A Matter-Wave Quantum Superposition of Inertial and Constant Acceleration Motions

Abstract

We present three different methods of calculating the non-relativistic dynamics of a quantum matter-wave evolving in a superposition of the inertial and accelerated motions. The relative phase between the two, which is classically unobservable as it is a gauge transformation, can be detected in a matter-wave interference experiment. The first method is the most straightforward and it represents the evolution as an exponential of the Hamiltonian. Based on the Heisenberg picture, the second method is insightful because it gives us extra insight into the independence of the wave-packet spreading of the magnitude of acceleration. Also, it demonstrates that the Heisenberg picture is perfectly suited to capturing all aspects of quantum interference. The final method shows the consistency with the full relativistic treatment and we use it to make a point regarding the equivalence principle.