V. I. Man'ko
The geometrical phase is shown to be integral of motion. Deformation of particle distribution function corresponding to nonstationary Casimir effect is expressed in terms of multivariable Hermite polynomials. Correction to Planck distribution due to q--nonlinearity is discussed.
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This is a review of publications on classical and quantum electrodynamics in cavities with moving boundaries (in the quantum case this subject is labeled frequently as "nonstationary Casimir effect" or "dynamical Casimir effect"), from 1921 to October of 2000, with an emphasis on analytical results related to cavities with resonantly oscillating boundaries.
We consider the nonstationary circuit QED setup in which a 3-level artificial atom in the $Δ$-configuration interacts with a single-mode cavity field of natural frequency $ω$. It is demonstrated that when some atomic energy level(s) undergoes a weak harmonic modulation, photons can be generated from vacuum via effective 1- and 3-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 $ω$ and $3ω$, respectively, and the generated field states exhibit strikingly different s…
We study the peculiarities of the nonstationary Casimir effect (creation of photons in cavities with moving boundaries) in the special case of two resonantly coupled modes with frequencies $ω_0$ and $(3Δ)ω_0$, parametrically excited due to small amplitude oscillations of the ideal cavity wall at the frequency $2ω_0(1δ)$ (with $|δ|,|Δ|\ll 1$). The effects of thermally induced oscillations in time dependences of the mean numbers of created photons and the exchange of quantum purities between the modes are discovered. Squeezing and photon distributions in each modes are calculated for initial vac…
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 $N\gg 1$. It is shown that all the resonant phenomena that occur for modulation frequencies $\sim 2ω_{0}$ (where $ω_{0}$ is the cavity frequency) also occur for the halved frequencies. How…
The antidynamical Casimir effect (ADCE) is a term coined to designate the coherent annihilation of excitations due to resonant external perturbation of system parameters, allowing for extraction of quantum work from nonvacuum states of some field. Originally proposed for a two-level atom (qubit) coupled to a single cavity mode in the context of nonstationary quantum Rabi model, it suffered from very low transition rate and correspondingly narrow resonance linewidth. In this paper we show analytically and numerically that the ADCE rate can be increased by at least one order of magnitude by repl…
An effective toy model for an ideal one-dimensional nonstationary cavity is taken to be the starting point to derive a fitting markovian master equation for the corresponding leaky cavity. In the regime where the generation of photons via the dynamical Casimir effect is bounded, the master equation thus constructed allows us to investigate the effects of decoherence on the average number of Casimir photons and their quantum fluctuations through the second-order correlation function.
We consider the nonstationary 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 a…
Nonlocal Static and Dynamical Vacuum Field Correlations and Casimir-Polder Interactions
本综述研究无质量标量场和电磁场在静态与非静态条件下的空间场关联的非局域特征，及其在范德瓦尔斯和卡西米尔-波尔德相互作用中的体现，并探讨了通过原子间作用间接探测真空场关联的可能性。
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 $N\gg 1$ 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 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 pair…
Metrological power of single-qubit dynamical Casimir effect in circuit QED
本研究通过量子拉比模型下的非平稳电路QED系统，利用可调频率二能级原子与单模谐振器耦合，数值计算表明量子Fisher信息显著超过经典极限，从而证明适当的参数调制可模拟动力学卡西米尔效应并产生具有计量学优势的非经典光态。
We consider an analog of particle production in a quartic $O(N)$ quantum oscillator with time-dependent frequency, which is a toy model of particle production in the dynamical Casimir effect and de Sitter space. We calculate exact quantum averages, Keldysh propagator, and particle number using two different methods. First, we employ a kind of rotating wave approximation to estimate these quantities for small deviations from stationarity. Second, we extend these results to arbitrarily large deviations using the Schwinger-Keldysh diagrammatic technique. We show that in strongly nonstationary sit…
We consider a superconducting qubit coupled to the nonstationary transmission line cavity with modulated frequency taking into account energy dissipation. Previously, it was demonstrated that in the case of a single nonadiabatical modulation of a cavity frequency there are two channels of a two-level system excitation which are due to the absorption of Casimir photons and due to the counterrotating wave processes responsible for the dynamical Lamb effect. We show that the parametric periodical modulation of the resonator frequency can increase dramatically the excitation probability. Remarkabl…
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