Speeding up the antidynamical Casimir effect with nonstationary qutrits

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 the nonstationary quantum Rabi model, it suffered from a 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 replacing the qubit by an artificial three-level atom (qutrit) in a properly chosen configuration. For the cavity thermal state we demonstrate that the dynamics of the average photon number and atomic excitation is completely different from the qubit's case, while the behavior of the total number of excitations is qualitatively similar yet significantly faster.

Figure 1

Difference of initial populations $P\left(m,\mathcal{T},\mathcal{S}\right)\equiv P_{m,\mathcal{T}}-P_{m-2,\mathcal{S}}$ for $m=4$ and different regimes as function of the absolute value of the detuning ${\mathrm{\Delta }}_1$. Regimes: 2-level atom (2L), double-resonant regime (r), dispersive regime (d), and mixed regime (m). Only the states for which $P\left(m,\mathcal{T},\mathcal{S}\right)>0$ are plotted and the values $(\mathcal{T},\mathcal{S})$ are indicated alongside the curves. (Here $G_{0,1}=1.2G_{0,0}$.)

Figure 2

(a) Transition rate for ADCE (involving the transition $|{\phi }_{4,\mathcal{T}}\rangle \to |{\phi }_{2,\mathcal{S}}\rangle$) as a function of ${\mathrm{\Delta }}_1/G_{0,0}$ for $m=4$ and modulation of $E_1$. The values of indexes $(\mathcal{T},\mathcal{S})$ are indicated alongside the curves in different regimes. (b) Same as (a) but for the simultaneous modulation of $E_1$ and $E_2$ with the same frequency. In the dispersive regime (d) we set ${\mathrm{\Delta }}_2=6G_{0,0}\mathrm{sgn}\left({\mathrm{\Delta }}_1\right)$. In the mixed regime (m) the lines $(0,D)$ and $(0,-D)$ are very close, so for the sake of compactness they are not discerned separately. We do not show the transition rate near $|{\mathrm{\Delta }}_1|=0$, since all the population differences $P\left(m,\mathcal{T},\mathcal{S}\right)$ are negative in this case. Notice the increment by at least one order of magnitude of the transition rate in the double-resonant regime (r) [compared to the qubit's case (2L)] for $|{\mathrm{\Delta }}_1|\gg G_{0,0}$.

Figure 3

Exact numerical dynamics of ADCE obtained for the Hamiltonian (1) and the initial local thermal state ${\widehat{\rho }}_0$ in the double-resonant regime. (a) 2-level atom and harmonic modulation of $E_1$. (b) 3-level atom and 2-tone modulation of $E_1$. (c) 3-level atom and 2-tone double modulation of $E_1$ and $E_2$. Notice that in all cases the number of annihilated excitations $n_{\mathrm{tot}}$ is roughly the same, while the duration of the process in (c) is roughly 40 times smaller than in (a).

Figure 4

Dynamics of populations of relevant dressed states for the 2-tone double modulation of $E_1$ and $E_2$ analyzed in Fig. 3. There is a coherent transfer of populations from the states $|{\phi }_{4,D}\rangle$ and $|{\phi }_{4,0}\rangle$ to the state $|{\phi }_{2,-D}\rangle$. Moreover, one observes periodic oscillations between the dressed states $|{\phi }_{k,D}\rangle \leftrightarrow |{\phi }_{k,0}\rangle$ for $k\ge 2$ due to the counter-rotating terms in the Hamiltonian (1).