@article {3264, title = {Self-dual quasiperiodic percolation}, journal = {Phys. Rev. E}, volume = {107}, year = {2023}, month = {2/27/2023}, pages = {024137}, abstract = {

How does the percolation transition behave in the absence of quenched randomness? To address this question, we study two nonrandom self-dual quasiperiodic models of square-lattice bond percolation. In both models, the critical point has emergent discrete scale invariance, but none of the additional emergent conformal symmetry of critical random percolation. From the discrete sequences of critical clusters, we find fractal dimensions of Df=1.911943(1) and Df=1.707234(40) for the two models, significantly different from Df=91/48=1.89583... of random percolation. The critical exponents ν, determined through a numerical study of cluster sizes and wrapping probabilities on a torus, are also well below the ν=4/3 of random percolation. While these new models do not appear to belong to a universality class, they demonstrate how the removal of randomness can fundamentally change the critical behavior.

}, doi = {10.1103/PhysRevE.107.024137}, url = {https://arxiv.org/abs/2206.11290}, author = {Sommers, Grace M. and Michael Gullans and Huse, David A.} } @article {3312, title = {A sharp phase transition in linear cross-entropy benchmarking}, year = {2023}, month = {5/8/2023}, abstract = {

Demonstrations of quantum computational advantage and benchmarks of quantum processors via quantum random circuit sampling are based on evaluating the linear cross-entropy benchmark (XEB). A key question in the theory of XEB is whether it approximates the fidelity of the quantum state preparation. Previous works have shown that the XEB generically approximates the fidelity in a regime where the noise rate per qudit ε satisfies εN<<1 for a system of N qudits and that this approximation breaks down at large noise rates. Here, we show that the breakdown of XEB as a fidelity proxy occurs as a sharp phase transition at a critical value of εN that depends on the circuit architecture and properties of the two-qubit gates, including in particular their entangling power. We study the phase transition using a mapping of average two-copy quantities to statistical mechanics models in random quantum circuit architectures with full or one-dimensional connectivity. We explain the phase transition behavior in terms of spectral properties of the transfer matrix of the statistical mechanics model and identify two-qubit gate sets that exhibit the largest noise robustness.

}, url = {https://arxiv.org/abs/2305.04954}, author = {Brayden Ware and Abhinav Deshpande and Dominik Hangleiter and Pradeep Niroula and Bill Fefferman and Alexey V. Gorshkov and Michael Gullans} } @article {2761, title = {Singularities in nearly-uniform 1D condensates due to quantum diffusion}, year = {2021}, month = {3/10/2021}, abstract = {

Dissipative systems can often exhibit wavelength-dependent loss rates. One prominent example is Rydberg polaritons formed by electromagnetically-induced transparency, which have long been a leading candidate for studying the physics of interacting photons and also hold promise as a platform for quantum information. In this system, dissipation is in the form of quantum diffusion, i.e., proportional to k2 (k being the wavevector) and vanishing at long wavelengths as k\→0. Here, we show that one-dimensional condensates subject to this type of loss are unstable to long-wavelength density fluctuations in an unusual manner: after a prolonged period in which the condensate appears to relax to a uniform state, local depleted regions quickly form and spread ballistically throughout the system. We connect this behavior to the leading-order equation for the nearly-uniform condensate -- a dispersive analogue to the Kardar-Parisi-Zhang (KPZ) equation -- which develops singularities in finite time. Furthermore, we show that the wavefronts of the depleted regions are described by purely dissipative solitons within a pair of hydrodynamic equations, with no counterpart in lossless condensates. We close by discussing conditions under which such singularities and the resulting solitons can be physically realized.

}, url = {https://arxiv.org/abs/2103.06293}, author = {Christopher L. Baldwin and P. Bienias and Alexey V. Gorshkov and Michael Gullans and M. Maghrebi} } @article {2213, title = {Single-photon bound states in atomic ensembles}, year = {2018}, abstract = {

We illustrate the existence of single-excitation bound states for propagating photons interacting with N two-level atoms. These bound states can be calculated from an effective spin model, and their existence relies on dissipation in the system. The appearance of these bound states is in a one-to-one correspondence with zeros in the single-photon transmission and with divergent bunching in the second-order photon-photon correlation function. We also formulate a dissipative version of Levinson\&$\#$39;s theorem for this system by looking at the relation between the number of bound states and the winding number of the transmission phases. This theorem allows a direct experimental measurement of the number of bound states using the measured transmission phases.

}, url = {https://arxiv.org/abs/1809.01147}, author = {Yidan Wang and Michael Gullans and Antoine Browaeys and J. V. Porto and Darrick E. Chang and Alexey V. Gorshkov} } @article {1692, title = {Sisyphus Thermalization of Photons in a Cavity-Coupled Double Quantum Dot}, journal = {Physical Review Letters}, volume = {117}, year = {2016}, month = {2016/07/25}, pages = {056801}, abstract = {

A strongly driven quantum system, coupled to a thermalizing bath, generically evolves into a highly non-thermal state as the external drive competes with the equilibrating force of the bath. We demonstrate a notable exception to this picture for a microwave resonator interacting with a periodically driven double quantum dot (DQD). In the limit of strong driving and long times, we show that the resonator field can be driven into a thermal state with a chemical potential given by a harmonic of the drive frequency. Such tunable chemical potentials are achievable with current devices and would have broad utility for quantum simulation in circuit quantum electrodynamics. As an example, we show how several DQDs embedded in an array of microwave resonators can induce a phase transition to a Bose-Einstein condensate of light.

}, doi = {http://dx.doi.org/10.1103/PhysRevLett.117.056801}, url = {http://arxiv.org/abs/1512.01248}, author = {Michael Gullans and J. Stehlik and Y. -Y. Liu and J. R. Petta and J. M. Taylor} } @article {1499, title = {Semiconductor double quantum dot micromaser}, journal = {Science}, volume = {347}, year = {2015}, month = {2015/01/15}, pages = {285 - 287}, abstract = { The coherent generation of light, from masers to lasers, relies upon the specific structure of the individual emitters that lead to gain. Devices operating as lasers in the few-emitter limit provide opportunities for understanding quantum coherent phenomena, from THz sources to quantum communication. Here we demonstrate a maser that is driven by single electron tunneling events. Semiconductor double quantum dots (DQDs) serve as a gain medium and are placed inside of a high quality factor microwave cavity. We verify maser action by comparing the statistics of the emitted microwave field above and below the maser threshold. }, doi = {10.1126/science.aaa2501}, url = {http://arxiv.org/abs/1507.06359v1}, author = {Y. -Y. Liu and J. Stehlik and C. Eichler and Michael Gullans and J. M. Taylor and J. R. Petta} } @article {1506, title = {Scattering resonances and bound states for strongly interacting Rydberg polaritons }, journal = {Physical Review A}, volume = {90}, year = {2014}, month = {2014/11/3}, abstract = { We provide a theoretical framework describing slow-light polaritons interacting via atomic Rydberg states. We use a diagrammatic method to analytically derive the scattering properties of two polaritons. We identify parameter regimes where polariton-polariton interactions are repulsive. Furthermore, in the regime of attractive interactions, we identify multiple two-polariton bound states, calculate their dispersion, and study the resulting scattering resonances. Finally, the two-particle scattering properties allow us to derive the effective low-energy many-body Hamiltonian. This theoretical platform is applicable to ongoing experiments. }, doi = {10.1103/PhysRevA.90.053804}, url = {http://arxiv.org/abs/1402.7333v1}, author = {P. Bienias and S. Choi and O. Firstenberg and Mohammad F. Maghrebi and Michael Gullans and M. D. Lukin and Alexey V. Gorshkov and H. P. B{\"u}chler} } @article {1504, title = {Single-photon nonlinear optics with graphene plasmons}, journal = {Physical Review Letters}, volume = {111}, year = {2013}, month = {2013/12/11}, abstract = { We show that it is possible to realize significant nonlinear optical interactions at the few photon level in graphene nanostructures. Our approach takes advantage of the electric field enhancement associated with the strong confinement of graphene plasmons and the large intrinsic nonlinearity of graphene. Such a system could provide a powerful platform for quantum nonlinear optical control of light. As an example, we consider an integrated optical device that exploits this large nonlinearity to realize a single photon switch. }, doi = {10.1103/PhysRevLett.111.247401}, url = {http://arxiv.org/abs/1309.2651v3}, author = {Michael Gullans and D. E. Chang and F. H. L. Koppens and F. J. Garc{\'\i}a de Abajo and M. D. Lukin} }