Quantum time-of-flight distribution for cold trapped atoms

Abstract

The time-of-flight distribution for a cloud of cold atoms falling freely under gravity is considered. We generalize the probability current density approach to calculate the quantum arrival time distribution for the mixed state describing the Maxwell-Boltzmann distribution of velocities for the falling atoms. We find an empirically testable difference between the time-of-flight distribution calculated using the quantum probability current and that obtained from a purely classical treatment which is usually employed in analyzing time-of-flight measurements. The classical time-of-flight distribution matches with the quantum distribution in the large mass and high temperature limits.