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arXiv:0906.2706 · Physical Review A

Extracavity quantum vacuum radiation from a single qubit

Simone De Liberato, Dario Gerace, Iacopo Carusotto, Cristiano Ciuti

Published Nov 9, 2009• 200 citations
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Abstract

We present a theory of the quantum vacuum radiation that is generated by a fast modulation of the vacuum Rabi frequency of a single two-level system strongly coupled to a single cavity mode. The dissipative dynamics of the Jaynes-Cummings model in the presence of antirotating-wave terms is described by a generalized master equation including non-Markovian terms. Peculiar spectral properties and significant extracavity quantum vacuum radiation output are predicted for state-of-the-art circuit cavity quantum electrodynamics systems with superconducting qubits.

DOI
10.1103/physreva.80.053810

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We present a theory of the quantum vacuum radiation that is generated by a fast modulation of the vacuum Rabi frequency of a single two-level system strongly coupled to a single cavity mode. The dissipative dynamics of the Jaynes-Cummings model in the presence of antirotating-wave terms is described by a generalized master equation including non-Markovian terms. Peculiar spectral properties and significant extracavity quantum vacuum radiation output are predicted for state-of-the-art circuit cavity quantum electrodynamics systems with superconducting qubits.
We study the extracavity quantum vacuum radiation generated by a sudden switch on and off of the vacuum Rabi frequency of a single two-level system coupled to a single cavity mode in the strong and ultrastrong coupling regime. Dissipation is described by including the qubit-resonator coupling in the derivation of the master equation. The output stream of photons and their second-order correlation functions are calculated by exploiting a recently developed input-output formulation of resonators valid for arbitrary light-matter couplings. The obtained output photon correlations provide direct information on the quantum correlations among the virtual excitations of the dressed vacuum.
We study theoretically the nonstationary circuit QED system in which the artificial atom transition frequency, or the atom-cavity coupling, have a small periodic time modulation, prescribed externally. The system formed by the atom coupled to a single cavity mode is described by the Rabi Hamiltonian. We show that, in the dispersive regime, when the modulation periodicity is tuned to the 'resonances', the system dynamics presents the dynamical Casimir effect, resonant Jaynes-Cummings or resonant Anti-Jaynes-Cummings behaviors, and it can be described by the corresponding effective Hamiltonians. In the resonant atom-cavity regime and under the resonant modulation, the dynamics is similar to the one occurring for a stationary two-level atom in a vibrating cavity, and an entangled state with two photons can be created from vacuum. Moreover, we consider the situation in which the atom-cavity coupling, the atomic frequency, or both have a small non-periodic time modulation, and show that photons can be created from vacuum in the dispersive regime. Therefore, an analog of the dynamical Casimir effect can be simulated in circuit QED, and several photons, as well as entangled states, can be generated from vacuum due to the anti-rotating term in the Rabi Hamiltonian.
We theoretically investigate quantum Rabi oscillations in a system consisting of a two-level atom (qubit) strongly coupled to a one-dimensional open waveguide. In contrast to conventional cavity quantum electrodynamics, the qubit interacts with a continuum of propagating modes, which gives rise to fundamentally different dynamical behavior. Within the rotating-wave approximation, we express the multimode Jaynes-Cummings Hamiltonian in terms of collective bosonic operators and show that the system possesses two integrals of motion, enabling an exact diagonalization of the Hamiltonian in the single-excitation subspace. We show that for a strongly interacting qubit-photon system, the dynamics are captured by a reduced two-level model. In this framework, each level is defined as the product of the atomic excited state and a specific field mode, which takes the form of a multiphoton Fock-like state. In this picture, the Rabi oscillations represent a collective phenomenon corresponding to oscillations between multiphoton states differing by a single photon. We then extend our analysis to multiphoton processes in which the initial field is a coherent state with a continuous spectrum. In this case, the Rabi frequency is shown to be sensitive to the spectral profile of the function that generates the coherent state.
We study numerically the dynamics of the Rabi Hamiltonian, which describes the interaction of a single cavity mode and a two-level atom without the rotating wave approximation. We analyze this system subjected to damping and dephasing reservoirs, included via the usual Lindblad superoperators in the master equation. We show that the combination of the antirotating term and the atomic dephasing leads to linear asymptotic photon generation from the vacuum. We reveal the origins of the phenomenon and estimate its importance in realistic situations.
We develop a general theory of the quantum vacuum radiation generated by an arbitrary time modulation of the vacuum Rabi frequency of an intersubband transition in a doped quantum well system embedded in a planar microcavity. Both nonradiative and radiative losses are included within an input-output quantum Langevin framework. The intensity and the spectral signatures of the extra-cavity emission are characterized versus the modulation properties. For realistic parameters, the photon pair emission is predicted to largely exceed the blackbody radiation in the mid and far infrared. For strong and resonant modulation a parametric oscillation regime is achievable.
A microscopic derivation of the master equation for the Jaynes–Cummings model with cavity losses is given, taking into account the terms in the dissipator which vary with frequencies of the order of the vacuum Rabi frequency. Our approach allows us to single out physical contexts wherein the usual phenomenological dissipator turns out to be fully justified and constitutes an extension of our previous analysis (Scala et al 2007 Phys. Rev. A 75 013811 ), where a microscopic derivation was given in the framework of the rotating wave approximation.