Quantum and classical simulations of parametric heating in gaussian potential wells

Optical dipole traps hold cold atoms in potential energy wells that are approximately quadratic at low energies but more closely approximated as gaussian at higher energies. Parametric heating is commonly used to eject atoms from dipole traps as a diagnostic for the low amplitude resonant frequency of oscillation in the trap. A gaussian trap with a depth of about 1000 times the low amplitude quantum of exictation was simulated quantum mechanically by finding the lowest 1500 states in the static gaussian well and then solving the time dependent Schrodinger equation with a parametric perturbation. Classical and quantum simulations of the heating process were compared and showed that a classical simulation does not match the quantum result for atoms deep in the trap but that it works much better as the particle energy increases as one would expect based on the Bohr correspondence principle. Both simulations show that a down-chirped pulse with a frequency variation of about 20 percent is effective at ejecting particles from the trap. We conclude that classical simulations are adequate for finding strategies for ejecting atoms, but that they do not model low energy dynamics well.