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arXiv:1905.10707 · Physical Review A

Dynamical Casimir effect via four- and five-photon transitions using a strongly detuned atom

Alexandre V. Dodonov

Published Sep 10, 2019• 9 citations
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Abstract

The scenario of a single-mode cavity with harmonically modulated frequency is revisited in the presence of strongly detuned qubit or cyclic qutrit. It is found that when the qubit frequency is close to $3\ensuremath{\nu}$ there is a peak in the photon generation rate via four-photon transitions for the modulation frequency $4\ensuremath{\nu}$, where $\ensuremath{\nu}$ is the average cavity frequency. Effective five-photon processes can occur for the modulation frequency $5\ensuremath{\nu}$ in the presence of a cyclic qutrit, and the corresponding transition rates exhibit series of peaks. Closed analytical description is derived for the unitary evolution, and numeric simulations indicate the feasibility of multiphoton dynamical Casimir effect under weak dissipation.

DOI
10.1103/physreva.100.032510

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The scenario of a single-mode cavity with harmonically modulated frequency is revisited in the presence of strongly detuned qubit or cyclic qutrit. It is found that when the qubit frequency is close to 3\ensuremathν3\ensuremath{\nu}3\ensuremathν there is a peak in the photon generation rate via four-photon transitions for the modulation frequency 4\ensuremathν4\ensuremath{\nu}4\ensuremathν, where \ensuremathν\ensuremath{\nu}\ensuremathν is the average cavity frequency. Effective five-photon processes can occur for the modulation frequency 5\ensuremathν5\ensuremath{\nu}5\ensuremathν in the presence of a cyclic qutrit, and the corresponding transition rates exhibit series of peaks. Closed analytical description is derived for the unitary evolution, and numeric simulations indicate the feasibility of multiphoton dynamical Casimir effect under weak dissipation.
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 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.
We show two examples in which the dynamical Casimir effect can be achieved by modulating the Kerr or higher-order nonlinearities. In the first case the cavity field is coupled to an arbitrary number of qubits or a harmonic oscillator via the dipole interaction. In the second case, the modulation of the nonlinearities is accompanied by the off-resonance modulation of the cavity frequency. We present the analytic description of the phenomenon and supplement it with numeric simulations, demonstrating that photons can be created from vacuum and the resulting hyper-Poissonian photon statistics is very different from the squeezed vacuum state.
Abstract We investigate analytically and numerically the nonstationary circuit QED setup in which N independent qubits interact with a single mode of the Electromagnetic field confined in a resonator. We consider the harmonic time modulation of some parameter (atomic transition frequency or the atom-field coupling strength) and derive the unitary dynamics up to the second order in the modulation depth for N = 1 and N ≫ 1 . It is shown that all the resonant phenomena that occur for modulation frequencies ∼ 2 ω 0 (where ω 0 is the cavity frequency) also occur for the halved frequencies. However, in the latter case the associated transition rates are significantly smaller and the modulation of the coupling strength is less effective. The transition rates are evaluated explicitly and the prospects of employing the second-order resonances in the phenomena related to the dynamical Casimir effect are examined.
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 consider the scenario in which a damped three-level atom in a ladder or V\mathsf{V}V configuration is coupled to a single cavity mode whose vacuum state is amplified by dint of the dynamical Casimir effect. We obtain approximate analytical expressions and exact numerical results for the time-dependent probabilities, demonstrating that the presence of the third level modifies the photon statistics and its population can serve as witness of photon generation from a vacuum.