Shortcut to adiabaticity for an interacting Bose-Einstein condensate

Abstract

We present an investigation of the fast decompression of a three-dimensional (3D) Bose-Einstein condensate (BEC) at finite temperature using an engineered trajectory for the harmonic trapping potential. Taking advantage of the scaling invariance properties of the time-dependent Gross-Pitaevskii equation, we exhibit a solution yielding a final state identical to that obtained through a perfectly adiabatic transformation, in a much shorter time. Experimentally, we perform a large trap decompression and displacement within a time comparable to the final radial trapping period. By simultaneously monitoring the BEC and the non-condensed fraction, we demonstrate that our specific trap trajectory is valid both for a quantum interacting many-body system and a classical ensemble of non-interacting particles.

Fast atomic transport without vibrational heating

“…This is admittedly not a proper transport problem, but its formal treatment is the same, and has recently been implemented experimentally [42], also for Bose-Einstein condensates [43]. As for further extensions or open questions of the invariant approach, one may investigate the use of more complex invariants, not restricted to being quadratic in p [44], in particular to tackle anharmonic transport.…”

“…The regime of Tonks-Girardeau gas can be treated along similar lines of the single particle case and for condensates, scaling techniques may be used as in [43,45].…”

Fully efficient time-parallelized quantum optimal control algorithm

“…This subject has been extensively studied in the past few years [51,52,[54][55][56][57][58]. Following Ref.…”

Shortcuts to adiabaticity: Fast-forward approach

“…Among other approaches let us mention (i) a transitionless tracking algorithm or "counterdiabatic" approach that adds to the original Hamiltonian extra terms to cancel transitions in the adiabatic or superadiabatic bases [8][9][10][11][12][13]; (ii) inverse engineering of the external driving [3,4,6,[21][22][23][24][25][26] based on Lewis-Riesenfeldt invariants [27], which has been applied in several expansion experiments [25,26]; (iii) optimal control (OC) methods [5,7,14,16], sometimes combined with other methods to enhance their performance [4,5,7]; (iv) the fast-forward (FF) approach advocated by Masuda and Nakamura [19,28]; (v) parallel adiabatic passage [29][30][31][32].…”