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arXiv:2201.07625 · Physical Review A

Dynamical Casimir effect via modulated Kerr or higher-order nonlinearities

Alexandre V. Dodonov, V. V. Dodonov

Published Jan 14, 2022• 6 citations
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Abstract

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.

DOI
10.1103/physreva.105.013709

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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 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 present and investigate an analogue model for controllable photon generation via the dynamical Casimir effect (DCE) in a cavity containing a degenerate optical parametric amplifier (OPA), which is pumped by an amplitude-modulated field. The time modulation of the pump field in the model OPA system is equivalent to a periodic modulation of the cavity length, which is responsible for the generation of the Casimir radiation. By taking into account the rapidly oscillating terms of the modulation frequency, the effects of the corresponding counter-rotating terms (CRTs) on the analogue Casimir radiation clearly emerge. We find that the mean number of generated photons and their quantum statistical properties exhibit oscillatory behaviors, which are controllable through the modulation frequency as an external control parameter. We also find that the time-modulated pumping may lead to the recently predicted phenomenon, the so-called “anti-DCE,” in which pair photons can be coherently annihilated. We show that the Casimir radiation exhibits quadrature squeezing, photon bunching, and super-Poissonian statistics, which are controllable by modulation frequency. We also calculate the power spectrum of the intracavity light field. We find that the appearance of sidebands in the spectrum is due to the presence of the CRTs.
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 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.
When one of the parameters in the Euler-Lagrange equations of motion of a system is modulated, particles can be generated out of the quantum vacuum. This phenomenon is known as the dynamical Casimir effect, and it was recently realized experimentally in systems of superconducting circuits, for example by using modulated resonators made of coplanar waveguides, or arrays of superconducting quantum intereference devices (SQUIDs) forming a Josephson metamaterial. In this paper, we consider a simple electrical circuit model for dynamical Casimir effects, consisting of an LC resonator, with the inductor modulated externally at 10.8 GHz and with the resonant frequency tunable over a range of ±\pm± 400 MHz around 5.4 GHz. The circuit is analyzed classically using a circuit simulator (APLAC). We demonstrate that if an additional source of classical noise couples to the resonator (on top of the quantum vacuum), for example via dissipative "internal modes", then the resulting spectrum of the photons in the cavity will present two strongly asymmetric branches. However, according to the theory of the dynamical Casimir effect, these branches should be symmetric, a prediction which is confirmed by our experimental data. The simulation presented here therefore shows that the origin of the photons generated in our experiment with Josephson metamaterials is the quantum vacuum, and not a spurious classical noise source.