Quantum interference between heralded single photon state and coherent state

Balanced homodyne detection has been introduced as a reliable technique of reconstructing the quantum state of a single photon Fock state, which is based on coupling the single photon state and a strong coherent local oscillator in a beam splitter and detecting the field quadrature at the output ports separately. The main challenge associated with a tomographic characterization of the single photon state is mode matching between the single photon state and the local oscillator. Utilizing the heralded single photon generated by the spontaneous parametric process, the multi-mode theoretical model of quantum interference between the single photon state and the coherent state in the fiber beam splitter is established.Moreover, the analytical expressions of the temporal-mode matching coefficient and interference visibility and relationship between the two parameters are shown. In the experimental scheme, the interference visibility under various temporalmode matching coefficients is demonstrated, which is almost accordant with the theoretical value. Our work explores the principle of temporal-mode matching between the single photon state and the coherent photon state, originated from a local oscillator, and could provide guidance for designing the high-performance balanced homodyne detection system.