One- and three-photon dynamical Casimir effects using a nonstationary cyclic qutrit

We consider a nonstationary circuit quantum electrodynamics setup in which a three-level artificial atom in the $\mathrm{\Delta }$ configuration interacts with a single-mode cavity field of natural frequency $\omega$. 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 $\omega$ and $3\omega$, respectively, and the generated field states exhibit strikingly different statistics from the squeezed vacuum state attained in the standard cavity dynamical Casimir effect.

Figure 1

System behavior for the three-photon DCE. (a) Dynamics of the average photon number $n_{\mathrm{ph}}$ and Mandel's $Q$ factor. (b) Dynamics of the atomic populations: the probability that the atom leaves the initial state is $\lesssim 12\%$. (c) Photon statistics $P\left(n\right)=\mathrm{Tr}\left(\widehat{\rho }\right|n\rangle \langle n\left|\right)$ for the time instant $\omega t_{*}=0.91\times {10}^5$ [marked by the green arrow in (a)], where $\widehat{\rho }$ is the total density operator. Note the local peaks at $n=3k$, asserting the effective three-photon nature of the process.

Figure 2

System behavior for the one-photon DCE. Similar to Fig. 1. The probability that the atom leaves the initial state is now $\lesssim 30\%$. For $\omega t_{*}=1.61\times {10}^5$ (c) the photon statistics lacks local peaks, indicating that the photons are generated via effective one-photon transitions.

Figure 3

Dissipative three-photon DCE. Behavior of $n_{\mathrm{ph}}, Q$, and $P_k$ under unitary (thin black lines) and dissipative (thick red lines) evolutions. For initial times (till the first maximum of $n_{\mathrm{ph}}$) the effects of dissipation are small; for larger times the dissipation strongly affects the dynamics, but the main qualitative features persist.