Acceleration of adiabatic quantum dynamics in electromagnetic fields

Shortcuts to adiabaticity: Fast-forward approach

“…These relations do not imply the full identity of the methods but their overlap and equivalence in a common domain. They are still useful heuristically as separate approaches since they are formulated in rather different terms [28,33]. Moreover they facilitate extensions beyond their common domain, as exemplified by the wave-splitting processes discussed in the previous section.…”

“…Based on some earlier results [34], the fast-forward formalism for adiabatic dynamics and several application examples were worked out in [19,28] by Masuda and Nakamura for the Gross-Pitaevskii (GP) or the corresponding Schrödinger equations. The objective of the method is to accelerate a "standard" system subjected to a slow variation of external parameters.…”

“…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 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 .…”

Quantum state transfer in spin chains via shortcuts to adiabaticity

“…In this respect, we note that, recently, a technique named "shortcuts to adiabaticity" (STA) [36][37][38][39][40][41][42], which aims at optimally designing Hamiltonian to speed up the quantum adiabatic process, has been put forward. The core of the STA is to drive the system following a relatively rapid adiabatic-like process which is not really adiabatic but leading to the same goals as the adiabatic process does.…”