Feature · Research

The Role of Disorder: Under the Microscope

One of the biggest problems with researching quantum mechanics is that it’s often hard to visualise what we’re dealing with. Are we talking particles, or are we talking waves? Or are we talking about abstract excitations of a quantum field, somewhere between neither and both?

For the most part, we focus on calculating properties that can be experimentally measured and we don’t worry too much about what really lies behind quantum mechanics, since we’ve currently no way to test that. So long as we can calculate properties that we can observe, and the observations in turn agree with the calculations, we can conclude that quantum mechanics is a pretty solid working theory, at least for the time being.

Quantum Gas Microscopes

The game changed in 2009 with the invention of the bosonic quantum gas microscope (which I’ll cover in more detail in a future post), a device capable of imaging individual bosonic atoms in a dilute ultracold atomic gas at temperatures a few tenths of a microKelvin above absolute zero. For the first time, we could literally ‘freeze’ a quantum mechanical system in place and take a snapshot of where the atoms are. This doesn’t address the issue of wave/particle duality, as the measurement process forces the atoms to appear as particles, but it does start to give us information about where atoms are located in a quantum system.

Experimental images from Sherson et al, Nature 467 (2010) reproduced here under the Fair Use policy. The bright orange points are individual atoms. These are the sorts of images we wanted to be able to reproduce with our computer simulations.

This information is not accessible to most bulk measurements, which measure properties of a material as a whole (e.g. electrical conductivity) and give no information about the location of particles in a system. A lot of theoretical calculations, on the other hand, do calculate properties that depend on the local density of particles in a material, and so quantum gas microscopes gave us a new way to test theoretical calculations and ensure we’re on the right track.

There was another leap forward in 2015 when several groups (first among them the University of Strathclyde in Scotland) developed quantum gas microscopes which work for the much trickier fermionic atoms. These could be used to study an atomic analogue of the so-called Hubbard model, the mathematical model that theorists think describes electrons in metals and might contain the secrets of high-temperature superconductivity. Most high-temperature superconducting materials, though, are not ‘pure’ systems and usually involve chemical doping or disorder.

However, to date and to the best of my knowledge, no one has yet used a quantum gas microscope for the type of experiment it is uniquely suited for: probing the effects of disorder and randomness on the scale of individual atoms. (During the preparation of our manuscript, one paper by the Bloch group in Munich appeared addressing a similar question but as I understand it they remained focused on the collective behaviour of a cloud of atoms rather than the local properties.)

Our New Idea

This brings us to a recent paper by my colleagues and I, published in Physical Review A as a Rapid Communication (open access arXiv link here), in which we show that quantum gas microscopes can be used to make a new type of measurement of disordered systems. The idea grew out of a conversation I had with experimental atomic physicist Graham Bruce who had worked on quantum gas microscopes. We were thinking about ways to distinguish different types of disordered phases and we realised that quantum gas microscopes were the ideal tool to investigate some of the theoretical predictions that I and others have made.

What I really wanted to measure were some specific correlation functions, sometimes known as Edwards-Anderson order parameters, which are indicators of unusual ‘glassy’ states of matter. Essentially, I was looking for proof that when we add background disorder into a quantum system it leads to very specific local changes in the average density of atoms in the regions where the randomness appeared. This is impossible to probe with bulk measurements, which look at the response of an entire sample, but by taking snapshots of where the atoms were, we realised that we could literally look at the material and see for ourselves whether there were density changes in disordered regions.

Some of the simulated images generated by our computer code – by eye, they are already a very good match the previous experimental results shown above.

With two other colleagues (Tiffany Harte and Liam Walker), we developed a mean-field computer simulation to model the experiments. We modelled the earlier bosonic experiments because the calculations are less complex than for fermions and we wanted to check whether our idea would work before extending it to the more difficult cases. With our model, we could simulate the snapshot images produced in real experiments, extend the experiments to include the effects of disorder and then perform the analysis routine we had in mind to check whether real experiments would be capable of making the measurements we wanted to.

Happily, we find that they are. In our paper, we show for the first time that quantum gas microscopes are capable of measuring an Edwards-Anderson order parameter from single atom resolution images of an ultracold gas of atoms. In particular, this will allow experiments to identify for the first time a state of matter known as the Bose glass, never directly detected before.

Panel i) shows a simulated image of the atoms. Panels ii) and iii) show the the regions of i) that we believe to be a state of matter known as a Bose glass, based on two different analyses of our simulated measurements of the Edwards-Anderson order parameter.

Our study is a proof-of-concept numerical simulation that shows quantum gas microscopes are capable of measuring novel properties of materials that, so far, have never been experimentally measured in strongly interacting quantum systems. For the first time, we can really look into the microscopic structure of a material in detail and see how disorder and randomness cause it to change, building up the changes in material properties from an atomic level.

What’s next?

Now that we’ve confirmed the basic principles of the idea are sound, I’d like to see more advanced numerical studies such as quantum Monte Carlo build up a more quantitatively realistic picture of these experiments, and look into alternative types of disorder to really start optimising how best to conduct these experiments.

Most importantly, though, we need someone somewhere to actually do the experiments and check that they really do work and we haven’t missed something. We don’t think we have, and neither did our peer reviewers (who were brilliant – thanks, anonymous reviewers!), but theory and experiment are symbiotic and it always strikes me as fundamentally unhealthy for either one to run too far in advance of the other.

I’m hopeful that in the near future, someone will do the experiment and test whether or not we’re right. If we are, we have a wholly new way to investigate disorder in quantum materials, literally just by really looking at them for the first time.

For more details on all of this work, please see our Physical Review A paper (open-access arXiv link here) and/or Chapter 5 of my PhD thesis. All data and code for this work is available here.

[NB: The opinions expressed in this post are mine alone and are not the responsibility of any of my co-authors on the paper. If you don’t like this post, blame me, not them!]

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