Time-reversal operation of tunneling dynamics of Bose-Einstein condensates in optical lattices

Abstract

We propose schemes that can perform perfect time-reversal operation of the tunneling dynamics of Bose-Einstein condensates in optical lattices. One of the time-reversal schemes is to reverse the sign of the tunneling coefficient by a time-periodic potential, maintaining its magnitude at a constant value. The other scheme utilizes a staggered $0\text{\ensuremath{-}}\ensuremath{\pi}$ phase imprinting on the optical lattices. If the reversal of the tunneling coefficient or the phase imprinting is performed at $\ensuremath{\tau}={\ensuremath{\tau}}_{p}$, the initial distribution of the condensates is regained at $\ensuremath{\tau}=2{\ensuremath{\tau}}_{p}$. Although the nonlinear interatomic interaction deteriorates the fidelity of the time-reversal operation, if the sign of the nonlinearity is reversed simultaneously with the phase imprinting at $\ensuremath{\tau}={\ensuremath{\tau}}_{p}$, the time-reversal operation at $\ensuremath{\tau}=2{\ensuremath{\tau}}_{p}$ becomes nearly perfect.