Interaction-induced period shift of the Kohn oscillation in a parity-time-symmetric harmonic trap

Abstract

The center of mass of a Bose--Einstein condensate in a harmonic trap oscillates at the trap frequency independently of the interactions. Without interactions a parity-time-symmetric gain-loss gradient leaves this frequency unchanged, and a cloud of the ground-state width is translated rigidly while the atom number is periodically modulated. With interactions the protection is lost, because the gain and the loss change the number of atoms; the modulated atom number drives the width of the cloud, and the width acts back on the center of mass. At small gain the period grows quadratically with the gain strength, with a coefficient that in the Thomas--Fermi regime is set by the size of the cloud alone. The family of periodic orbits continued from the Kohn oscillation can be followed up to a critical gain, where it comes into resonance with highly excited states of the trap, and over the computed families this critical gain decreases with the amplitude of the oscillation and with the size of the cloud. A five-variable moment model reproduces the period and the width of the cloud along the orbits nearly up to the critical gain.