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arXiv:0806.4035

Photon generation from vacuum in non-stationary circuit QED

Alexandre V. Dodonov, Lucas C. Céleri, F. Pascoal, Mikhail D. Lukin, Susanne F. Yelin

Published Jun 25, 2008• 10 citations
arXivHTMLPDF

Abstract

We study theoretically the non-stationary circuit QED system in which the artificial atom transition frequency has a small periodic modulation in time, prescribed externally. We show that, in the dispersive regime, when the modulation periodicity meets the `resonances', the dynamics may be described by the dynamical Casimir effect, Jaynes-Cummings or Anti-Jaynes-Cummings effective Hamiltonians. In the resonant atom-cavity regime, under the modulation `resonance' the dynamics resembles the behavior of the dynamical Casimir effect in a vibrating cavity containing a resonant two-level atom, and entangled states with two photons can be created from vacuum. Thus, an analog of the dynamical Casimir effect may 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.

DOI
10.48550/arxiv.0806.4035

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We study theoretically the non-stationary circuit QED system in which the artificial atom transition frequency has a small periodic modulation in time, prescribed externally. We show that, in the dispersive regime, when the modulation periodicity meets the resonances', the dynamics may be described by the dynamical Casimir effect, Jaynes-Cummings or Anti-Jaynes-Cummings effective Hamiltonians. In the resonant atom-cavity regime, under the modulation resonance' the dynamics resembles the behavior of the dynamical Casimir effect in a vibrating cavity containing a resonant two-level atom, and entangled states with two photons can be created from vacuum. Thus, an analog of the dynamical Casimir effect may 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 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 study analytically and numerically the dynamical Casimir effect in a cavity containing two stationary two-level atoms that interact with the resonance field mode via the Tavis-Cummings Hamiltonian. We determine the modulation frequencies for which the field and atomic excitations are generated and study the corresponding dynamical behaviors in the absence of damping. It is shown that the two-atom setup allows for monitoring of photon generation without interrupting the growth, and different entangled states can be generated during the process.
We develop a microscopic toy model for cavity dynamical Casimir effect (DCE), namely, the photon generation from vacuum due to a nonstationary dielectric slab in a fixed single-mode cavity. We represent the slab by N ≫ 1 noninteracting two-level atoms coupled to the field via the standard dipole interaction. We show that the DCE is contained implicitly in the light–matter interaction Hamiltonian when its parameters are assumed externally prescribed functions of time. We also predict several new phenomena, such as saturation of the photon growth due to effective Kerr nonlinearity, generation of pairs of atomic excitations instead of photons (‘inverse DCE’) and coherent annihilation of pair of system excitations due to the atomic modulation (‘anti-DCE’). These results are extended to the circuit QED architecture where similar effects can be implemented with a single qubit, providing an alternative way to generate novel cavity and atom–field entangled states.
We consider a nonstationary circuit quantum electrodynamics setup in which a three-level artificial atom in the $\mathrm{\ensuremath{\Delta}}$ configuration interacts with a single-mode cavity field of natural frequency $\ensuremath{\omega}$. It is demonstrated that when some atomic energy level(s) undergoes a weak harmonic modulation, photons can be generated from vacuum via effective one- and three-photon transitions, while the atom remains approximately in the ground state. These phenomena occur in the dispersive regime when the modulation frequency is accurately tuned near $\ensuremath{\omega}$ and $3\ensuremath{\omega}$, respectively, and the generated field states exhibit strikingly different statistics from the squeezed vacuum state attained in the standard cavity dynamical Casimir effect.
We study analytically and numerically the dynamics of the quantum non-stationary system composed of a two-level atom interacting with a single mode cavity field whose frequency is rapidly modulated in time (with a small amplitude). We identify modulation laws resulting in qualitatively different dynamical regimes and we present analytical solutions in some simple cases. In particular, we analyse minutely the influence of the field–atom coupling on the photon generation from vacuum via the dynamical Casimir effect.
We consider the dissipative single-qubit circuit QED architecture in which the atomic transition frequency undergoes a weak external time modulation. For sinusoidal modulation with linearly varying frequency we derive effective Hamiltonians that resemble the Landau-Zener problem of finite duration associated with a two- or multilevel systems. The corresponding off-diagonal coupling coefficients originate either from the rotating or the counter-rotating terms in the Rabi Hamiltonian, depending on the values of the modulation frequency. It is demonstrated that in the dissipationless case one can accomplish almost complete transitions between the eigenstates of the bare Rabi Hamiltonian even for relatively short durations of the frequency sweep. To assess the experimental feasibility of our scheme we solved numerically the phenomenological and the microscopic quantum master equations in the Markovian regime at zero temperature. Both models exhibit qualitatively similar behavior and indicate that photon generation from vacuum via effective Landau-Zener transitions could be implemented with the current technology on the time scales of a few microseconds. Moreover, unlike the harmonic dynamical Casimir effect implementations, our proposal does not require precise knowledge of the resonant modulation frequency to accomplish meaningful photon generation.