Fast-forward problem in quantum mechanics

Masuda, S.; Nakamura, Katsuhiro

doi:10.1103/physreva.78.062108

Cited by 118 publications

(187 citation statements)

References 11 publications

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“…We shall now reformulate the above results to conect them with the FF approach in [19,34]. The notation is made close but not necessarily in full agreement with [19,34].…”

Section: Connection With the Fast-forward Approachmentioning

confidence: 99%

“…Based on some earlier results [34], the fast-forward formalism for adiabatic dynamics and several application examples were worked out in [19,28] by Masuda and Nakamura for the Gross-Pitaevskii (GP) or the corresponding Schrödinger equations. The objective of the method is to accelerate a "standard" system subjected to a slow variation of external parameters.…”

Section: Introductionmentioning

confidence: 99%

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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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“…We shall now reformulate the above results to conect them with the FF approach in [19,34]. The notation is made close but not necessarily in full agreement with [19,34].…”

Section: Connection With the Fast-forward Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Shortcuts to adiabaticity: Fast-forward approach

et al. 2012

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“…(9), when the later are expressed in the basis {|β(t ′ ) }. The condition for the sudden approximation to hold becomes…”

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confidence: 99%

“…Specifically we shall use a simple inversion method: a streamlined version [6] of the fast-forward technique of Masuda and Nakamura [7] applied to GrossPitaievski (GP) or Schrödinger equations. We have previously found some obstacles to apply the invariantsbased method (at least using quadratic-in momentum invariants [6]) and the transitionless-driving algorythm [8] (because of difficulties to implement in practice the counter-diabatic terms).Fast-forward approach.-The fast-forward method [6,7,9] may be used to generate external potentials to drive the matter wave from the initial single well to a final symmetric double well. The starting point of the streamlined version in [6] is the 3D time-dependent GP equation…”

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confidence: 99%

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Engineering fast and stable splitting of matter waves

et al. 2013

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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. PACS numbers:Introduction.-The splitting of a wavefunction is an important operation for matter wave interferometry [1][2][3][4]. It is a peculiar one though, as adiabatic following, rather than being robust, is intrinsically unstable with respect to a small external potential asymmetry [5]. The ground-state wavefunction "collapses" into the slightly lower well so that a very slow trap potential bifurcation in fact fails to split the wave except for perfectly symmetrical potentials. An arbitrarily fast bifurcation may remedy this but at the price of a strong excitation which is also undesired. We propose here a way out to these problems by using shortcuts to adiabaticity that speed up the adiabatic process along a non-adiabatic route. The wave splitting via shortcuts avoids the final excitation and turns out to be signifficantly more stable than the adiabatic following with respect to the asymmetric perturbation. Specifically we shall use a simple inversion method: a streamlined version [6] of the fast-forward technique of Masuda and Nakamura [7] applied to GrossPitaievski (GP) or Schrödinger equations. We have previously found some obstacles to apply the invariantsbased method (at least using quadratic-in momentum invariants [6]) and the transitionless-driving algorythm [8] (because of difficulties to implement in practice the counter-diabatic terms).Fast-forward approach.-The fast-forward method [6,7,9] may be used to generate external potentials to drive the matter wave from the initial single well to a final symmetric double well. The starting point of the streamlined version in [6] is the 3D time-dependent GP equation

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Controlling Quantum Dynamics with Assisted Adiabatic Processes

Masuda

Rice

2016

Advances in Chemical Physics

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Fast-forward problem in quantum mechanics

Cited by 118 publications

References 11 publications

Shortcuts to adiabaticity: Fast-forward approach

Shortcuts to adiabaticity: Fast-forward approach

Engineering fast and stable splitting of matter waves

Controlling Quantum Dynamics with Assisted Adiabatic Processes

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