Photon Capture into a Bound State in the Continuum of a Waveguide-Qubit System

We show that it is possible to excite an exact bound state in the continuum (BIC) of a waveguide-qubit system by using a two photon pulse. The existence of such BIC states in the single photon sector is well-known but populating these states with an injected pulse is problematic. We study photon capture-- two photons are injected but only one comes out because the other is trapped in the BIC-- in two geometries, a single qubit in a semi-infinite waveguide or two qubits in an infinite waveguide. Photon capture proceeds by inelastic scattering due to the nonlinearity of the qubit and is suppressed for small qubit-qubit or qubit-mirror separation. Thereby, the system should in fact be in the non-Markovian regime due to non-negligible photon delay times. We investigate this effect in both a continuum model with linear dispersion and a coupled cavity array. In the case of two qubits, one outcome is heralded generation of very long-lived entanglement.