Shortcuts to adiabaticity for non-Hermitian systems

Abstract

Adiabatic processes driven by non-Hermitian, time-dependent Hamiltonians may be sped up by generalizing inverse engineering techniques based on Berry's transitionless driving algorithm or on dynamical invariants. We work out the basic theory and examples described by two-level Hamiltonians: the acceleration of rapid adiabatic passage with a decaying excited level and of the dynamics of a classical particle on an expanding harmonic oscillator

Fast transitionless expansion of cold atoms in optical Gaussian-beam traps

“…We assume that V 0 (t) is set to satisfy the designed longitudinal expansion according to Eq. (21). Substituting this into Eq.…”

“…1 In general, changes of the confining trap will excite the state of motion of the atoms unless they are done very slowly or, in the usual quantum-mechanical sense of the word, "adiabatically," but slow-change processes are also prone to perturbations and decoherence or are impractical for performing many cycles. Engineering fast expansions without final excitation is thus receiving much attention recently, both theoretically and experimentally [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Most theoretical treatments so far are for idealized one-dimensional (1D) systems, but the implementation requires a three-dimensional (3D) trap [11,14,15], in principle with anharmonicities and couplings among different directions.…”

Optimal trajectories for efficient atomic transport without final excitation

“…These works on transport share concepts and techniques with other "shortcuts to adiabaticity" in expansion or compressions [12,[16][17][18][19][20][21][22][23][24], rotations [25], and internal state population transfer and control [26][27][28][29][30][31][32][33]. Several approaches have been proposed, including counter-diabatic [26][27][28] or, equivalently, transitionless driving algorithms [29][30][31], optimal control theory [20], "fast-forward" scaling [12], and inverse engineering based on Lewis-Riesenfeld invariants [14][15][16][17][18][19]23,24,[31][32][33][34].…”

“…Several approaches have been proposed, including counter-diabatic [26][27][28] or, equivalently, transitionless driving algorithms [29][30][31], optimal control theory [20], "fast-forward" scaling [12], and inverse engineering based on Lewis-Riesenfeld invariants [14][15][16][17][18][19]23,24,[31][32][33][34].…”

Shortcuts to Adiabatic Pumping in Classical Stochastic Systems

“…Equation (10) should be contrasted with the non-Hermitian control field of Ref. [35], which is given as L cd (t) = |∂ t π(t) 1|, and which is related to the geometry of the stationary state as ||L cd || F = N g tt [π(t)]. In this respect, our control matrix can be regarded as a next-order non-adiabatic generalization of L cd .…”