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arXiv:1607.04119 · Physical Review A

Shortcut to adiabaticity in spinor condensates

A. Sala, David López Núñez, Joan Martorell, L. De Sarlo, Tilman Zibold, Fabrice Gerbier, A. Polls, Bruno Juliá-Díaz

Published Oct 12, 2016• 19 citations
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Abstract

We devise a method to shortcut the adiabatic evolution of a spin-1 Bose gas with an external magnetic field as the control parameter. An initial many-body state with almost all bosons populating the Zeeman sublevel $m=0$ is evolved to a final state very close to a macroscopic spin-singlet condensate, a fragmented state with three macroscopically occupied Zeeman states. The shortcut protocol, obtained by an approximate mapping to a harmonic oscillator Hamiltonian, is compared to linear and exponential variations of the control parameter. We find a dramatic speedup of the dynamics when using the shortcut protocol.

DOI
10.1103/physreva.94.043623

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We devise a method to shortcut the adiabatic evolution of a spin-1 Bose gas with an external magnetic field as the control parameter. An initial many-body state with almost all bosons populating the Zeeman sublevel m=0m=0m=0 is evolved to a final state very close to a macroscopic spin-singlet condensate, a fragmented state with three macroscopically occupied Zeeman states. The shortcut protocol, obtained by an approximate mapping to a harmonic oscillator Hamiltonian, is compared to linear and exponential variations of the control parameter. We find a dramatic speedup of the dynamics when using the shortcut protocol.
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.
We extend a recent method to shortcut the adiabatic following to internal bosonic Josephson junctions in which the control parameter is the linear coupling between the modes. The approach is based on the mapping between the two-site Bose-Hubbard Hamiltonian and a one-dimensional effective Schr\"odinger-like equation, valid in the large-NNN (number of particles) limit. Our method can be readily implemented in current internal bosonic Josephson junctions and it substantially improves the production of spin squeezing with respect to the usually employed linear rampings.
We present measurements and a theoretical model for the interplay of spin-dependent interactions and external magnetic fields in atomic spinor condensates. We highlight general features such as quadratic Zeeman dephasing and its influence on coherent spin mixing processes by focusing on a specific coherent superposition state in a F=1F=1F=1 87Rb^{87}\mathrm{Rb}87Rb Bose-Einstein condensate. In particular, we observe the transition from coherent spinor oscillations to the thermal equilibration.
Abstract We derive from first principles the experimentally observed effective dynamics of a spinor Bose gas initially prepared as a Bose–Einstein condensate and then left free to expand ballistically. In spinor condensates, which represent one of the recent frontiers in the manipulation of ultra-cold atoms, particles interact with a two-body spatial interaction and a spin–spin interaction. The effective dynamics is well-known to be governed by a system of coupled semi-linear Schrödinger equations: we recover this system, in the sense of marginals in the limit of infinitely many particles, with a mean-field re-scaling of the many-body Hamiltonian. When the resulting control of the dynamical persistence of condensation is quantified with the parameters of modern observations, we obtain a bound that remains quite accurate for the whole typical duration of the experiment.
The possible ground states of spin-2 Bose-Einstein condensates in an external magnetic field are obtained analytically and classified systematically according to the population of the condensed atoms at the hyperfine sublevels. It is shown that the atoms can populate simultaneously at four hyperfine sublevels in a weak magnetic field with only the linear Zeeman energy, in contrast to that in a stronger magnetic field with the quadratic Zeeman energy, where condensed atoms can at most populate at three hyperfine sublevels in the ground states. Any spin configuration we obtained will give a closed subspace in the order parameter space of the condensates.