We propose a device architecture capable of direct quantum electro-optical conversion of microwave to optical photons. The hybrid system consists of a planar superconducting microwave circuit coupled to an integrated whispering-gallery-mode microresonator made from an electrooptical material. We show that by exploiting the large vacuum electric field of the planar microwave resonator, electro-optical (vacuum) coupling rates g0 as large as ∼ 2π O(10 − 100) kHz are achievable with currently available technology -a more than three order of magnitude improvement over prior designs and realizations. Operating at millikelvin temperatures, such a converter would enable high-efficiency conversion of microwave to optical photons. We analyze the added noise, and show that maximum quantum coherent conversion efficiency is achieved for a multi-photon cooperativity of unity which can be reached with optical power as low as O(1) mW.The interconversion of microwave and optical signals is of practical relevance in a broad range of electronic applications, from optical and wireless communications to timing. The spectacular advances of the past decade in manipulating the quantum states of the microwave field [1, 2] has increased interest in techniques to convert them to optical fields, since the latter can be propagated via optical fiber at room temperature while preserving their quantum state. In the long term, converting quantum states between microwave and optical photons may enable long distance quantum communication [3,4], and in the near term, it provides a path towards realizing single photon detectors of the microwave field that may find use in quantum science and metrology, radio astronomy and technology alike. For these reasons, hybrid systems for such microwave to optical interfaces have recently attracted significant experimental efforts. Several approaches have been investigated [5,6]: optomechanical and electromechanical devices [7][8][9][10] as well as cold atoms [11] and spin ensembles [12,13]. Indeed, a bi-directional and efficient link has been established recently using a mechanical oscillator coupled to both optical and microwave modes. Alternatively, it has been proposed that the parametric coupling of an LC circuit to an optical cavity via an electro-optical crystal would realize an effective optomechanical-type interaction [14]. Such a system could convert states from the microwave to the optical domain by driving sideband cooling transitions [15][16][17]. Similar to optomechanical systems, the interaction requires large vacuum coupling rates and the resolved-sideband regime [15][16][17] to be efficient as well as a optical cavity decay rate that greatly exceeds the microwave decay rate. Despite interest in the scheme, to date, it has not been realized. Previous demonstrations attained vacuum coupling rates of ∼ 2π O(1 − 10)Hz insufficient for an efficient transfer. In addition, several previous schemes operated with a microwave dissipation that was larger than the optical one, preventing efficient transfer...
We review recent developments regarding non-equilibrium quantum dynamics and many-body physics with light, in superconducting circuits and Josephson analogues. 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 to an electromagnetic resonator. Then, we discuss extensions to Quantum Electrodynamics (QED) Networks allowing 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 with ultra-cold atoms in optical lattices -using time-dependent Floquet perturbations periodic in time, for exampleas well as in photonic lattice systems. Finally, we discuss the Josephson effect related to Bose-Hubbard models in ladder and two-dimensional geometries. 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. arXiv:1505.00167v2 [cond-mat.mes-hall] 15 Jan 2016 be either Rydberg atoms (cold atoms) or trapped ions [3, 4] for example. A step towards the realization of manybody physics has also been made through the realization of model Hamiltonians such as the Dicke Hamiltonian [5], where the associated super-radiant quantum phase transition has been observed in non-equilibrium conditions [6]. A solid-state version of cavity quantum electrodynamics, related to circuit quantum electrodynamics, built with superconducting quantum circuits [7,8], is also a very active field both from experimental and theoretical points of view. Theorists have predicted novel emergent quantum phenomena either in relation with strong light-matter coupling [9] or non-equilibrium quantum physics [10,11].The goal here is to review developments, both theoretical and experimental, towards realizing many-body physics and quantum simulation in circuit QED starting from small networks to larger ensembles of superconducting elements in the microwave limit. An experimental endeavor has been accomplished towards the realization of larger arrays in circuit QED [12,13,14,15] and towards controlling trajectories in small systems [16,17]. This research is c...
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