Effective Landau-Zener transitions in the circuit dynamical Casimir effect with time-varying modulation frequency

Abstract

We consider the dissipative single-qubit circuit QED architecture in which the atomic transition frequency undergoes a weak external time-modulation. For sinusoidal modulation with linearly varying frequency we derive effective Hamiltonians that resemble the Landau-Zener problem of finite duration associated to a two-or multi-level systems. The corresponding off-diagonal coupling coefficients originate either from the rotating or the counter-rotating terms in the Rabi Hamiltonian, depending on the values of the modulation frequency. It is demonstrated that in the dissipationless case one can accomplish almost complete transitions between the eigenstates of the bare Rabi Hamiltonian even for relatively short duration of the frequency sweep. To assess the experimental feasibility of our scheme we solved numerically the phenomenological and the microscopic quantum master equations in the Markovian regime at zero temperature. Both models exhibit qualitatively similar behavior and indicate that photon generation from vacuum via effective Landau-Zener transitions could be implemented with the current technology on the timescales of a few microseconds. Moreover, unlike the harmonic dynamical Casimir effect implementations, our proposal does not require the precise knowledge of the resonant modulation frequency to accomplish meaningful photon generation.

Antidynamical Casimir effect as a resource for work extraction

“…We did solve it numerically and verified that for the parameters of Figs. 1 and 2 the results are almost indistinguishable from the predictions of a much simpler 'standard master equation' of Quantum Optics: [38,40,83,86] …”

“…For constant η the total number of system excitations presents a periodic behavior, with the typical period of oscillation on the order of ∼ 10 −4 g −1 for realistic experimental parameters. One way to get a reduction in the total number of excitations without a subsequent return to its initial value is to use a time-dependent modulation frequency, η(t), swept across the expected resonance associated with the ADCE [40]. A steep decrease in the number of excitations is observed when η(t) ≈ η ADCE , and as η(t) moves away from η ADCE the resonance condition is forfeit.…”

“…Fortunately, we do not have to solve analytically the time evolution according to the Hamiltonian H eff , since this was made independently in 1932 by Landau, Zener, Stueckelberg and Majorana, in what became known as Landau-Zener problem [94][95][96][97]. As shown in the appendix A, for sufficiently slowη the transition from |g, 3 to |e, 0 is almost complete, even for finite duration of the process [40]. Therefore, the work extracted from the system tends to a steady value W ≈ −0.2 ω.…”

“…We overcome these possible limitations by using a time-dependent modulation frequency η(t) [40]. As discussed in section II A, when the modulation frequency varies over time, it can assume values close to the resonance frequency η ADCE , that corresponds to the ADCE regime for a given initial state.…”

“…[37][38][39] that by properly adjusting the modulation frequency one can induce a coherent photon annihilation from non-vacuum states, in what became known as the anti-dynamical Casimir effect (ADCE). Moreover, by letting the modulation frequency to slowly change with time, effective Landau-Zener transitions may occur between the dressed states of the time-independent Rabi Hamiltonian [40].…”