On the consistency, extremal, and global properties of counterdiabatic fields

Abstract

The control of population transfer can be affected by the adiabatic evolution of a system under the influence of an applied field. If the field is too rapidly varying or too weak, the conditions for adiabatic transfer are not satisfactorily met. We report the results of an analysis of properties of counterdiabatic fields (CDFs) that restore the adiabatic dynamics of a system by suppressing diabatic effects as they are generated. We observe that a CDF is not unique and find the one that has minimum intensity, and we provide natural upper and lower bounds to the integrated intensity of a CDF in terms of integrals of the eigenvalues of the system Hamiltonian. For Hamiltonians that are separable with respect to their parameters, we prove that the time integral of an associated CDF is path independent. Finally we explain why and when, in the neighborhood of an avoided crossing, a CDF can be approximated by Lorentzian pulses.

Efficient shortcuts to adiabatic passage for fast population transfer in multiparticle systems

“…Recently, a lot of work has been done in finding shortcuts to adiabaticity for the two-or three-level atomic system [8][9][10][11][12][13][14][15]. By means of resonant laser pulses, Chen and Muga have successfully performed fast population transfer (FPT) in three-level systems via invariantbased inverse engineering [13].…”

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,...…”

Nearly optimal quantum control: an analytical approach

“…Many techniques to do this have been developed for spin-1/2 systems [6][7][8]. Here we will focus on the class of such solutions called shortcuts to adiabaticity [8,[11][12][13][14][15]. This class covers not only spin-1/2 but also many practically interesting multistate situations [16].…”