Fast transport of Bose–Einstein condensates

Abstract

We propose an inverse method to accelerate without final excitation the adiabatic transport of a Bose-Einstein condensate. The method is based on a partial extension of the Lewis-Riesenfeld invariants and provides transport protocols that satisfy exactly the no-excitation conditions without approximations. This inverse method is complemented by optimizing the trap trajectory with respect to different physical criteria and by studying the effect of perturbations such as anharmonicities and noise.

Shortcuts to adiabaticity: Fast-forward approach

“…The non-linear GP equation could also be treated, as in [4,22], but it does not allow in general for the state-independent potential forms that we shall describe for g = 0.…”

“…Performing now the unitary transformation [3,4] ψ n (x, t) = e im [ρ|x| 2 /2ρ+(αρ−αρ)·x/ρ] 1 ρ 3/2 χ n (σ), (23) the state ψ n is easily obtained from the solution χ n (σ) (normalized in σ-space) of the auxiliary stationary Schrödinger equation…”

“…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].…”

Speeding up the spatial adiabatic passage of matter waves in optical microtraps by optimal control

“…We note that a similar study has been carried out in Ref. [33], where the optimal transport of a BEC in magnetic microtraps, like the ones produced with atom chips [4], has been investigated, and that, very recently, the optimal control pulses for harmonically trapped BECs have been analytically determined [36]. We underscore that, while the goal of those investigations was to transfer a BEC between spatially separated locations, here, in addition to this goal, we aim at minimizing the occupancy of the middle well in a triple-well configuration, as showed in Fig.…”

“…It is therefore imperative to reduce the time needed to transport an atom or ion from the quantum memory to the processing units and, therefore, to engineer robust control transport pulses. In this respect, optimal control theory is a prominent candidate for a drastic improvement of the design of accurate QIP protocols, and, recently, several theoretical investigations on the optimal transport of both a single atom and an atomic ensemble have been undertaken [33][34][35][36]. Besides this, very recently, control pulses numerically obtained by using iterative optimization algorithms have been experimentally applied, with great success, in order to efficiently transfer a one-dimensional (1D) degenerate Bose gas from the transverse ground to the lower excited state of a waveguide potential [37].…”