Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics A Mathematical and Theoretical

Analytical description of nonstationary circuit QED in the dressed-states basis

Alexandre V. Dodonov

Published Jun 30, 2014• 17 citations
Publisher

Abstract

We have studied the nonstationary circuit QED system in which N qubits or a ( N + 1)-level ladder atom interact with a single mode of the cavity field in the presence of external one- and two-photon drivings. It is assumed that all the system parameters can be simultaneously time-modulated by arbitrary external modulations. We have derived new analytical expressions for the system dynamics in the dressed-states basis and have shown that one can implement different regimes of light–matter interaction by adjusting the modulation form.

DOI
10.1088/1751-8113/47/28/285303

Related papers

Prospects for observing dynamical and anti- dynamical Casimir effects in circuit QED due to fast modulation of qubit parameters

D. S. Veloso, Alexandre V. Dodonov

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.

arXiv:1504.04783•Journal of Physics B Atomic Molecular and Optical Physics•Jul 8, 2015•32 citations

Two-photon exchange interaction from the Dicke Hamiltonian under parametric modulation

Alexandre V. Dodonov

We consider the nonstationary circuit QED architecture in which a single-mode cavity interacts with $N>1$ identical qubits, and some system parameters undergo a weak external perturbation. It is shown that in the dispersive regime one can engineer the two-photon exchange interaction by adjusting the frequency of harmonic modulation to (approximately) $2|{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{-}}|$, where ${\mathrm{\ensuremath{\Delta}}}_{\ensuremath{-}}$ is the average atom-field detuning. A closed analytic description is derived for the weak atom-field coupling regime, and the system dynamics under realistic conditions is studied numerically.

arXiv:1703.00836•Physical Review A•Feb 12, 2018•0 citations

Photon creation from vacuum and interactions engineering in nonstationary circuit QED

Alexandre V. Dodonov

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.

arXiv:0812.0475•Journal of Physics Conference Series•Apr 1, 2009•31 citations

Analytical comparison of the first- and second-order resonances for implementation of the dynamical Casimir effect in nonstationary circuit QED

E L S Silva, Alexandre V. Dodonov

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.

arXiv:1607.07103•Journal of Physics A Mathematical and Theoretical•Nov 17, 2016•12 citations

Microscopic toy model for the cavity dynamical Casimir effect

I M de Sousa, Alexandre V. Dodonov

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.

arXiv:1504.02413•Journal of Physics A Mathematical and Theoretical•May 27, 2015•30 citations

Analytical and numerical analysis of the atom–field dynamics in non-stationary cavity QED

Alexandre V. Dodonov, Roberto Lo Nardo, Rosanna Migliore +2 more

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.

Journal of Physics B Atomic Molecular and Optical Physics•Nov 1, 2011•33 citations
We have studied the nonstationary circuit QED system in which N qubits or a ( N + 1)-level ladder atom interact with a single mode of the cavity field in the presence of external one- and two-photon drivings. It is assumed that all the system parameters can be simultaneously time-modulated by arbitrary external modulations. We have derived new analytical expressions for the system dynamics in the dressed-states basis and have shown that one can implement different regimes of light–matter interaction by adjusting the modulation form.
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.
We consider the nonstationary circuit QED architecture in which a single-mode cavity interacts with N>1N>1N>1 identical qubits, and some system parameters undergo a weak external perturbation. It is shown that in the dispersive regime one can engineer the two-photon exchange interaction by adjusting the frequency of harmonic modulation to (approximately) $2|{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{-}}|$, where ${\mathrm{\ensuremath{\Delta}}}_{\ensuremath{-}}$ is the average atom-field detuning. A closed analytic description is derived for the weak atom-field coupling regime, and the system dynamics under realistic conditions is studied numerically.
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.
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.
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.