arXiv subjects

S. Martínez-Garaot

Publications and source records attributed to S. Martínez-Garaot.

23 records · Page 2Linked to original sources

arXiv2015

Fast quasi-adiabatic dynamics

We work out the theory and applications of a fast quasi-adiabatic approach to speed up slow adiabatic manipulations of quantum systems by driving a control parameter as near to the adiabatic limit as possible over the entire protocol duration. Specifically, we show that the population inversion in a two-level system, the splitting and cotunneling of two-interacting bosons, and the stirring of a Tonks-Girardeau gas on a ring to achieve mesoscopic superpositions of many-body rotating and non-rotating states, can be significantly speeded up.

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arXiv2014

Shortcuts to adiabaticity in three-level systems using Lie transforms

Sped-up protocols (shortcuts to adiabaticity) that drive a system quickly to the same populations than a slow adiabatic process may involve Hamiltonian terms difficult to realize in practice. We use the dynamical symmetry of the Hamiltonian to find, by means of Lie transforms, alternative Hamiltonians that achieve the same goals without the problematic terms. We apply this technique to three-level systems (two interacting bosons in a double well, and beam splitters with two and three output channels) driven by Hamiltonians that belong to the four-dimensional algebra U3S3.

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arXiv2014

Hamiltonian engineering via invariants and dynamical algebra

We use the dynamical algebra of a quantum system and its dynamical invariants to inverse engineer feasible Hamiltonians for implementing shortcuts to adiabaticity. These are speeded up processes that end up with the same populations than slow, adiabatic ones. As application examples we design families of shortcut Hamiltonians that drive two and a three-level systems between initial and final configurations imposing physically motivated constraints on the terms (generators) allowed in the Hamiltonian.

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arXiv2012

Engineering fast and stable splitting of matter waves

When attempting to split coherent cold atom clouds or a Bose-Einstein condensate (BEC) by bifurcation of the trap into a double well, slow adiabatic following is unstable with respect to any slight asymmetry, and the wave "collapses" to the lower well, whereas a generic fast chopping splits the wave but it also excites it. Shortcuts to adiabaticity engineered to speed up the adiabatic process through non-adiabatic transients, provide instead quiet and robust fast splitting. The non-linearity of the BEC makes the proposed shortcut even more stable.

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arXiv2012

Shortcuts to adiabaticity: fast-forward approach

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.

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