Shortcuts to Adiabaticity for Optical Beam Propagation in Nonlinear Gradient Refractive-Index Media

Kong, Qian; Ying, Huimin; Chen, Xi

doi:10.3390/e22060673

Cited by 8 publications

(4 citation statements)

References 60 publications

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“…Furthermore, the smooth regularization is further used to smooth out the controller in terms of the shooting method. Though we consider quasi-1D soliton expansion as an example, our results presented here can be easily extended to soliton decompression or compression [29,49], by varying either the trap frequency or the interaction strength or both [13,32], and other nonlinear optical systems [53], by connecting to other methods of enhanced STA working for previously intractable Hamiltonians as well [54]. We find that the exper-imental relevance can benefit from our smooth time-optimal STA protocols by suppressing the heating and atom losses.…”

Section: Discussionmentioning

confidence: 99%

Time-optimal variational control of a bright matter-wave soliton

Huang

Zhang

et al. 2020

Phys. Rev. A

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Motivated by recent experiments, we present the time-optimal variational control of a bright matter-wave soliton trapped in the harmonic trap by manipulating the atomic interaction through Feshbach resonances. More specifically, we first apply the variational technique to derive the motion equation for capturing the soliton's shape and, second, combine an inverse-engineering method with optimal control theory to design the scatter length for implementing time-optimal decompression. Since the minimum-time solution is of the "bang-bang" type, the smooth regularization is further adopted to smooth the on-off controller out, thus avoiding the heating and atom loss induced from the magnetic field ramp across a Feshbach resonance, in practice.

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Section: Discussionmentioning

confidence: 99%

Time-optimal variational control of a bright matter-wave soliton

Huang

Zhang

et al. 2020

Phys. Rev. A

Self Cite

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show abstract

“…Furthermore, the smooth regularization is further used to smooth out the controller in terms of shooting method. Though we consider quasi-1D soliton expansion as an example, our results presented here can be easily extended to soliton decompression/compression [28,48], by varying either the trap frequency or the interaction strength or both [11,31], and other nonlinear optical systems [52], by connecting to other method of enhanced STA working for previously intractable Hamiltonians as well [53]. We find that the experimental relevance can benefit from our smooth time-optimal STA protocols, by suppressing the heating and atom losses.…”

Section: Discussionmentioning

confidence: 99%

Time-optimal variational control of bright matter-wave soliton

Huang,

Zhang,

et al. 2020

Preprint

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Motivated by recent experiments, we present the time-optimal variational control of bright matter-wave soliton trapped in a quasi-one-dimensional harmonic trap by manipulating the atomic attraction through Feshbach resonances. More specially, we first apply a time-dependent variational method to derive the motion equation for capturing the soliton's shape, and secondly combine inverse engineering with optimal control theory to design the atomic interaction for implementing time-optimal decompression. Since the time-optimal solution is of bang-bang type, the smooth regularization is further adopted to smooth the on-off controller out, thus avoiding the heating and atom loss, induced from magnetic field ramp across a Feshbach resonance in practice.

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“…In linear systems, STAs can preserve the optimality of the quantum speed in a system which evolves at the quantum speed limit 40 . The extension of STAs to nonlinear quantum systems is at the incipient stage [41][42][43][44][45][46] and raises the question of the influence of non linearities on the quantum speed limit 47 . In this paper, we propose to accelerate classical and quantum synchronization, an inherently non-linear and non-perturbative phenomenon 1 .…”

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confidence: 99%

Shortcut to synchronization in classical and quantum systems

Impens

Guéry-Odelin

2023

Sci Rep

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Synchronization is a major concept in nonlinear physics. In a large number of systems, it is observed at long times for a sinusoidal excitation. In this paper, we design a transiently non-sinusoidal driving to reach the synchronization regime more quickly. We exemplify an inverse engineering method to solve this issue on the classical Van der Pol oscillator. This approach cannot be directly transposed to the quantum case as the system is no longer point-like in phase space. We explain how to adapt our method by an iterative procedure to account for the finite-size quantum distribution in phase space. We show that the resulting driving yields a density matrix close to the synchronized one according to the trace distance. Our method provides an example of fast control of a nonlinear quantum system, and raises the question of the quantum speed limit concept in the presence of nonlinearities.

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Shortcuts to Adiabaticity for Optical Beam Propagation in Nonlinear Gradient Refractive-Index Media

Cited by 8 publications

References 60 publications

Time-optimal variational control of a bright matter-wave soliton

Time-optimal variational control of a bright matter-wave soliton

Time-optimal variational control of bright matter-wave soliton

Shortcut to synchronization in classical and quantum systems

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