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. The robustness against dissipation of two generic kinds of entanglement is studied: the qubit can be entangled with either the phase or amplitude of the oscillator's motion. In the zero-temperature limit, an 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.