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AIP conference proceedings

Quantum Phase Transitions in Coupled Arrays of Cavities

Fernando G. S. L. Brandão, Michael J. Hartmann, Martin Bodo Plenio, Theodore E. Simos, George Maroulis

Published Jan 1, 2007• 0 citations
Publisher

Abstract

Recent experimental progress in cavity quantum‐electrodynamics has lead to the fabrication of arrays of coupled cavities, which could be employed to create strongly correlated many‐body systems, when operated in the strong coupling regime. In this work, we show that two models of interest to both, condensed matter physics and quantum information science, namely the Bose‐Hubbard model and the anisotropic Heisenberg model (XYZ‐model), could be realized in such systems with present or near future experimental capabilities.We also discuss the feasibility of realizing a Mott‐insulator of photons in such systems. Crucial for this proposal is the possibility of creating very strong photonic Kerr nonlinearities, several oders of magnitude larger than previously considered feasible. We show how this could be achieved with the setting based on electromagnetically induced transparency and with a new scheme, which is experimentally less demanding than the former.

DOI
10.1063/1.2836197

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Recent experimental progress in cavity quantum‐electrodynamics has lead to the fabrication of arrays of coupled cavities, which could be employed to create strongly correlated many‐body systems, when operated in the strong coupling regime. In this work, we show that two models of interest to both, condensed matter physics and quantum information science, namely the Bose‐Hubbard model and the anisotropic Heisenberg model (XYZ‐model), could be realized in such systems with present or near future experimental capabilities.We also discuss the feasibility of realizing a Mott‐insulator of photons in such systems. Crucial for this proposal is the possibility of creating very strong photonic Kerr nonlinearities, several oders of magnitude larger than previously considered feasible. We show how this could be achieved with the setting based on electromagnetically induced transparency and with a new scheme, which is experimentally less demanding than the former.
Abstract The increasing level of experimental control over atomic and optical systems gained in recent years has paved the way for the exploration of new physical regimes in quantum optics and atomic physics, characterised by the appearance of quantum many‐body phenomena, originally encountered only in condensed‐matter physics, and the possibility of experimentally accessing them in a more controlled manner. In this review article we survey recent theoretical studies concerning the use of cavity quantum electrodynamics to create quantum many‐body systems. Based on recent experimental progress in the fabrication of arrays of interacting micro‐cavities and on their coupling to atomic‐like structures in several different physical architectures, we review proposals on the realisation of paradigmatic many‐body models in such systems, such as the Bose‐Hubbard and the anisotropic Heisenberg models. Such arrays of coupled cavities offer interesting properties as simulators of quantum many‐body physics, including the full addressability of individual sites and the accessibility of inhomogeneous models.
The increasing level of experimental control over atomic and optical systems gained in recent years has paved the way for the exploration of new physical regimes in quantum optics and atomic physics, characterised by the appearance of quantum many-body phenomena, originally encountered only in condensed-matter physics, and the possibility of experimentally accessing them in a more controlled manner. In this review article we survey recent theoretical studies concerning the use of cavity quantum electrodynamics to create quantum many-body systems. Based on recent experimental progress in the fabrication of arrays of interacting micro-cavities and on their coupling to atomic-like structures in several different physical architectures, we review proposals on the realisation of paradigmatic many-body models in such systems, such as the Bose-Hubbard and the anisotropic Heisenberg models. Such arrays of coupled cavities offer interesting properties as simulators of quantum many-body physics, including the full addressability of individual sites and the accessibility of inhomogeneous models. © 2008 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
We show that a system of polaritons - combined atom and photon excitations - in an array of coupled cavities, under an experimental set-up usually considered in electromagnetically induced transparency, is described by the Bose-Hubbard model. This opens up the possibility of using this system as a quantum simulator, allowing for the observation of quantum phase transitions and for the measurement of local properties, such as single site observables. All the basic building blocks of the proposed setting have already been achieved experimentally, showing the feasibility of its realization in the near future.
We propose a physical system where photons could exhibit strongly correlated effects. We demonstrate how a Mott-insulator phase of atom-photon excitations (polaritons) can arise in an array of individually addressable coupled electromagnetic cavities when each of these cavities is coupled resonantly to a single two-level system (atom, quantum dot, or Cooper pair). This Mott phase is characterized by the same integral number of net polaritonic excitations with photon blockade providing the required repulsion between the excitations in each site. Detuning the atomic and photonic frequencies suppresses this effect and induces a transition to a photonic superfluid. Finally, on resonance the system can straightforwardly simulate the dynamics of many-body spin systems.
In recent years, the control of photon-photon interactions in optical nonlinear media has led to the realization of quantum fluids of light. One of the current challenges is to increase the strength of these interactions and enter the so-called strongly correlated regime. To achieve this goal, arrays of nonlinear cavities are a very promising candidate. In this thesis, theoretical results on arrays of nonlinear cavities described by a driven-dissipative Bose-Hubbard model are presented. In particular, a general method to compute the mean-field phase diagram of this model is described. Due to the finite life time of photons, the system is intrinsically dissipative: cavity losses must be compensated by an external driving field. This nonequilibrium nature gives rise to interesting features, such as a transition between monostable and bistable phases induced by tunneling. In the limit of weak dissipation and weak driving, analytical results describing generalized Mott insulating phases are derived. These states survive up to a critical tunneling strength, above which a crossover to a classical coherent state takes place. Finally, the issue of how to go beyond the mean-field approximation is addressed by performing exact numerical simulations. Large arrays of cavities were simulated by implementing a new method specifically tailored for driven-dissipative systems.