Temporal coherence in an unbalanced SU(1,1) interferometer

In classical coherence theory, coherence time is typically related to the bandwidth of the optical field. Narrowing the bandwidth by optical filtering will result in the lengthening of the coherence time. In the case of a delayed pulse photon interference, this will lead to pulse overlap and recovery of interference, which is otherwise absent due to time delay. However, this is changed for entangled optical fields. In this Letter, we investigate how the temporal coherence of the fields in a pulse-pumped SU(1,1) interferometer changes with the bandwidth of optical filtering. We find that the effect of optical filtering is not similar to the classical coherence theory in the presence of quantum entanglement. A full quantum theory is presented and can explain the phenomena well.