Two-Particle Asynchronous Quantum Correlation: Wavefunction Collapse Acting as a Beamsplitter

A two-body quantum correlation is calculated for a particle reflecting from a moving mirror. Correlated interference results when the incident and reflected particle substates and their associated mirror substates overlap. Using the Copenhagen interpretation of measurement, an asynchronous joint probability density (PDF), which is a function both of the different positions and different times at which the particle and mirror are measured, is derived assuming that no interaction occurs between each measurement. Measurement of the particle first, in the correlated interference region, results in a splitting of the mirror substate into ones which have and have not reflected the particle. An analog of the interference from the Doppler effect for only measurements of the particle (a marginal PDF), in this two-body system, is shown to be a consequence of the asynchronous measurement. The simplification obtained for a microscopic particle reflecting from a mesoscopic or macroscopic mirror is used to illustrate asynchronous correlation interferometry. In this case, the small displacement between these mirror states can yield negligible environmental decoherence times. In addition, interference of these mirror states does not vanish in the limit of large mirror mass due to the small momentum exchange in reflecting a microscopic particle.