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arXiv:2011.11454 · Physical Review Letters

Photon Transport in a Bose-Hubbard Chain of Superconducting Artificial Atoms

Gleb Fedorov, S. V. Remizov, D. S. Shapiro, W. V. Pogosov, Elena Yu. Egorova, Ivan Tsitsilin, Michail Andronik, Alina A. Dobronosova, Ilya A. Rodionov, O. V. Astafiev, A. V. Ustinov

Published May 7, 2021• 64 citations
arXivHTMLPDF

Abstract

We demonstrate nonequilibrium steady-state photon transport through a chain of five coupled artificial atoms simulating the driven-dissipative Bose-Hubbard model. Using transmission spectroscopy, we show that the system retains many-particle coherence despite being coupled strongly to two open spaces. We find that cross-Kerr interaction between system states allows high-contrast spectroscopic visualization of the emergent energy bands. For vanishing disorder, we observe the transition of the system from the linear to nonlinear regime of photon blockade in excellent agreement with the input-output theory. Finally, we show how controllable disorder introduced to the system suppresses nonlocal photon transmission. We argue that proposed architecture may be applied to analog simulation of many-body Floquet dynamics with even larger arrays of artificial atoms paving an alternative way towards quantum supremacy.

DOI
10.1103/physrevlett.126.180503

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We demonstrate nonequilibrium steady-state photon transport through a chain of five coupled artificial atoms simulating the driven-dissipative Bose-Hubbard model. Using transmission spectroscopy, we show that the system retains many-particle coherence despite being coupled strongly to two open spaces. We find that cross-Kerr interaction between system states allows high-contrast spectroscopic visualization of the emergent energy bands. For vanishing disorder, we observe the transition of the system from the linear to nonlinear regime of photon blockade in excellent agreement with the input-output theory. Finally, we show how controllable disorder introduced to the system suppresses nonlocal photon transmission. We argue that proposed architecture may be applied to analog simulation of many-body Floquet dynamics with even larger arrays of artificial atoms paving an alternative way towards quantum supremacy.
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We study the non-equilibrium behavior of optically driven dissipative coupled resonator arrays. Assuming each resonator is coupled with a two-level system via a Jaynes–Cummings interaction, we calculate the many-body steady state behavior of the system under coherent pumping and dissipation. We propose and analyze the many-body phases using experimentally accessible quantities such as the total excitation number, the emitted photon spectra and photon coherence functions for different parameter regimes. In parallel, we also compare and contrast the expected behavior of this system assuming the local nonlinearity in the cavities is generated by a generic Kerr effect as described by the Bose–Hubbard (BH) model rather than a Jaynes–Cummings interaction. We find that the behavior of the experimentally accessible observables produced by the two models differs for realistic regimes of interactions even when the corresponding nonlinearities are of similar strength. We analyze in detail the extra features available in the Jaynes–Cummings–Hubbard (JCH) model originating from the mixed nature of the excitations and investigate the regimes where the BH approximation would faithfully match the JCH physics. We find that the latter is true for values of the light–matter coupling and losses beyond the reach of current technology. Throughout the study we operate in the weak pumping, fully quantum mechanical regime where approaches such as mean field theory fail, and instead use a combination of quantum trajectories and the time evolving block decimation algorithm to compute the relevant steady state observables. In our study we have assumed small to medium size arrays (from 3 up to 16 sites) and values of the ratio of coupling to dissipation rate g / γ ∼ 20, which makes our results implementable with current designs in circuit QED and with near future photonic crystal set ups.
By means of numerical simulations and the input-output formalism, we study photon transport through a chain of coupled nonlinear optical cavities subject to uniform dissipation. Photons are injected from one end of the chain by means of a coherent source. The propagation through the array of cavities is sensitive to the interplay between the photon hopping strength and the local nonlinearity in each cavity. We characterize photon transport by studying the populations and the photon correlations as a function of the cavity position. When complemented with input-output theory, these quantities provide direct information about photon transmission through the system. The position of single-photon and multiphoton resonances directly reflects the structure of the many-body energy levels. This shows how a study of transport along a coupled cavity array can provide rich information about the strongly correlated (many-body) states of light even in presence of dissipation. The numerical algorithm we use, based on the time-evolving block decimation scheme adapted to mixed states, allows us to simulate large arrays (up to 60 cavities). The scaling of photon transmission with the number of cavities does depend on the structure of the many-body photon states inside the array.
We investigate the non-equilibrium dynamics and steady-state properties of a driven-dissipative Bose-Hubbard chain using a self-consistent Gutzwiller mean-field (GMF) approach. By employing a robust Picard iteration scheme, we solve the non-linear master equation for the non-equilibrium steady state (NESS) in the presence of strong Kerr nonlinearity. We identify two distinct dynamical regimes governed by the interplay between coherent drive, dissipation, and interaction: a regular quasilinear regime and a chaotic regime. Linear stability analysis reveals that the transition to the chaotic regime is triggered by parametric instabilities arising from the drive-induced coherence. Furthermore, we characterize the onset of quantum chaos by calculating the out-of-time-order correlator (OTOC). Our results show that in the strong coupling regime, the OTOC exhibits rapid exponential growth and saturation, providing a clear signature of information scrambling in this open quantum system. The proposed numerical framework offers an efficient pathway to explore many-body correlations in larger photonic lattices.
Networks of nonlinear resonators offer intriguing perspectives as quantum simulators for nonequilibrium many-body phases of driven-dissipative systems. Here, we employ photon correlation measurements to study the radiation fields emitted from a system of two superconducting resonators in a driven-dissipative regime, coupled nonlinearly by a superconducting quantum interference device, with cross-Kerr interactions dominating over on-site Kerr interactions. We apply a parametrically modulated magnetic flux to control the linear photon hopping rate between the two resonators and its ratio with the cross-Kerr rate. When increasing the hopping rate, we observe a crossover from an ordered to a delocalized state of photons. The presented coupling scheme is intrinsically robust to frequency disorder and may therefore prove useful for realizing larger-scale resonator arrays.
The emergence of equilibrium universality from intrinsically nonequilibrium dynamics is a fundamental open problem. Bose-Hubbard lattices realized in photonic and circuit-QED platforms provide a versatile setting to engineer nonlinear interactions, dissipation, and multiphoton processes. Here we investigate a Bose-Hubbard lattice subject to three-photon parametric driving, whose nonequilibrium steady state spontaneously breaks a Z3\mathbb Z_3Z3​ symmetry and realizes the criticality of the three-state Potts model, a three-state generalization of the Ising model. Using a variational phase-space approach with systematically controllable accuracy based on a Variational Multi-Gaussian ansatz, we perform finite-size scaling analyses in one and two spatial dimensions. We find that, in two-dimensional lattices with single-photon losses, the nonequilibrium steady-state transition belongs to the universality class of the 2D classical three-state Potts model. In contrast, in one-dimensional lattices with three-photon losses, the transition is governed by the one-dimensional quantum three-state Potts universality class. These results establish driven-dissipative bosonic lattices as a platform for emergent Potts criticality and identify multiphoton dissipation as a mechanism that promotes nonequilibrium critical behavior from classical to quantum universality classes.