Population Inversion of a Driven Two-Level System in a Structureless Bath

We derive a master equation for a driven double quantum dot damped by an unstructured phonon bath, and calculate the spectral density. We find that bath-mediated photon absorption is important at relatively strong driving, and may even dominate the dynamics, inducing population inversion of the double-dot system. This phenomenon is consistent with recent experimental observations.

Figure 1

Energy level diagrams for dressed-state raising and lowering processes in (a) the dressed basis and (b) the bare eigenbasis, for $\eta <0$, where $|-⟩\approx |e⟩$ and $|+⟩\approx |g⟩$. Solid arrows indicate photon absorption, and dotted arrows indicate phonon emission. When $|\eta |\gg \Omega$, ${\Omega }^{\prime }\approx |\eta |={\omega }_0-\varphi$.

Figure 2

(a) Occupation of left dot, $M$, for increasing Rabi frequency from ${\Omega }_0=0.01{\omega }_0$ to $0.17{\omega }_0$ in steps of $0.02{\omega }_0$. Other parameters are ${\omega }_p=0.2{\omega }_0=\Delta$, $k_{B}T=0.05{\omega }_0$, and $\delta =\pi /2$ corresponding to driving the tunneling rate. (b) Increasing temperature from $k_{B}T=0$ to $0.3{\omega }_0$ in steps of $0.06{\omega }_0$. As above, ${\omega }_p=0.2{\omega }_0=\Delta$ while ${\Omega }_0=0.16{\omega }_0$.