Spectral localization in cavity-mediated entanglement harvesting

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, Cg(Q)=2e-π /(2Q)(1+e-π /(2Q))/(1+3e-π /Q) C g ( Q ) = 2 e - π / ( 2 Q ) ( 1 + e - π / ( 2 Q ) ) / ( 1 + 3 e - π / Q ) , where Q≡ |Δ |/κ Q ≡ | Δ | / κ is the ratio of the qubit-cavity detuning Δ Δ to the cavity linewidth κ κ . This reference time is inherited from the first maximally entangling unitary gate. At finite loss, Cg C g is the conditional concurrence at this prescribed readout time. In the high- Q limit, Cg 1-π ²/(16Q²) C g ≃ 1 - π 2 / ( 16 Q 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 Cg(Q) C g ( Q ) curve can, in principle, be examined in circuit QED with ideal monitoring and no-jump post-selection.