Environment-Governed Dynamics in Driven Quantum Systems

We show that the dynamics of a driven quantum system weakly coupled to the environment can exhibit two distinct regimes. While the relaxation basis is usually determined by the $\mathrm{\text{system}}+\mathrm{\text{drive}}$ Hamiltonian (system-governed dynamics), we find that under certain conditions it is determined by specific features of the environment, such as, the form of the coupling operator (environment-governed dynamics). We provide an effective coupling parameter describing the transition between the two regimes and discuss how to observe the transition in a superconducting charge pump.

Figure 1

A model driven two-level system. (a) Due to the driving field, the tip of the effective magnetic field $\overrightarrow{B}$ draws a closed loop in pseudospin space. The explicit time dependence of $\overrightarrow{B}$ can be obtained by that of the parameters $J_L$, $J_R$, and $n_g$, provided in Fig. 3b, with the help of the expressions given in the text. The solid angle spanned by $\overrightarrow{B}$ is controlled by the angle $\phi$, that we regard as a tunable parameter. (b) Quasienergy spectrum as a function of $\phi$. A weakly avoided quasienergy crossing occurs at ${\phi }_c=-0.26$.

Figure 2

SGD to EGD transition. $n_z$ (full lines) and $n_{\perp }$ (dashed lines) versus $\phi$ for $A={\sigma }_z$ and $g^2=0.01$ (a), versus $g^2$ for $A={\sigma }_z$ and $\phi =-0.24$ (b), and versus $\alpha$ for $\phi =-0.16$ (black) and $\phi =-0.25$ (red) and $g^2=0.1$ (c). EGD is attained in the highlighted regions of panels (a), (b), and everywhere in panel (c). The drive parameters are the same as in Fig. 3.

Figure 3

Application to the Cooper-pair sluice. (a) Equivalent circuit of the sluice. (b) Time dependence of $J_L$, $J_R$, and $n_g$ during a pumping cycle. (c) Pumped charge $Q_p$ versus $\phi$ for selected values of $g^2$. Relevant drive parameters are $\tau =1\mathrm{ns}$, $E_C=1\mathrm{K}$, $\Delta n_g=0.2$, $J_{\max }=0.1E_C$, $J_{\min }={10}^{-3}{J}_{\max }$.