Shortcut to Adiabatic Passage in Two- and Three-Level Atoms

Abstract

We propose a method to speed up adiabatic passage techniques in two-level and three-level atoms extending to the short-time domain their robustness with respect to parameter variations. It supplements or substitutes the standard laser beam setups with auxiliary pulses that steer the system along the adiabatic path. Compared to other strategies, such as composite pulses or the original adiabatic techniques, it provides a fast and robust approach to population control.

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

“…To speed up the transfer by using the dynamics of invariant-based inverse engineering, we need to introduce an invariant Hermitian operator I S 2 (t), which satisfies i∂I S 2 (t)/∂t = [H S 2 (t), I S 2 (t)] [10,13,14,23,24], for H S 2 (t) possesses the SU(2) dynamical symmetry. And I S 2 (t) is given by…”

“…From refs [10,13,17], we know that it is very hard to directly design and perform the FPT in a system which is more complicated than the three-level single-atom system.…”

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].…”

Pulse design without the rotating-wave approximation

“…The formal construction of the CD term is explained in the original references [10,15,[17][18][19][20]. We shall apply the counterdiabatic method to speed up an adiabatic population inversion process for a two-level systems beyond the RWA, where the (reference) Hamiltonian of the system is given by Eq.…”