The surprising persistence of time-dependent quantum entanglement

Abstract

The mismatch between elegant theoretical models and the detailed experimental reality is particularly pronounced in quantum nonlinear interferometry (QNI). In stark contrast to theory, experiments contain pump beams that start in impure states and that are depleted, quantum noise that affects—and drives—any otherwise gradual build up of the signal and idler fields, and nonlinear materials that are far from ideal and have a complicated time-dependent dispersive response. Notably, we would normally expect group velocity mismatches to destroy any possibility of measurable or visible entanglement, even though it remains intact—the mismatches change the relative timings of induced signal-idler entanglements, thus generating ‘which path’ information. Using an approach based on the positive-P representation, which is ideally suited to such problems, we are able to keep detailed track of the time-domain entanglement crucial for QNI. This allows us to show that entanglement can be—and is—recoverable despite the obscuring effects of real-world complications; and that recovery is attributable to an implicit time-averaging present in the detection process.