Correlation after reflection in a quantum system

Abstract

Reflection of a microscopic non-zero rest mass particle from a macroscopic mirror generates two-particle interference from the incident and reflected particle substates and the associated mirror substates. This amplifies effects such as fringe spacing since they are essentially determined not by the mass of the macroscopic mirror but rather by the much smaller mass of the microscopic particle. Coherence can be transferred during reflection from the initial particle substate to the mirror substate. Interference of multiple such two-particle states is discussed. These effects could lead to extending measurements of the quantum-classical boundary to larger masses. The possibility of non-simultaneous measurement of the positions of the particle and the mirror is also discussed. The joint probability density, 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 the measurement times. An analog of the Doppler shift for this correlated system is discussed along with interference of multiple such two-particle states.