expense of rocket fuel. You have to give some to get some:

Fuel--;
Particles++;

The math that describes my particles relates to the math that describes entanglement.* Entanglement is a relationship between quantum systems. Say you entangle two particles, then separate them. If you measure one, you instantaneously affect the other, even if the other occupies another city.

Say we encode information in quantum particles stored in a box.** Just as you encode messages by writing letters, we write messages in the ink of quantum particles. Say the box zooms off on a rocket. Just as acceleration led me to see particles in a vacuum, acceleration entangles the particles in our box. Since entanglement facilitates computation, you can process information by shaking a box. And performing another few steps.

When an RQIer told me so, she might as well have added that space-time has 106 dimensions and the US would win the World Cup. Then my T-shirt came to mind. To get some, you have to give some. When you give something, you might get something. Giving fuel gets you entanglement. To prove that statement, I need to do and interpret math. Till I have time to,

Fuel--;
Entanglement++;

offers intuition.

After cropping up in Nottingham, my T-shirt reared its head (collar?) in physics problem after physics problem. By “consuming entanglement”—forfeiting that ability to affect the particle in another city—you can teleport quantum information.

Entanglement--;
Quantum teleportation++;

My research involves tradeoffs between information and energy. As the Hungarian physicist Leó Szilárd showed, you can exchange information for work. Say you learn which half of a box*** a particle occupies, and you trap the particle in that half. Upon freeing the particle—forfeiting your knowledge about its location—you can lift a weight, charge a battery, or otherwise store energy.

Information--;
Energy++;

If you expend energy, Rolf Landauer showed, you can gain knowledge.

Energy--;
Information++;

No wonder my computer-science friends joked about sleep deprivation. But information can energize. For fuel, I forage in the blending of fields like QI and relativity, and in physical intuitions like those encapsulated in the pseudo-Java above. Much as Szilard’s physics enchants me, I’m glad that the pursuit of physics contradicts his conclusion:

while(not_dead){

Information++;

Energy++;

}

The code includes awesome++ implicitly.

*Bogoliubov transformations, to readers familiar with the term.

**In the fields in a cavity, to readers familiar with the terms.

***Physicists adore boxes, you might have noticed.

With thanks to Ivette Fuentes and the University of Nottingham for their hospitality and for their introduction to RQI.

Of sensors and science students

Click click.

Once the clasps unfastened, the tubular black case opened like a yard-long mussel. It might have held a bazooka, a collapsible pole tent, or enough shellfish for three plates of paella.

“This,” said Rob Young, for certain types of light, “is the most efficient detector in the world.”

The Navajo connection

A few months ago, Prof. Keith Schwab brought visiting students and teachers from Navajo Preparatory School to tour some of the IQIM labs, listen to some quick lectures on optics, and talk to scientists. Since this opportunity was only allowed to the one carload that made the 11.5 hour drive from Farmington, NM, everyone involved agreed that we could reach far more students if the IQIM sent Caltech students there. Ana Brown and I both enjoyed speaking with the visiting students and teachers, and responded enthusiastically when Prof. Schwab offered to send us.  My enthusiasm momentarily dimmed when I realized our trip would be occurring in the dead of winter and it was projected to snow while we were there (having only lived in northern and southern California, let’s say I have a heightened sensitivity to weather), but I excitedly spent thanksgiving putting together demonstrations with supplies I found in my closet and garage. I’ve always enjoyed talking about applied math, science, and engineering to anyone, especially anyone young enough to have only heard “math is boring” or “science is too hard” few enough times I can convince them otherwise.  Navajo Prep seemed ideal for this, since the school prepares the students well and sends over 95% of the students to college, and is working to increase student interest in math, science, and engineering.

Panorama from the center of Navajo Prep

With a suitcase half full of clothes and half full of tools and hacked-together electronics, I was picked up from the airport, and arrived at the school in the afternoon the Monday after Thanksgiving weekend. While Monday was spent arranging which classes I would attend, and what topics I would discuss, my second day involved a trip with the school’s outreach coordinator and Cody, one of the two students who visited Caltech, taking a tour of some of the local highlights, including a traditional Navajo lunch (steam corn stew, roast mutton, and I even tried ach’ii”) and toured the remnants of the cliff dwellings at Mesa Verde, about half an hour from the school. Exploring a region with such a rich history and discussing it with my hosts, who are descendants in part from that history was an incredible experience.

Rooms at the Oak Tree House at Mesa Verde

On Wednesday, I began talking to the freshman physics classes about optics, intending to discuss the properties of light, like frequency, speed, wavelength, velocity, energy, and momentum, but to give some context I began with a historical summary of discoveries in optics. I know I was surprised when I was preparing, so you might enjoy answering the same questions that I asked the class. Take a second, and guess when you think the first lenses were made and when wearable glasses were first used. (After you think you have a guess, scroll to the bottom to see how you did.)  When I realized that the class was more interested in seeing rather than hearing about optics, I skimmed over what I’d prepared in order to spend more time on the demonstrations where I showed refraction in glass and explained how that can be derived from assuming a different speed of light in the material. We found lenses for the students to manipulate/play with, and even though historically there were about 300 years between invention of glasses (and the proliferation of lens-making) and the invention of the telescope, some of the students unintentionally built telescopes after taking a second lens from their friends and were shocked to hear that what they had just made was better than the one Galileo used to first discover the four largest moons of Jupiter.

Measuring focal lengths and observing lensing with a drop of water on a glass slide

We also demonstrated double slit diffraction and calculated light’s wavelength for three different laser pointers to within 5% accuracy using only a tape measure, a post-it, and a knife. I decided not to bring a demonstration to measure the speed of light with a laser, a few mirrors, a computer fan, and a reverse-biased photodiode hooked up to an old speaker, because I couldn’t get the fan to spin fast enough to get a reasonably short delay length. (From that can you guess what my set-up was?) On Thursday, Ana and I gave a similar lecture to a different pair of 90 minute freshman physics classes, and spent the other periods talking with math classes. In calculus, I described the different kinds of math classes offered in college, their applications, and their connections to each other in an attempt to give more meaning to the course titles they would no doubt be reading next fall. In geometry and trigonometry I answered the perennial high school math question: “when will we ever use this?” by talking about some applications in geometric optics.

Since I figure you readers like thinking about this sort of thing, I’ll elaborate: I started with the fact that a light beam’s incident angle (measured from the perpendicular of a surface) is equal to its reflected angle. This means that light propagation, like much of (but not all of) physics, is reversible in all but a few specific cases. As a result, light generated at or passing through the center of a circle is reflected off the circle back to the center. An ellipse has a similar property where light through one focus is all reflected to the other. Try deriving that from the fact that an ellipse is defined to be the set of all points where the sum of the distances to the two foci equals some fixed constant. In the lecture, I then used the fact that a parabola is the set of all points equidistant from a point (the focus) and a line (the directrix) to show that light from the focus is reflected off the parabola and collimated (focused at infinity).

Ana brought some IQIM hats and shirts, which the freshman physics classes seemed to definitely enjoy when we met with each class for 40 minutes on Friday.

One of the four freshman physics classes we got to spend time with

I tried to give them an impression of what we do in the IQIM, but I had a hard time giving a satisfactory explanation of the significance of quantum information, and Ana easily convinced me that it would be more engaging to use the 90 minute introduction I had already given them on optics to explain and describe solar energy, since many buildings deep in the Navajo reservation are off the power grid.  There are also plans to construct a large solar power plant on the reservation that will be much cleaner than the three local coal power plants in the region.

Action shot during the lecture on solar

Ana and I also spoke to the senior seminar, which contained the entire graduating class, where she talked about the difficulties transitioning to college experienced by some of her friends in college who were from the Navajo reservation. She gave such great advice on applying to schools, applying for fellowships, and developing a healthy work/life balance, that the only thing I felt like I could contribute was some advice on picking a major (since I’ve picked about 4 different majors), where I described the difference between science and engineering, and talked about different fields within each. I loved how truly helpful I felt when so many of the students told us that they either found certain pieces of advice to be useful, thanked us for introducing them to an idea they hadn’t heard of, or asked us to come back soon.

Occasionally a student asked what I personally do, and their curiosity was rewarded with an explanation that lasted as long as they were interested.  The shortest lasted two sentences and the longest explanation (given to a calculus class of 5 people) involved 30 minutes with my laptop out showing all the steps I take to fabricate nanoscale devices to trap light in almost a cubic-wavelength volume in proximity to an “optically interesting” rare earth ion which my advisor and I hope will provide a viable quantum optical memory.  (Here‘s a little more about our work.)

In the evenings we cheered for the school’s basketball team, had dinner with some of the students and teachers, and discussed the school’s science curriculum and science fair projects. Ana and I consulted on a solar water heating project some of the students were working on, and, after the students all went home for the weekend, I even spent 2 hours in 17ºF weather the last night calibrating an 8″ diameter Schmidt-Cassegrain telescope that had been donated to the school. Compared to Pasadena the viewing was spectacular, and I could easily spot galaxies, nebulae, and discern stripes on Jupiter and the four Galilean moons. I can only expect that some of the students I met will be as excited as I was.

From wikipedia: “The earliest known lenses were made from polished crystal, often quartz, and have been dated as early as 700 BC for Assyrian lenses” and “Around 1284 in Italy, Salvino D’Armate is credited with inventing the first wearable eye glasses.” For anyone who’s interested in the history of science, I’d suggest you check it out.

Jostling the unreal in Oxford

So wrote Philip Pullman, author of The Golden Compass and its sequels. In the series, a girl wanders from the Oxford in another world to the Oxford in ours.

I’ve been honored to wander Oxford this fall. Visiting Oscar Dahlsten and Jon Barrett, I’ve been moonlighting in Vlatko Vedral’s QI group. We’re interweaving 21st-century knowledge about electrons and information with a Victorian fixation on energy and engines. This research program, quantum thermodynamics, should open a window onto our world.

A new world. At least, a world new to the author.

To study our world from another angle, Oxford researchers are jostling the unreal. Oscar, Jon, Andrew Garner, and others are studying generalized probabilistic theories, or GPTs.

What’s a specific probabilistic theory, let alone a generalized one? In everyday, classical contexts, probabilities combine according to rules you know. Suppose you have a 90% chance of arriving in London-Heathrow Airport at 7:30 AM next Sunday. Suppose that, if you arrive in Heathrow at 7:30 AM, you’ll have a 70% chance of catching the 8:05 AM bus to Oxford. You have a probability 0.9 * 0.7 = 0.63 of arriving in Heathrow at 7:30 and catching the 8:05 bus. Why 0.9 * 0.7? Why not 0.90.7, or 0.9/(2 * 0.7)? How might probabilities combine, GPT researchers ask, and why do they combine as they do?

Not that, in GPTs, probabilities combine as in 0.9/(2 * 0.7). Consider the 0.9/(2 * 0.7) plucked from a daydream inspired by this City of Dreaming Spires. But probabilities do combine in ways we wouldn’t expect. By entangling two particles, separating them, and measuring one, you immediately change the probability that a measurement of Particle 2 yields some outcome. John Bell explored, and experimentalists have checked, statistics generated by entanglement. These statistics disobey rules that govern Heathrow-and-bus statistics. As do entanglement statistics, so do effects of quantum phenomena like discord, negative Wigner functions, and weak measurements. Quantum theory and its contrast with classicality force us to reconsider probability.