Flatbands: then and now

We published a review article on flatband fine-tuning and its photonic applications in Nanophotonics last week! This follows up on our earlier perspective on photonic flatbands published in APL Photonics in 2018.

How has the field changed in 6 years?

In 2018, we identified promising areas for future research where flatbands had not yet been extensively explored yet: coupled resonator lattices, circuit QED, and photonic crystals.

For the case of coupled resonators, the idea of synthetic dimensions (considering coupling in the frequency domain rather than space) has since emerged as a new direction for non-Hermitian and topological photonics, with the ability to fine-tune short- and long-range hoppings to realize flat band lattices using coupled optical fiber loops.

Circuit QED now sees broad interest as a platform for quantum simulation, especially for studying lattices on hyperbolic space. 

Flatband photonic crystals have received a great amount of attention, driven especially by the rise of moire materials which exhibit flat bands at "magic" twist angles. This breakthrough in condensed matter physics inspired the development of theory (see Phys. Rev. Lett. 126, 136101 (2021), Phys. Rev. Lett. 126, 223601 (2021), and Phys. Rev. Research 4, L032031 (2022), for example), with applications to photonic crystal lasers and shaping free electron radiation being actively explored. 

The huge growth of interest in flat bands in photonic crystals and related platforms such as metasurfaces has been quite remarkable. It is driven by the realization that one does not need to carefully control symmetries or suppress long range couplings, guided by simple tight binding models for flat bands, to design them. Rather, a sufficiently complex system supporting parameter fine-tuning is all that you need to realize flat bands! Equipped with this knowledge, our latest review is timely in that it covers novel phenomena that can emerge in fine-tuned flat band systems. 

A busy January

There's been a lot going on here...

Machine Learning & Physics

Unsupervised learning of quantum many-body scars using intrinsic dimension - Now available on arXiv! We applied manifold learning techniques to identify scar states in the PXP model The take-home message: manifold learning techniques are a powerful alternative to more popular deep learning methods, especially in physics problems where you might not have access to enough training data for deep learning to work well.

Identifying topology of leaky photonic lattices with machine learning - Just published in Nanophotonics! We apply various machine learning methods to distinguish different topological phases in a photonic lattice, assuming one only has access to intensity measurements. This can serve as an alternative to full state tomography or phase retrieval methods, but one needs to be careful when training the models on ideal / pristine systems and then applying them to disordered systems. The journal also published a press release on WeChat!

Quantum Computing

Computing electronic correlation energies using linear depth quantum circuits - Finally published in Quantum Science & Technology, after more than a year and a half working through the peer review system. We use perturbation theory to determine electronic correlation energies in small molecular systems (hydrogen, lithium hydride, etc.) using a large set of shallow circuits, giving an alternative to existing methods which require deeper circuits infeasible for current quantum processors. We also tested the algorithm on cloud quantum processors, observing the detrimental impacts of noise. It would be interesting to run this again now to see how much (or how little) the performance from the different cloud providers has improved!

Landscape approximation of low-energy solutions to binary optimization problems - Published in Physical Review A. We present a method to obtain approximate solutions to binary optimization problems using the localization landscape, a function which is able to place bounds on the regions of Anderson localized eigenstates in disordered media without solving the underlying eigenvalue problem. We lay out the conditions required for these bounds to hold, outline how a quadratic unconstrained binary optimization problem can be transformed to fit these conditions, and provide details on how the quantum state representing the landscape function can be produced and sampled using techniques developed for near-term quantum devices.

 

On a related note, I was interested to see this month a new arXiv preprint in which the localization landscape was used to engineer multifractal resonances in SiN membranes!

Photonic Flatband Resonances

Photonic Flatband Resonances in Multiple Light Scattering - Published in Physical Review Letters. We reveal that flatbands can emerge as collective resonances in fine-tuned arrays of Mie-resonant nanoparticles, leading to giant values of the Purcell factor for dipolar emitters. The article was also highlighted with a Synopsis in Physics Magazine!

Talks-to-papers with Whisper

Last year I wrote about a neat and lightweight implementation of the Whisper speech-to-text model. One of the potential applications I mentioned was converting recorded presentations (seminars, lectures, etc.) into written notes. A few weeks ago a review article I wrote using this approach was published in AAPPS Bulletin. Here's how I did it:

 1. Identify source material. In this case, I had an online conference talk that had been recorded and uploaded to Youtube.

2. Download the raw audio using a tool such as yt-dlp

3. Convert audio to a text transcript. I used whisper.cpp (can run on CPU). The base and small models sizes already do pretty well in terms of accuracy and run quickly.

4. Transcript editing. Whisper won't have perfect accuracy, especially when attempting to transcribe scientific jargon. So it's necessary to carefully review the generated text.

5. Figure conversion. In this case since it was my own talk, I had access to high resolution version of the figures I wanted to include in the paper. Minor reformatting required.

6. Add references. While I cited papers in the slides, the citations need to be converted to a .bib file or other reference manager format. It would be helpful to have an AI assistant that could do this automatically.

And with that I had a first draft completed! Very nice, since the first draft is usually the hardest to write. I did spend some more time polishing the text, adding some details that didn't make it into the original talk, and making the language more formal in parts, but it ended up being a lot easier than writing the whole text from scratch!

Enhancing free-electron radiation using photonic flatbands

Highlighting the preprint "Observation of enhanced free-electron radiation from photonic flatband resonances" that appeared on arXiv the other day.

 

The efficiency at which free electrons radiate electromagnetic energy is dictated by phase matching between the electron and photons. In other words, the two should remain in phase. Phase matching requires an intersection in momentum (k) space between the electronic and photonic dispersion relations. 

In a uniform medium, phase matching can occur when the electron travels faster than the speed of light in the medium, corresponding to Cherenkov radiation. For periodic media, phase matching is no longer limited to a single wavevector, but can occur at a discrete set of points thanks to the periodicity of the Brillouin zone, known as Smith-Purcell resonances. 

Fine-tuning the band structure of a photonic crystal, one can achieve phase matching along a continuous line of momenta in the Brllouin zone. The authors predict orders-of-magnitude enhancement of the radiation intensity due to a flatband resonance, observing a 100-fold enhancement in their experiments. Discrepancies between simulations and observations are attributed to electron beam-induced doping of their photonic crystal.

I found this study particularly noteworthy for a few reasons:

• One of the main selling points of photonic flatbands is their ability to enhance nonlinear optical effects, which are most commonly considered in the framework of nonlinear Schrodinger-type equations describing phenomena such as solitons and lasing. This work establishes a new application of flatbands: mediating efficient interactions between free-electrons and light by bridging their distinct spatial scales.
• Flatbands are usually studied under the tight binding approximation, where they occur exactly. In photonic crystals the tight binding approximation doesn't hold, making it hard to achieve a sufficiently flat dispersion throughout the entire Brillouin zone (we tried this unsuccessfully in the past). However, enhancement of free electron-light interaction does not require a perfectly flat 2D dispersion relation, but merely flat dispersion along 1D line in the Brillouin zone. Such line degeneracies occur more generically at critical points between elliptic and hyperbolic isoenergy contours. This makes it easier to design and harness flatbands in practical systems.

IBS Conference on Flatbands: symmetries, disorder, interactions and thermalization

Last week my former affiliation, the Institute for Basic Science, hosted a conference on the physics of flatband lattices. I was fortunate to be invited to virtually present a colloquium talk, where I recounted how I became interested in flatband lattices during my PhD studies. I have uploaded my presentation slides, and the recorded talk is also available to watch on Youtube. 

 Unfortunately I was on leave for most of the week and missed most of the conference talks, so I hope all of the presentations will be uploaded for viewing. One of the talks I was able to watch live was by Hal Tasaki, one of the founders of the field back in the early 1990s, who shared some of his early encounters with flatbands, including learning about new results by reading preprints distributed via snail mail.