Discovery vs. Q&A Experiments

When one looks through the history of condensed matter experiment, it is strange to see how many times discoveries were made in a serendipitous fashion (see here for instance). I would argue that most groundbreaking findings were unanticipated. The discoveries of superconductivity by Onnes, the Meissner effect, superfluidity in He-4, cuprate (and high temperature) superconductivity, the quantum Hall effect and the fractional quantum Hall effect were all unforeseen by the very experimentalists that were conducting the experiments! Theorists also did not anticipate these results. Of course, a whole slew of phases and effects were theoretically predicted and then experimentally observed as well, such as Bose-Einstein condensation, the Kosterlitz-Thouless transition, superfluidity in He-3 and the discovery of topological insulators, not to diminish the role of prediction.

For the condensed matter experimentalist, though, this presents a rather strange paradigm.  Naively (and I would say that the general public by and large shares this view), science is perceived as working within a question and answer framework. You pose a concrete question, and then conduct and experiment to try to answer said question. In condensed matter physics, this often not the case, or at least only loosely the case. There are of course experiments that have been conducted to answer concrete questions — and when they are conducted, they usually end up being beautiful experiments (see here for example). But these kinds of experiments can only be conducted when a field reaches a point where concrete questions can be formulated. For exploratory studies, the questions are often not even clear. I would, therefore, consider these kinds of Q&A experiments to be the exception to the rule rather than the norm.

More often then not, discoveries are made by exploring uncharted territory, entering a space others have not explored before, and tempting fate. Questions are often not concrete but posed in the form, “What if I do this…?”. I know that this makes condensed matter physics sound like it lacks organization, clarity and structure. But this is not totally untrue. Most progress in the history of science did not proceed in a straight line like textbooks make it seem. When weird particles were popping up all over the place in particle physics in the 1930s and 40s, it was hard to see any organizing principles. Experimentalists were discovering new particles at a rate with which theory could not keep up. Only after a large number of particles had been discovered did Gell-Mann come up with his “Eightfold Way”, which ultimately led to the Standard Model.

This is all to say that scientific progress is tortuous, thought processes of scientists are highly nonlinear, and there is a lot of intuition required in deciding what problems to solve or what space is worth exploring. In condensed matter experiment, it is therefore important to keep pushing boundaries of what has been done before, explore, and do something unique in hope of finding something new!

Exposure to a wide variety of observations and methods is required to choose what boundaries to push and where to spend one’s time exploring. This is what makes diversity and avoiding “herd thinking” important to the scientific endeavor. Exploratory science without concrete questions makes some (especially younger graduate students) feel uncomfortable, since there is always the fear of finding nothing! This means that condensed matter physics, despite its tremendous progress over the last few decades, where certain general organizing principles have been identified, is still somewhat of a “wild west” in terms of science. But it is precisely this lack of structure that makes it particularly exciting — there are still plenty of rocks that need overturning, and it’s hard to foresee what is going to be found underneath them.

In experimental science, questions are important to formulate — but the adventure towards the answer usually ends up being more important than the answer itself.

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 (). 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 was key to observing Bloch oscillations in semiconductor superlattices.

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 ! 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 , but much like the quantum harmonic oscillator (where the levels are split by ), 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) in a semiconducting superlattice since it is an insulator! 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 , 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.