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REVIEW ARTICLE Shortcut to adiabaticity in harmonic traps

Xi Chen, A. Ruschhaupt, Sebastian Schmidt, Juan Gonzalo Muga

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

We review the methods to preserve the initial state populations in a fast harmonic trap expansion. The design of the time dependence of the frequency using inverse techniques presents advantages over the slow adiabatic approach, band-bang methods, or the non-local transitionless tracking algorithm. Many operations with cold atoms make use of adiabatic expansions and may benefit from such a shortcut to adiabaticity.

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We review the methods to preserve the initial state populations in a fast harmonic trap expansion. The design of the time dependence of the frequency using inverse techniques presents advantages over the slow adiabatic approach, band-bang methods, or the non-local transitionless tracking algorithm. Many operations with cold atoms make use of adiabatic expansions and may benefit from such a shortcut to adiabaticity.
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.