Entanglement with a mode observable via a tunable interaction with a qubit

We study the possibility of detection of "spin-boson" entanglement by qubit only measurements. Such entanglement is impossible to detect by previously proposed schemes that involve a fixed system-environment interaction, because of inherent symmetries within the coupling and the initial state of the environment. We take advantage of the possibility of tuning of qubit-environment coupling, that is available in some qubit realizations. As an example we study a superconducting transmon qubit interacting with a microwave cavity, which is one of such systems and is, furthermore, essential in the context of quantum information processing. We propose suitable Hamiltonian parameters for the preparation and measurement phases of the detection scheme that allow for an experimental test, and verify that the reported signal is nonnegligibly large still at finite temperatures.