Abstract
We study experimentally and theoretically the controlled transfer of harmonically trapped ultracold gases between different quantum states. In particular, we experimentally demonstrate a fast decompression and displacement of both a non-interacting gas and an interacting Bose–Einstein condensate, which are initially at equilibrium. The decompression parameters are engineered such that the final state is identical to that obtained after a perfectly adiabatic transformation despite the fact that the fast decompression is performed in the strongly non-adiabatic regime. During the transfer the atomic sample goes through strongly out-of-equilibrium states, while the external confinement is modified until the system reaches the desired stationary state. The scheme is theoretically based on the invariants of motion and scaling equation techniques and can be generalized to decompression trajectories including an arbitrary deformation of the trap. It is also directly applicable to arbitrary initial non-equilibrium states.
Highlights
Scaling properties of harmonically confined ultracold gases: two examplesWe recall how the density and velocity distributions of a 1D non-interacting gas are affected by a change of the harmonic confinement
We study experimentally and theoretically the controlled transfer of harmonically trapped ultracold gases between different quantum states
Methods can be used on the motional degrees of freedom of ultracold gases confined in timedependent harmonic traps and experimentally demonstrate the validity of the approach
Summary
We recall how the density and velocity distributions of a 1D non-interacting gas are affected by a change of the harmonic confinement. We show that the dynamics is fully described by two scaling functions, one associated with the cloud’s size and the other with its center-of-mass position and exhibit the exact solutions of the Schrodinger equation. This will be used in the rest of the paper to realize shortcuts to adiabaticity (cf section 3). The analogy between the invariant method used for the non-interacting gas [15] and the scaling often used for BECs [16,17,18] is underlined
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