A major topic of research in our theory group is the study of many-body optical phenomena arising in ensembles of atoms or other quantum emitters. When emitters decay into a common bath, dissipative interactions generate correlations and entanglement between them. This is the perfect playground for observing the physics that we are interested in: a combination of complexity, emergence, dissipation, long-range interactions, and non-linearity. Other topics of interest include optics of 2D materials, and measurement based quantum computing using photonic cluster states. Please see below for a more detailed description of our research interests.

### Quantum optics in atomic arrays

In dense and ordered atomic arrays, strong constructive or destructive interference of light emitted by excited atoms can give rise to exotic phenomena, which have no counterpart in disordered atomic gases. Arrays potentially comprise a powerful new platform for quantum optics. Interference in photon emission gives rise to the emergence of dark (subradiant) states, with extremely long lifetimes, which can be of use in applications in quantum information science, sensing, and metrology. We are interested in understanding both the single-excitation and many body properties of highly-correlated dark states in ordered and disordered arrays of different dimensionality and topology. We have recently proposed to use atomic arrays as quantum dielectrics, as we discuss here. We also investigate potential applications of correlated dissipation in the areas of quantum information science, nonlinear optics, and metrology. For references on these topics, please click here, here and here.

The figure in the right shows the physics of subradiant single-excitation states of one-dimensional atomic arrays: (a) Decay rate of the most subradiant eigenstate vs. atom number N, for different lattice constants, normalized to the resonance wavelength. The continuous lines are guides to the eye and scale as ∼1/N^{3}. (b) Field intensity emitted by the most subradiant mode in a chain of N = 50 atoms. The field is largely evanescent transverse to the bulk of the chain, while most of the energy is radiated out through scattering at the ends of the chain, as expected for an optical waveguide. Red circles denote atomic positions.

We are also interested in advancing the understanding of correlated, many-body dissipative dynamics, which remains a challenging task. To do so, we work in developing new analytical methods as well as computational techniques. Correlated dissipation allows us to go beyond well-studied models for quantum magnetism, into the domain of driven, out-of-equilibrium physics. In atomic arrays, many body phenomena may involve a large number of excitations (or photons), or just one excitation entangled with other degrees of freedom, such as in the case of multiple ground states, which we have explored here.

One interesting problem is the long standing question of what is the role of the symmetry and topology on the dynamics of photon emission, which is a stochastic process. It is known that initially-inverted atoms that are in close proximity (at a volume much smaller than the atomic resonance wavelength) strongly synchronize as they decay, and light is emitted in a burst (known as “Dicke’s superradiance”). We are interested in exploring at which point phase-locking and synchronization survives finite separations in extended geometries, such as chains, rings, or arrays of higher dimension. We have started to investigate this problem in a collaboration involving colleagues at the University of Maryland and Université Paris-Saclay in France. If you are interested, you can read a recent paper here. We plan to continue exploring this physics, adding disorder and other sources of imperfections, as well as investigating the role of different types of reservoirs beyond free space.

### Waveguide Quantum Electrodynamics

Photon-mediated interactions can be modified by placing atoms in different dielectric environments. Waveguide Quantum Electrodynamics (QED) deals with one dimensional reservoirs, such as fibers, transmission lines or photonic crystals. The interaction between atoms can be modified by their relative position along this 1D channel or by structuring the reservoir. For instance, photonic crystals – periodically modulated dielectric structures – display a bandgap in which light cannot propagate. This switches off dissipation through the photonic guided mode, making the interaction between atoms purely coherent (if one neglects dissipation into free space). This makes photonic crystals suitable platforms for quantum simulation, as well as fascinating atom-light interfaces. Of course, dark states also emerge in systems consisting of superconducting qubits coupled through a common transmission line, as we have explored here.

We are interested in expanding the quantum optics theoretical toolbox and guide state of the art experiments in this area. To read about our theory work describing how to understand atom-atom interactions in the presence of complex dielectrics, using the electromagnetic Green’s function, click here. For recent collaboration work with experimentalists, involving atoms in photonic crystals and superconducting qubits in transmission lines, click here, and here. Waveguide QED is also an interesting platform to study many body localization in open systems, which we have done here.

### Optics of quantum materials

We are interested in the optical properties of 2D materials (such as graphene, transition metal dichalcogenides, etc). Twisting and sliding the layers of these materials creates superstructures with emergent properties. The tunability of these systems make them perfect candidates to engineer their intrinsic optical response, as well as that of the quasiparticles (such as phonons, excitons, or plasmons) that they host. We have recently explored the optical response in moire insulators. Owing to their chiral symmetry, twisted bilayers display circular dichroism (different absorption of left and right circularly polarized light) as shown in the figure on the right, and detailed here. Our calculations exemplify how subtle properties of the electronic wave functions, encoded in current correlations between the layers, control physical observables of moire materials.

We are fortunate to be part of the Energy Frontiers Research Center pro-QM, which involves experimentalists at Columbia as well as other institutions. You can see an example of a recent collaboration on the nonlinear response of hBN here.

We regularly partner up with leading experimental groups at Columbia and other universities. We currently collaborate with Prof. Jeff Kimble at Caltech, with Profs. Antoine Browaeys and Igor Ferrier-Barbut at Institut d’Optique (Univ Paris-Saclay), and with Prof. Luis Orozco at JQI and the University of Maryland. At Columbia, we work with Profs. Michal Lipson, Sebastian Will, Nanfang Yu, Dmitri Basov, and Alex Gaeta.