Erratum: Fast optimal transition between two equilibrium states [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.82.03343082, 033430 (2010)]

Abstract

We noticed an error in the invariant of motion given in Eq.(2). The correct invariant readsIt is invariant if Eqs. (3) and (4) of the paper are satisfied. Given the boundary conditions considered, I (t) commutes with H (t) for t 0 and t t f , and thus nothing is changed concerning the rest of the paper. In particular, the validity of the method and of the experimental results is not affected by this error.059911-1

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.…”

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].…”

Fast frictionless expansion of an optical lattice

“…The dynamical responses of the particle to the constant force and periodically changing force are the well-known phenomena of Bloch oscillations [32][33][34] and dynamical localization [35], respectively. 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).…”

“…This has motivated researchers to find a way to speed up the process to reach the same instantaneous adiabatic eigenstate [1]. Recently, a new technique has been introduced and experimentally realized with ultracold 87 Rb atoms in a harmonic trap [11,12]. The technique is based on engineering the time dependent parameters of the Hamiltonian.…”