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arXiv:1805.04887 · Physical Review A

One- and three-photon dynamical Casimir effects using a nonstationary cyclic qutrit

H. Dessano, Alexandre V. Dodonov

Published Aug 31, 2018• 7 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.98.022520

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We consider a nonstationary circuit quantum electrodynamics setup in which a three-level artificial atom in the \ensuremathΔ\mathrm{\ensuremath{\Delta}}\ensuremathΔ configuration interacts with a single-mode cavity field of natural frequency \ensuremathω\ensuremath{\omega}\ensuremathω. 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 \ensuremathω\ensuremath{\omega}\ensuremathω and 3\ensuremathω3\ensuremath{\omega}3\ensuremathω, 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 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 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.
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.
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 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.
Abstract We consider the nonstationary circuit quantum electrodynamics (circuit QED) architecture, where a single artificial two-level atom interacts with a cavity field mode under external modulation of one or more system parameters. Two different approaches are employed to study the effects of Markovian dissipation on modulation-induced transitions between the atom–field dressed states: the standard master equation of quantum optics and the recently formulated dressed-picture master equation. We estimate the associated transition rates and show that photon generation from vacuum (‘dynamical Casimir effect’, DCE) and coherent photon annihilation from nonvacuum states (‘anti-DCE’) are possible with the current state-of-the-art parameters.