Tag Archives: Good Science

Citizen First, Scientist Second

I have written previously in praise of the scientific community becoming more diverse over time. I emphasized its importance because people with different cultural backgrounds often synthesize ideas that are sometimes not juxtaposed in other cultures. It is almost unquestionable that the US scientific enterprise has benefited greatly from the inclusion of scientists from around the world. Because the scientific community has become more diverse in the past few decades, it has also meant that science (at least in the academic sense) has become more open and international. As a member of the international community myself (I am a Thai citizen), recent events have been tough to watch as a scientist, immigrant and person.

This past week has seen some, I would consider, unsavory events affecting the scientific and higher education communities in the US. There was a temporary ban put in place by the US government barring citizens from seven Middle Eastern and African countries from entering the US. Some students are stranded outside the US, unable to return before the spring semester starts.

Day to day, science requires enormous attention to detail, patience doing precise theoretical or experimental work, and time to work without distractions. It is easy to get wrapped up in one’s own work, forgetting to pick one’s head up to look at what is going on around you. If events are not directly affecting you or someone close to you, it is easy to forget that these things are even happening.

In this spirit, I encourage you to attend (or organize!) department town hall meetings and speak up in support of your international colleagues. There is a planned Scientists’ March being arranged, and I urge you to attend if there is a gathering near you. To be perfectly honest (like most scientists), I am a person of thought rather than a person of action, but it is always necessary to be a citizen first and a scientist second.

Wannier-Stark Ladder, Wavefunction Localization and Bloch Oscillations

Most people who study solid state physics are told at some point that in a totally pure sample where there is no scattering, one should observe an AC response to a DC electric field, with oscillations at the Bloch frequency (\omega_B). These are the so-called Bloch oscillations, which were predicted by C. Zener in this paper.

However, the actual observation of Bloch oscillations is not as simple as the textbooks would make it seem. There is an excellent Physics Today article by E. Mendez and G. Bastard that outline some of the challenges associated with observing Bloch oscillations (which was written while this paper was being published!). Since the textbook treatments often use semi-classical equations of motion to demonstrate the existence of Bloch oscillations in a periodic potential, they implicitly assume transport of an electron wave-packet. To generate this wave-packet is non-trivial in a solid.

In fact, if one undertakes a full quantum mechanical treatment of electrons in a periodic potential under the influence of an electric field, one arrives at the Wannier-Stark ladder, which shows that an electric field can localize electrons! It is this ladder and the corresponding localization which is key to observing Bloch oscillations.

Let me use the two-well potential to give you a picture of how this localization might occur. Imagine symmetric potential wells, where the lowest energy eigenstates look like so (where S and A label the symmetric and anti-symmetric states):

Now, imagine that I start to make the wells a little asymmetric. What happens in this case? Well, it turns out that that the electrons start to localize in the following way (for the formerly symmetric and anti-symmetric states):

G. Wannier was able to solve the Schrodinger equation with an applied electric field in a periodic potential in full and showed that the eigenstates of the problem form a Stark ladder. This means that the eigenstates are of identical functional form from quantum well to quantum well (unlike in the double-well shown above) and the energies of the eigenstates are spaced apart by \Delta E=\hbar \omega_B! The potential is shown schematically below. It is also shown that as the potential wells slant more and more (i.e. with larger electric fields), the wavefunctions become more localized (the image is taken from here (pdf!)):


A nice numerical solution from the same document shows the wavefunctions for a periodic potential well profile with a strong electric field, exhibiting a strong wavefunction localization. Notice that the wavefunctions are of identical form from well to well.


What can be seen in this solution is that the stationary states are split by \hbar \omega_B, but much like the quantum harmonic oscillator (where the levels are split by \hbar \omega), nothing is actually oscillating until one has a wavepacket (or a linear superposition of eigenstates). Therefore, the Bloch oscillations cannot be observed in the ground state (which includes the the applied electric field) — one must first generate a wavepacket in the solid.

In the landmark paper that finally announced the existence of Bloch oscillations, Waschke et. al. generated a wavepacket in a GaAs-GaAlAs superlattice using a laser pulse. The pulse was incident on a sample with an applied electric field along the superlattice direction, and they were able to observe radiation emitted from the sample due to the Bloch oscillations. I should mention that superlattices must be used to observe the Wannier-Stark ladder and Bloch oscillations because \omega_B, which scales with the width of the quantum well, needs to be fast enough that the electrons don’t scatter from impurities and phonons. Here is the famous plot from the aforementioned paper showing that the frequency of the emitted radiation from the Bloch oscillations can be tuned using an electric field:


This is a pretty remarkable experiment, one of those which took 60 years from its first proposal to finally be observed.

Coupled and Synchronized Metronomes

A couple years ago, I saw P. Littlewood give a colloquium on exciton-polariton condensation. To introduce the idea, he performed a little experiment, a variation of an experiment first performed and published by Christiaan Huygens. Although he performed it with only two metronomes, below is a video of the same experiment performed with 32 metronomes.

A very important ingredient in getting this to work is the suspended foam underneath the metronomes. In effect, the foam is a field that couples the oscillators.

Data Representation and Trust

Though popular media often portrays science as purely objective, there are many subjective sides to it as well. One of these is that there is a certain amount of trust we have in our peers that they are telling the truth.

For instance, in most experimental papers, one can only present an illustrative portion of all the data taken because of the sheer volume of data usually acquired. What is presented is supposed to be to a representative sample. However, as readers, we are never sure this is actually the case. We trust that our experimental colleagues have presented the data in a way that is honest, illustrative of all the data taken, and is reproducible under similar conditions. It is increasingly becoming a trend to publish the remaining data in the supplemental section — but the utter amount of data taken can easily overwhelm this section as well.

When writing a paper, an experimentalist also has to make certain choices about how to represent the data. Increasingly, the amount of data at the experimentalist’s disposal means that they often choose to show the data using some sort of color scheme in a contour or color density plot. Just take a flip through Nature Physics, for example, to see how popular this style of data representation has become. Almost every cover of Nature Physics is supplied by this kind of data.

However, there are some dangers that come with color schemes if the colors are not chosen appropriately. There is a great post at medvis.org talking about the ills of using, e.g. the rainbow color scheme, and how misleading it can be in certain circumstances. Make sure to also take a look at the articles cited therein to get a flavor of what these schemes can do. In particular, there is a paper called “Rainbow Map (Still) Considered Harmful”, which has several noteworthy comparisons of different color schemes including ones that are and are not perceptually linear. Take a look at the plots below and compare the different color schemes chosen to represent the same data set (taken from the “Rainbow Map (Still) Considered Harmful” paper):


The rainbow scheme appears to show more drastic gradients in comparison to the other color schemes. My point, though, is that by choosing certain color schemes, an experimentalist can artificially enhance an effect or obscure one he/she does not want the reader to notice.

In fact, the experimentalist makes many choices when publishing a paper — the size of an image, the bounds of the axes, the scale of the axes (e.g. linear vs. log), the outliers omitted, etc.– all of which can have profound effects on the message of the paper. This is why there is an underlying issue of trust that lurks in within the community. We trust that experimentalists choose to exhibit data in an attempt to be as honest as they can be. Of course, there are always subconscious biases lurking when these choices are made. But my hope is that experimentalists are mindful and introspective when representing data, doubting themselves to a healthy extent before publishing results.

To be a part of the scientific community means that, among other things, you are accepted for your honesty and that your work is (hopefully) trustworthy. A breach of this implicit contract is seen as a grave offence and is why cases of misconduct are taken so seriously.

Ruminations on Raman

The Raman effect concerns the inelastic scattering of light from molecules, liquids, or solids. Brian has written a post about it previously, and it is worth reading. Its use today is so commonplace, that one almost forgets that it was discovered back in the 1920s. As the story goes (whether it is apocryphal or not I do not know), C.V. Raman became entranced by the question of why the ocean appeared blue while on a ship back from London to India in 1921. He apparently was not convinced by Rayleigh’s explanation that it was just the reflection of the sky.

When Raman got back to Calcutta, he began studying light scattering from liquids almost exclusively. Raman experiments are nowadays pretty much always undertaken with the use of a laser. Obviously, Raman did not initially do this (the laser was invented in 1960). Well, you must be thinking, he must have therefore conducted his experiments with a mercury lamp (or something similar). In fact, this is not correct either. Initially, Raman had actually used sunlight!

If you have ever conducted a Raman experiment, you’ll know how difficult it can be to obtain a spectrum, even with a laser. Only about one in a million of the incident photons (and sometimes much fewer) actually gets scattered with a change in wavelength! So for Raman to have originally conducted his experiments with sunlight is really a remarkable achievement. It required patience, exactitude and a great deal of technical ingenuity to focus the sunlight.

Ultimately, Raman wrote his results up and submitted them to Nature magazine in 1928. Although these results were based on sunlight, he had just obtained his first mercury lamp to start his more quantitative studies by then. The article made big news because it was a major result confirming the new “quantum theory”, but Raman immediately recognized the capability of this effect in the study of matter as well. After many years of studying the effect, he came to realize that the reason that water is blue is basically the same as why the sky is blue — Rayleigh scattering goes as 1/\lambda^4.

Readers of this blog will actually notice that I have written about Raman scattering in several different contexts on this site, for instance, in measuring the Damon-Eschbach mode and the Higgs amplitude mode in superconductorsilluminating the nature of LO-TO splitting polar insulators and measuring unusual collective modes in Kondo insulators demonstrating its power as probe of condensed matter even in the present time.

On this blog, one of the major themes I’ve tried to highlight is the technical ingenuity of experimentalists to observe certain phenomena. I find it quite amazing that the Raman effect had its rather meager origins in the use of sunlight!

Schrodinger’s Cat and Macroscopic Quantum Mechanics

A persisting question that we inherited from the forefathers of the quantum formalism is why quantum mechanics, which works emphatically well on the micro-scale, seem at odds with our intuition at the macro-scale. Intended to demonstrate the absurdity of applying quantum mechanics on the macro-scale, the mirco/macro logical disconnect was famously captured by Schrodinger in his description of a cat being in a superposition of both alive and dead states. There have been many attempts in the theoretical literature to come to grips with this apparent contradiction, the most popular of which goes under the umbrella of decoherence, where interaction with the environment results in a loss of information.

Back in 1999, Arndt, Zellinger and co-workers observed a two-slit interference of C60 molecules (i.e. buckyballs), in what was the largest molecule to exhibit such interference phenomena at the time. The grating used had a period of about 100 nm in the experiment, while the approximate de Broglie wavelength of the C60 molecules was 2.5 picometers. This was a startling discovery for a couple reasons:

  1. The beam of C60 molecules used here was far from being perfectly monochromatic. In fact, there was a pretty significant spread of initial velocities, with the full width at half maximum (\Delta v/v) getting to be as broad as 60%.
  2. The C60 molecules were not in their ground state. The initial beam was prepared by sublimating the molecules in an oven which was heated to 900-1000K. It is estimated, therefore, that there were likely 3 to 4 photons exchanged with the background blackbody field during the beam’s passage through the instrument. Hence the C60 molecules can be said to have been strongly interacting with the environment.
  3. The molecule consists of approximately 360 protons, 360 neutrons and 360 electrons (about 720 amu), which means that treating the C60 molecule as a purely classical object would be perfectly adequate for most purposes.

In the present, the record set by the C60 molecule has since been smashed by the larger molecules with mass up to 10,000 amu. This is now within one order of magnitude of a small virus. If I was a betting man, I wouldn’t put money against viruses exhibiting interference effects as well.

This of course raises the question as to how far these experiments can go and to what extent they can be applied to the human scale. Unfortunately, we will probably have to wait for a while to be able to definitively have an answer to that question. However, these experiments are a tour-de-force and make us face some of our deepest discomforts concerning the quantum formalism.

Science for Science’s Sake

A couple weeks ago, Sheila Patek was on the PBS News Hour and discussed eloquently how science and scientists work. She talked about how scientists are driven by curiosity to venture into the unknown, which may or may not lead to applications for humans. When you go somewhere no one has gone before, who knows if it’s going to be of any use? However, that doesn’t mean you shouldn’t go. Here’s the video: