Time-optimal variational control of a bright matter-wave soliton

Abstract

Motivated by recent experiments, we present the time-optimal variational control of a bright matter-wave soliton trapped in the harmonic trap by manipulating the atomic interaction through Feshbach resonances. More specifically, we first apply the variational technique to derive the motion equation for capturing the soliton's shape and, second, combine an inverse-engineering method with optimal control theory to design the scatter length for implementing time-optimal decompression. Since the minimum-time solution is of the "bang-bang" type, the smooth regularization is further adopted to smooth the on-off controller out, thus avoiding the heating and atom loss induced from the magnetic field ramp across a Feshbach resonance, in practice.

Effective Scaling Approach to Frictionless Quantum Quenches in Trapped Bose Gases

“…In this sense, the effective scaling approach has more reasonable accuracy, when the atomic interaction with the arbitrary value is considered. Finally, some extensions are interesting for further exploration, for instance, the soliton dynamics by quenching the interactions of the BEC from repulsive to attractive [34,43], or the expansion of a Bose gas in the crossover from TF to TG regimes [44].…”

“…However, tracking back to a BEC described by the GP equation in the meanfield approximation, one can realize that the original Ermakov equation obtained in non-interacting case needs to be modified in the TF limit or in the case of a time-dependent interaction [21,26] . To remedy it, the variational approximation [30] (which is equivalent to moment method [31]), can be complemented by the concept of STA, for studying the dynamics of BECs [32][33][34], valid for the range from zero to small atomic interaction, with the implication on the quantum speed limits and quantum thermodynamics [35,36]. As a matter of fact, the accuracy of the variational approximation depends on the presumed ansatz in terms of nonlinearity [33,34].…”

“…To remedy it, the variational approximation [30] (which is equivalent to moment method [31]), can be complemented by the concept of STA, for studying the dynamics of BECs [32][33][34], valid for the range from zero to small atomic interaction, with the implication on the quantum speed limits and quantum thermodynamics [35,36]. As a matter of fact, the accuracy of the variational approximation depends on the presumed ansatz in terms of nonlinearity [33,34]. Thus, the motivation of this work is to fill the gap in more general theory on STA design for 1D Bose gas with arbitrary interactions.…”

Shortcut to synchronization in classical and quantum systems

“…In linear systems, STAs can preserve the optimality of the quantum speed in a system which evolves at the quantum speed limit 40 . The extension of STAs to nonlinear quantum systems is at the incipient stage [41][42][43][44][45][46] and raises the question of the influence of non linearities on the quantum speed limit 47 . In this paper, we propose to accelerate classical and quantum synchronization, an inherently non-linear and non-perturbative phenomenon 1 .…”

Shortcut to synchronization in classical and quantum systems

“…However, most STA techniques exploits the linearity of the Schrödinger equation, as illustrated by numerous applications to simple quantum systems [34,35]. The extension to nonlinear quantum systems is at the incipient stage [36][37][38][39][40][41] and raises the question of the influence of non linearities on quantum speed limit [42]. In this paper, we propose to accelerate classical and quantum synchronization, an inherently non-linear and non-perturbative phenomenon [1].…”