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Optica Pura y Aplicada

Shortcuts to adiabaticity

Juan Gonzalo Muga, X. Chen, E. Torrontegui, Sergio García‐Ibáñez, Ion Lizuain

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

Different ways to accelerate adiabatic processes in cold atom physics and atomic state preparation are reviewed. The invariant-based inverse engineering approach is applied to trap expansions and contractions, and to atomic transport. Berry's Hamiltonian is applied to produce fast versions of adiabatic passage methods.

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By definition, quantum adiabatic process means a slow process which allows the state to follow the instantaneous eigenstates of time-dependent Hamiltonian. For some reasons, for example, to avoid the decoherence effects, or to implement large-scale quantum information processing, we may want to speed up the adiabatic process, that is, to achieve the adiabatic-like control but in very short time. In this talk, we present new methods to speeded-up expansion and transport of cold atoms in a harmonic trap. Such shortcuts to adiabaticity provide the fast expansion or transport, in which the final atomic state is the same as in the adiabatic process, but in arbitrarily short time, keeping the same populations of vibrational levels in the initial and final trap. These methods can also be generalized to Bose-Einstein Condensates. Moreover, we present shortcuts to adiabatic passage from one internal atomic state to another in twoor three-level atoms. In detail, we can apply Berry’s transitionless quantum driving method and invariant-based inverse engineering method to accelerate the Rapid Adiabatic Passage (RAP) and Stimulated Raman Adiabatic Passage (STIRAP) in twoand three-level atomic systems, respectively. We also examine and compare the stability of different schemes concerning different types of noise and system errors. Finally, we show that the technique of shortcuts to adiabaticity in two-level system can be applied in fast and robust spin flip in a quantum dot, to avoid the decoherent effects.
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We use the dynamical invariants associated with the Hamiltonian of an atom in a one dimensional moving trap to inverse engineer the trap motion and perform fast atomic transport without final vibrational heating. The atom is driven nonadiabatically through a shortcut to the result of adiabatic, slow trap motion. For harmonic potentials this only requires designing appropriate trap trajectories, whereas perfect transport in anharmonic traps may be achieved by applying an extra field to compensate the forces in the rest frame of the trap. The results can be extended to atom stopping or launching. The limitations due to geometrical constraints, energies, and accelerations involved are analyzed along with the relation to previous approaches based on classical trajectories or ``fast-forward'' and ``bang-bang'' methods, which can be integrated in the invariant-based framework.
The ``fast-forward''approach by Masuda and Nakamura generates driving potentials to accelerate slow quantum adiabatic dynamics. First we present a streamlined version of the formalism that produces the main results in a few steps. Then we show the connection between this approach and inverse engineering based on Lewis-Riesenfeld invariants. We identify in this manner applications in which the engineered potential does not depend on the initial state. Finally we discuss more general applications exemplified by wave splitting processes.