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arXiv:1505.00167 · Comptes Rendus Physique

Many-body quantum electrodynamics networks: Non-equilibrium condensed matter physics with light

Karyn Le Hur, Loïc Henriet, Alexandru Petrescu, Kirill Plekhanov, Guillaume Roux, Marco Schirò

Published Jun 29, 2016• 113 citations
arXivHTMLPDF

Abstract

We review recent developments regarding the quantum dynamics and many-body physics with light, in superconducting circuits and Josephson analogues, by analogy with atomic physics. We start with quantum impurity models addressing dissipative and driven systems. Both theorists and experimentalists are making efforts towards the characterization of these non-equilibrium quantum systems. We show how Josephson junction systems can implement the equivalent of the Kondo effect with microwave photons. The Kondo effect can be characterized by a renormalized light frequency and a peak in the Rayleigh elastic transmission of a photon. We also address the physics of hybrid systems comprising mesoscopic quantum dot devices coupled with an electromagnetic resonator. Then, we discuss extensions to Quantum Electrodynamics (QED) Networks allowing one to engineer the Jaynes–Cummings lattice and Rabi lattice models through the presence of superconducting qubits in the cavities. This opens the door to novel many-body physics with light out of equilibrium, in relation with the Mott–superfluid transition observed with ultra-cold atoms in optical lattices. Then, we summarize recent theoretical predictions for realizing topological phases with light. Synthetic gauge fields and spin–orbit couplings have been successfully implemented in quantum materials and with ultra-cold atoms in optical lattices — using time-dependent Floquet perturbations periodic in time, for example — as well as in photonic lattice systems. Finally, we discuss the Josephson effect related to Bose–Hubbard models in ladder and two-dimensional geometries, producing phase coherence and Meissner currents. The Bose–Hubbard model is related to the Jaynes–Cummings lattice model in the large detuning limit between light and matter (the superconducting qubits). In the presence of synthetic gauge fields, we show that Meissner currents subsist in an insulating Mott phase.

DOI
10.1016/j.crhy.2016.05.003

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We review recent developments regarding the quantum dynamics and many-body physics with light, in superconducting circuits and Josephson analogues, by analogy with atomic physics. We start with quantum impurity models addressing dissipative and driven systems. Both theorists and experimentalists are making efforts towards the characterization of these non-equilibrium quantum systems. We show how Josephson junction systems can implement the equivalent of the Kondo effect with microwave photons. The Kondo effect can be characterized by a renormalized light frequency and a peak in the Rayleigh elastic transmission of a photon. We also address the physics of hybrid systems comprising mesoscopic quantum dot devices coupled with an electromagnetic resonator. Then, we discuss extensions to Quantum Electrodynamics (QED) Networks allowing one to engineer the Jaynes–Cummings lattice and Rabi lattice models through the presence of superconducting qubits in the cavities. This opens the door to novel many-body physics with light out of equilibrium, in relation with the Mott–superfluid transition observed with ultra-cold atoms in optical lattices. Then, we summarize recent theoretical predictions for realizing topological phases with light. Synthetic gauge fields and spin–orbit couplings have been successfully implemented in quantum materials and with ultra-cold atoms in optical lattices — using time-dependent Floquet perturbations periodic in time, for example — as well as in photonic lattice systems. Finally, we discuss the Josephson effect related to Bose–Hubbard models in ladder and two-dimensional geometries, producing phase coherence and Meissner currents. The Bose–Hubbard model is related to the Jaynes–Cummings lattice model in the large detuning limit between light and matter (the superconducting qubits). In the presence of synthetic gauge fields, we show that Meissner currents subsist in an insulating Mott phase.
In this review we discuss the works in the area of quantum simulation and many-body physics with light, from the early proposals on equilibrium models to the more recent works in driven dissipative platforms. We start by describing the founding works on Jaynes-Cummings-Hubbard model and the corresponding photon-blockade induced Mott transitions and continue by discussing the proposals to simulate effective spin models and fractional quantum Hall states in coupled resonator arrays (CRAs). We also analyse the recent efforts to study out-of-equilibrium many-body effects using driven CRAs, including the predictions for photon fermionisation and crystallisation in driven rings of CRAs as well as other dynamical and transient phenomena. We try to summarise some of the relatively recent results predicting exotic phases such as super-solidity and Majorana like modes and then shift our attention to developments involving 1D nonlinear slow light setups. There the simulation of strongly correlated phases characterising Tonks-Girardeau gases, Luttinger liquids, and interacting relativistic fermionic models is described. We review the major theory results and also briefly outline recent developments in ongoing experimental efforts involving different platforms in circuit QED, photonic crystals and nanophotonic fibres interfaced with cold atoms.
In its infancy circuit quantum electrodynamics (cQED) has quickly started reproducing fundamental quantum optical experiments, e.g. observation of vacuum rabi oscillations in frequency and time domain, with unprecedented cooperativity. This was possible because of the large coupling of the quasi one-dimensional microwave field of the superconducting transmission line resonators to the macroscopic dipole moment of superconducting qubits. cQED has matured to a discipline of experimental physics capable of performing fundamental quantum information tasks and is currently on the verge of crossing the border between few- to many body physics [1]. This opens up a exciting realm of completely new physical phenomena. Because of the ubiquitous influence of the electromagnetic environment however the number of microwave photons is not conserved which separates cQED systems from other quantum simulators involving atoms, e.g. cold atoms in optical latices. Instead cQED is ideally suited for exploring quantum many-body physics in the driven dissipative regime where the interplay of constantly injecting microwave photons and the unpreventable loss of microwave photons into the electromagnetic environment generates a whole new class of steady- but not equilibrium states. We propose an array of capacitively coupled superconducting resonators each coupled to an superconducting charge qubit and show that this device can be considered as an simulator for Bose Hubbard physics combined with the high flexibility of network topologies unique to cQED systems[2]. We further investigate the driven dissipative dynamics of this device. We refine this approach and calculate the eigenmodes and nonlinearities of a Josephson junction intersected transmission line resonator[3](c.f. fig.1a). This spectrum of eigenmodes shows the ultrastrong coupling of the Josephson junction to the resonator modes and nonlinearities are attainable that are significant on the single photon limit. We now proceed one step further and and consider the incorporation of multiple Josephson junctions. A novel transfer matrix technique has to be employed to investigate the eigenmode spectrum of the device.
This thesis deals with the study of dynamical properties of out-of-equilibrium quantum systems. We introduce in particular a general class of Spin-Boson models, which describe for example light-matter interaction or dissipative phenomena. We contribute to the development of a stochastic approach to describe the spin dynamics in these models. In this context, the effect of the bosonic environment is encapsulated into additional stochastic degrees of freedom whose time-correlations are determined by spectral properties of the bosonic environment. We use this approach to study many-body phenomena such as the dissipative quantum phase transition induced by an ohmic bosonic environment. Synchronization phenomena as well as dissipative topological transitions are identified. We also progress in the study of arrays of interacting light-matter systems. These theoretical developments follow recent experimental achievements, which could ensure a quantitative study of these phenomena. This notably includes ultra-cold atoms, trapped ions and cavity and circuit electrodynamics setups. We finally investigate hybrid systems comprising electronic quantum dots coupled to electromagnetic resonators, which enable us to provide a spectroscopic analysis of many-body phenomena linked to the Kondo effect. We also introduce thermoelectric applications in these devices.
Recent progress in Cavity QED (CQED) has brought forth the possibility of wiring up individual CQED systems into lattices to investigate collective behavior and correlated phases of strongly coupled light and matter [1-9]. Such Lattice CQED systems operate on polaritonic quasi-particles that are hybrids of light and matter in a controllable proportion, combining long-range coherence of photons and strong interactions typically displayed by massive particles. In this talk, I will review recent work on proposed quantum simulation of Hubbard models with Lattice CQED systems, which are akin to the celebrated Bose-Hubbard model extensively studied with cold atomic gases in optical lattices and Josephson junction arrays. A crucial feature of Lattice CQED systems that I will focus on is their non-equilibrium nature. Unavoidable photon loss coupled with the ease of feeding in additional photons through continuous external driving renders such lattices open quantum systems. Under the influence of drive and dissipation, Lattice CQED systems typically display steady-state phases thereby providing a platform for realizing novel, non-equilibrium phases of light and matter that may be very dierent from those realized with condensed matter systems.
In cavity quantum electrodynamics (QED), the key physical systems include Fabry-Pérot cavity resonators and multilevel cold atoms. Since ultra-strong electromagnetic interaction between photons and quantized cavity modes occurs in cavity QED, many novel quantum optical effects such as optical Rabi oscillation, quantum collapse/revival of atomic-level population and atom-field quantum entanglement can be realized in such quantum microcavities. As is known in quantum optics, these schemes can be generalized to circuit QED, which is a circuit analog of cavity QED. Fundamental devices in circuit QED are superconducting coplanar waveguide microwave resonators and mesoscopic Cooper-pair boxes. Here, the coplanar waveguide resonator with photons stored can be identified as a resonant cavity and the Cooper-pair boxes with large electric dipoles play the role of multilevel cold atoms. Thus, all the quantum optical effects in conventional cavity QED can also be exhibited in the present superconducting circuit QED system. We consider the theoretical working mechanism of superconducting charge qubits based on tunable Josephson junction coupling. It can be found that an analog of optical Rabi oscillation in Cooper-pair boxes can be achieved by tuning an applied external magnetic field. Time evolution of energy levels in a Cooper-pair box, which is manipulated by a time-dependent magnetic flux through its Josephson-junction ring, is studied within the framework of time-dependent quantum mechanics.
Abstract The Jaynes‐Cummings model describes the coupling between photons and a single two‐level atom in a simplified representation of light‐matter interactions. In circuit QED, this model is implemented by combining microwave resonators and superconducting qubits on a microchip with unprecedented experimental control. Arranging qubits and resonators in the form of a lattice realizes a new kind of Hubbard model, the Jaynes‐Cummings‐Hubbard model, in which the elementary excitations are polariton quasi‐particles. Due to the genuine openness of photonic systems, circuit QED lattices offer the possibility to study the intricate interplay of collective behavior, strong correlations and non‐equilibrium physics. Thus, turning circuit QED into an architecture for quantum simulation, i.e., using a well‐controlled system to mimic the intricate quantum behavior of another system too daunting for a theorist to tackle head‐on, is an exciting idea which has served as theorists’ playground for a while and is now also starting to catch on in experiments. This review gives a summary of the most recent theoretical proposals and experimental efforts.