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arXiv:1504.06379 · Journal of the Optical Society of America B

Influence of the Kerr nonlinearity in a single nonstationary cavity mode

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

Published May 22, 2017• 21 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1364/josab.34.001170

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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 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 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 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.
We propose an experimentally feasible optomechanical system (OMS) that is dispersively driven and operates in the reversed dissipation regime (RDR), where the mechanical damping rate far exceeds the cavity decay rate. We demonstrate that coherent, fast-time modulation of the driving laser frequency on time scales longer than the mechanical decoherence time allows for adiabatic elimination of the mechanical mode, resulting in strong parametric amplification of quantum vacuum fluctuations of the intracavity field. This mechanism, known as the parametric dynamical Casimir effect (parametric-DCE), leads to the generation of Casimir photons. In the dispersive RDR, we find that the total system Hamiltonian-including the DCE term-is intrinsically modified by a generalized optomechanical Kerr-type nonlinearity. This nonlinearity not only saturates the mean number of radiated Casimir photons on short time scales, even without dissipation, but also induces oscillatory behavior in their dynamics and quantum characteristics. Remarkably, the presence of the Kerr nonlinearity causes the generated DCE photons to exhibit nonclassical features, including simultaneous sub-Poissonian statistics and negative Wigner function, as well as quadrature squeezing, which can be controlled by adjusting the system parameters. Surprisingly, the controllable simultaneous nonclassical dynamics in the same physical parameter regime, which is induced by the optomechanical Kerr nonlinearity to the parametric DCE cannot occur in the standard DCE or Kerr-type systems. The proposed nonclassical microwave radiation source possesses the potential to be applied in quantum information processing, quantum computing as well as microwave quantum sensing.
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.
In this paper, we investigate the interaction between a vee-type three-level atom and a single mode of the electromagnetic field in the presence of a nonlinear Kerr-like medium and an intensity-dependent coupling. We have elucidated the system by a nonlinear Hamiltonian constructed from the standard Jaynes–Cummings model by deforming the field operators and adding some nonlinear terms. Using the initial conditions that the atom is prepared in an excited state and the field is in a coherent state, the state vector of the entire system is determined analytically. The time evolution of nonclassical properties such as Mandel Q, quantum entanglement and position-momentum uncertainty relation (squeezing) of the field are investigated. The quasiprobability distributions are also computed for the resultant state. The effects of the detuning parameters, generalized Kerr medium and intensity-dependent coupling on the previous nonclassicality signs are analysed, in detail.