Quantum time of flight distribution for cold trapped atoms

The time of flight distribution for a cloud of cold atoms falling freely under gravity is considered. We generalise 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 analysing time of flight measurements. The classical time of flight distribution matches with the quantum distribution in the large mass and high temperature limits.