Spectral Localization in Cavity-Mediated Entanglement Harvesting

Abstract

We investigate the relation between spectral localization and entanglement harvesting in an analytically solvable model of two qubits coupled to a leaky single-mode cavity, which in turn couples to a continuous electromagnetic bath. We derive the no-jump concurrence at a prescribed reference gate time in closed form, $\mathcal C_g(Q)=2e^{-\pi/(2Q)}(1+e^{-\pi/(2Q)})/(1+3e^{-\pi/Q})$, where $Q\equiv|\Delta|/\kappa$ is the ratio of the qubit-cavity detuning $\Delta$ to the cavity linewidth $\kappa$. This reference time is inherited from the first maximally entangling unitary gate. At finite loss, $\mathcal C_g$ is the conditional concurrence at this prescribed readout time. In the high-$Q$ limit, $\mathcal C_g\simeq1-\pi^2/(16Q^2)$, while in the low-$Q$ limit it decays exponentially. For the Lorentzian spectral family, $Q$ is proportional to a detuning-normalized inverse participation ratio and simultaneously measures the balance between coherent exchange and collective decay. This yields a compact, model-specific description of the crossover from nearly unit conditional entanglement to overdamped suppression. The predicted $\mathcal C_g(Q)$ curve can, in principle, be examined in circuit QED with ideal monitoring and no-jump post-selection.