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 the Optical Society of America B

Study of the combined effects of a Kerr nonlinearity and a two-level atom upon a single nonstationary cavity mode

A. Paredes, J. Récamier

Published May 21, 2019• 2 citations
Publisher

Abstract

We study a simple version of the dynamical Casimir effect in a single electromagnetic cavity mode containing a Kerr medium and a two-level atom. We obtain approximate expressions for the time-evolution operator valid at short times and/or low average photon number. We have found an interplay between the effect of the nonlinear Kerr medium, which is to decrease the growth of photon generation from the vacuum state, and that of the two-level atom, which is to increase the photon generation. We explore an ample range of Hamiltonian parameters going from the resonant to the dispersive regimes.

DOI
10.1364/josab.36.001538

Related papers

Influence of the Kerr nonlinearity in a single nonstationary cavity mode

R. Román-Ancheyta, Carlos A. González-Gutiérrez, J. Récamier

We study a simple version of the dynamical Casimir effect in a single electromagnetic cavity mode containing a Kerr medium. We obtain an approximate expression for the time evolution operator valid for short times and/or low average photon number. We have found that the generation of photons from quantum vacuum is strongly affected by the presence of the Kerr medium. In the time domain it shows strong oscillations, whose frequency increases with the intensity of the nonlinear medium, sharing physical features with the case of two two-level atoms in a cavity with oscillating walls. Using a semiclassical approach, we show that Kerr nonlinearity produces a faster decrease in the photon production rate than that reported in previous studies working on quasi-resonant nonstationary cavities. We also found that the initial vacuum state can evolve in a cat sate. We expect that these results could be relevant for any study involving the dynamical Casimir effect that is willing to incorporate Kerr nonlinearities.

arXiv:1504.06379•Journal of the Optical Society of America B•May 22, 2017•21 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

Approximate analytical results on the cavity dynamical Casimir effect in the presence of a two-level atom

Alexandre V. Dodonov, V. V. Dodonov

We analytically study the photon generation from vacuum due to the dynamical Casimir effect in a cavity with a two-level atom, initially prepared in an arbitrary pure state. Performing small unitary transformations, we obtain closed analytical expressions for the probability amplitudes and other important quantities in the resonant and dispersive regimes.

arXiv:1112.0523•Physical Review A•Jan 17, 2012•35 citations

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

H. Dessano, Alexandre V. Dodonov

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.

arXiv:1805.04887•Physical Review A•Aug 31, 2018•7 citations

Dynamical Casimir effect in two-atom cavity QED

Alexandre V. Dodonov, V. V. Dodonov

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.

arXiv:1203.3776•Physical Review A•May 29, 2012•37 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
We study a simple version of the dynamical Casimir effect in a single electromagnetic cavity mode containing a Kerr medium and a two-level atom. We obtain approximate expressions for the time-evolution operator valid at short times and/or low average photon number. We have found an interplay between the effect of the nonlinear Kerr medium, which is to decrease the growth of photon generation from the vacuum state, and that of the two-level atom, which is to increase the photon generation. We explore an ample range of Hamiltonian parameters going from the resonant to the dispersive regimes.
We study a simple version of the dynamical Casimir effect in a single electromagnetic cavity mode containing a Kerr medium. We obtain an approximate expression for the time evolution operator valid for short times and/or low average photon number. We have found that the generation of photons from quantum vacuum is strongly affected by the presence of the Kerr medium. In the time domain it shows strong oscillations, whose frequency increases with the intensity of the nonlinear medium, sharing physical features with the case of two two-level atoms in a cavity with oscillating walls. Using a semiclassical approach, we show that Kerr nonlinearity produces a faster decrease in the photon production rate than that reported in previous studies working on quasi-resonant nonstationary cavities. We also found that the initial vacuum state can evolve in a cat sate. We expect that these results could be relevant for any study involving the dynamical Casimir effect that is willing to incorporate Kerr nonlinearities.
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 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 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.