Frictionless atom cooling in harmonic traps: A time-optimal approach

Abstract

In this article we formulate frictionless atom cooling in harmonic traps as a time-optimal control problem, permitting imaginary values of the trap frequency for transient time intervals during which the trap becomes an expulsive parabolic potential. We show that the minimum time solution has a "bang-bang" form, where the frequency jumps suddenly at certain instants and then remains constant, and calculate estimates of the minimum cooling time for various numbers of such jumps. A numerical optimization method based on pseudospectral approximations is used to obtain suboptimal realistic solutions without discontinuities, which may be implemented experimentally.

Energy consumption for shortcuts to adiabaticity

“…We use the degeneracy of the STAs to design a protocol that minimizes energy consumption, combining inverseengineering STAs with optimal-control theory [21,30]. In this section we assume that the harmonic model holds.…”

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].…”

“…Motivated by the practical need to accelerate quantum adiabatic processes in different contexts (transport [1][2][3][4][5], expansions [6,7], population inversion and control [8][9][10][11][12][13], cooling cycles [6,14,15], wavefunction splitting [16][17][18][19]), and by related fundamental questions (about the quantum limits to the speed of processes, the viability of adiabatic computing [20], or the third principle of thermodynamics [14,21]), a flurry of theoretical and experimental activity has been triggered by the proposal of several approaches to design "shortcuts to adiabaticity". 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,...…”

Fast frictionless expansion of an optical lattice

“…The additional force, F (t) transforms as F (τ )Λ 3 (τ ) in the equation (11). Hence, the picture for Bloch oscillation and dynamical localization change a lot for the trajectories (13,14,15). The fast frictionless expansion without destroying the Bloch oscillation and dynamical localization would be possible if the force transforms as F/Λ 3 .…”