Dephasing and breakdown of adiabaticity in the splitting of Bose–Einstein condensates

Pezzé, Luca; Smerzi, Augusto; Berman, G. P.; Bishop, A. R.; Collins, L. A.

doi:10.1088/1367-2630/7/1/085

Cited by 11 publications

(12 citation statements)

References 20 publications

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“…Splitting a wavefunction without excitating it is important in matter wave interferometry (Hohenester et al, 2007;Grond et al, 2009a,b;Pezze et al, 2005). For linear waves, described by the Schrödinger equation, it is a peculiar operation, as adiabatic following is not robust but unstable with respect to a small external potential asymmetry (Gea-Banaloche, 2002;Torrontegui et al, 2012b).…”

Section: Wavepacket Splittingmentioning

confidence: 99%

Shortcuts to Adiabaticity

Torrontegui

Ibáñez

Martínez-Garaot

et al. 2013

Advances in Atomic, Molecular, and Optical Physics

696

776

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arXiv:1212.6343International audienceQuantum adiabatic processes--that keep constant the populations in the instantaneous eigenbasis of a time-dependent Hamiltonian--are very useful to prepare and manipulate states, but take typically a long time. This is often problematic because decoherence and noise may spoil the desired final state, or because some applications require many repetitions. "Shortcuts to adiabaticity" are alternative fast processes which reproduce the same final populations, or even the same final state, as the adiabatic process in a finite, shorter time. Since adiabatic processes are ubiquitous, the shortcuts span a broad range of applications in atomic, molecular, and optical physics, such as fast transport of ions or neutral atoms, internal population control, and state preparation (for nuclear magnetic resonance or quantum information), cold atom expansions and other manipulations, cooling cycles, wavepacket splitting, and many-body state engineering or correlations microscopy. Shortcuts are also relevant to clarify fundamental questions such as a precise quantification of the third principle of thermodynamics and quantum speed limits. We review different theoretical techniques proposed to engineer the shortcuts, the experimental results, and the prospects

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Section: Wavepacket Splittingmentioning

confidence: 99%

Shortcuts to Adiabaticity

Torrontegui

Ibáñez

Martínez-Garaot

et al. 2013

Advances in Atomic, Molecular, and Optical Physics

696

776

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“…Section IV relates the fast-forward approach to the inverse method for dynamical invariants which are quadratic in momentum. Section V discusses applications beyond this domain, in particular wavefunction splitting, which is an important operation for matter wave interferometry [16][17][18]35]. Finally Sec.…”

Section: Introductionmentioning

confidence: 99%

Shortcuts to adiabaticity: Fast-forward approach

et al. 2012

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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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“…As we slow down the insertion, the difference from the adiabatic limit decreases drastically. This point is especially important in splitting a wave function within a finite time [24][25][26][27]. In case of a quick protocol, the excitation to higher-energy modes, as manifested by the dip around the origin, makes the wave function rugged in further time evolution [ Fig.…”

Section: Numerical Calculationmentioning

confidence: 99%

“…This model deserves attention in its own right as a generalization of the particle in a box problem, because the Schrödinger equation is not explicitly solvable in the presence of a time-dependent potential except a few special cases [19][20][21][22][23]. It is also of experimental relevance in the context of splitting matter waves such as Bose-Einstein condensates [24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Particle in a box with a time-dependentδ-functionpotential

Baek

Kim

2016

Phys. Rev. A

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In quantum information processing, one often considers inserting a barrier into a box containing a particle to generate one bit of Shannon entropy. We formulate this problem as a one-dimensional Schrödinger equation with a time-dependent δ-function potential. It is a natural generalization of the particle in a box, a canonical example of quantum mechanics, and we present analytic and numerical investigations on this problem. After deriving an exact Volterra-type integral equation, composed of an infinite sum of modes, we show that approximate formulas with the lowestfrequency modes correctly capture the qualitative behavior of the wave function. If we take into account hundreds of modes, our numerical calculation shows that the quantum adiabatic theorem actually gives a very good approximation even if the barrier height diverges within finite time, as long as it is sufficiently longer than the characteristic time scale of the particle. In particular, if the barrier is slowly inserted at an asymmetric position, the particle is localized by the insertion itself, in accordance with a prediction of the adiabatic theorem. On the other hand, when the barrier is inserted quickly, the wave function becomes rugged after the insertion because of the energy transfer to the particle. Regardless of the position of the barrier, the fast insertion leaves the particle unlocalized so that we can obtain meaningful information by a which-side measurement. Our numerical procedure provides a precise way to calculate the wave function throughout the process, from which one can estimate the amount of this information for an arbitrary insertion protocol.

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Dephasing and breakdown of adiabaticity in the splitting of Bose–Einstein condensates

Cited by 11 publications

References 20 publications

Shortcuts to Adiabaticity

Shortcuts to Adiabaticity

Shortcuts to adiabaticity: Fast-forward approach

Particle in a box with a time-dependentδ-functionpotential

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