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

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 ∼ 2ω0 (where ω0 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.

Antidynamical Casimir effect as a resource for work extraction

“…is the k-th modulation amplitude. It is worth noting that this particular choice for the modulation does not restrict the generality of our results, since for the regime considered here (g ω, Ω) a weak modulation of any system parameter produces similar results [21,37,85]. We suppose that the modulation frequency η (k) (t) may also slowly change as function of time.…”

“…However, in Refs. [37][38][39]85] the authors showed that the number of excitations can be reduced instead, in what they called ADCE. This effect consists of coherent annihilation of two system excitations due to the approximate transition |g, n ←→ |e, n − 3 (for n ≥ 3), and takes place for the modulation frequency η ADCE ≈ 3ω − Ω 0 .…”

Fifty Years of the Dynamical Casimir Effect

“…The results of that experiments stimulated many theoretical papers, suggesting further improvements of the experimental schemes [324][325][326][327][328][329][330][331][332][333][334][335][336][337]. The circuit QED with "artificial atoms" (qubits) was the subject of studies [338][339][340][341][342][343][344][345][346][347][348][349][350]. The most recent review on parametric effects in circuit QED can be found in [351].…”

Dynamical Casimir effect via four- and five-photon transitions using a strongly detuned atom

“…The resulting dynamics resembles the well known phenomenon of parametric amplification [5], namely, photon pairs are generated from vacuum for the harmonic perturbation ω(t) = ν + ε sin(ηt), where ν is the unperturbed cavity frequency, ε is the amplitude and η = 2ν is the frequency of modulation [2]. Photon pairs can also be generated for fractional frequencies 2ν/k due to higher harmonics (for nonmonochromatic modulation [13]) or k-th order effects (for harmonic perturbation [14]), where k is a positive integer. Moreover, when the cavity field is coherently coupled to other quantum subsystems (e. g., multilevels atom or harmonic oscillators [15][16][17]) photons can be generated (or annihilated [18,19]) for several other modulation frequencies at the cost of entangling the subsystems.…”