Entanglement Dynamics in a Dispersively Coupled Qubit-Oscillator System

We study entanglement dynamics in a system consisting of a qubit dispersively coupled to a finite-temperature, dissipative, driven oscillator. We show that there are two generic ways to generate entanglement: one can entangle the qubit either with the phase or the amplitude of the oscillator's motion. Using an exact solution of the relevant quantum master equation, we study the robustness of both these kinds of entanglement against the effects of dissipation and temperature; in the limit of zero temperature (but finite damping), a simple analytic expression is derived for the logarithmic negativity. We also discuss how the generated entanglement may be detected via dephasing revivals, being mindful that revivals can occur even in the absence of any useful entanglement. Our results have relevance to quantum electromechanics, as well as to circuit QED systems.