Quantum random walk of a Bose-Einstein condensate in momentum space

Summy, Gil; Wimberger, Sandro

doi:10.1103/physreva.93.023638

Cited by 36 publications

(59 citation statements)

References 34 publications

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“…These two kinds of features are controllable in the Floquet-driven system by manipulating the external potential. For example, the spatially-nonsymmetric driving potential leads to the directed motion of cold atoms in optical lattice [9][10][11][12]. A double-kicking extension of quantum kicked rotor (QKR) model exhibits topological momentum current [13].…”

Section: Introductionmentioning

confidence: 99%

Directed momentum current induced by the PT -symmetric driving

Zhao

Wang

et al. 2019

Phys. Rev. E

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We investigate the directed momentum current in the quantum kicked rotor model with PT symmetric deriving potential. For the quantum non-resonance case, the values of quasi-energy become to be complex when the strength of imaginary part of the kicking potential exceeds a threshold value, which demonstrates the appearance of the spontaneous PT symmetry breaking. In the vicinity of the transition point, the momentum current exhibits a staircase growth with time. Each platform of the momentum current corresponds to the mean momentum of some eigenstates of the Floquet operator whose imaginary parts of the quasi-energy are significantly large. Above the transition point, the momentum current increases linearly with time. Interestingly, its acceleration rate exhibits a kind of "quantized" increment with the kicking strength. We propose a modified classical acceleration mode of the kicked rotor model to explain such an intriguing phenomenon. Our theoretical prediction is in good agreement with numerical results.

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Section: Introductionmentioning

confidence: 99%

Directed momentum current induced by the PT -symmetric driving

Zhao

Wang

et al. 2019

Phys. Rev. E

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“…where the distribution is presented for a one dimensional cavity (d · E(x) = Ω cos kx) at a time t = 80Ω −1 , long before the Doppler shift becomes comparable to Ω. The two-peaked distribution is characteristic of the quantum random walk as explored theoretically for optical [51,52] and cold atom systems [53]. The situation is richer when more spatial dimensions are considered.…”

Section: A Dynamics: Which-path Informationmentioning

confidence: 99%

Masked states of an atom coupled to a standing-wave cavity mode

Gutiérrez-Jáuregui

2020

Phys. Rev. A

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The form of the eigenstates of an atom coupled to a cavity mode displaying a three dimensional periodic profile are obtained. It is shown that the quantized motion leads to degenerate states where the atomic degrees of freedom are masked, that is, upon detection of one component of this composite system the others remain in an entangled state. When the system is extended to include drive and dissipation it is found to undergo a dissipative quantum phase transition at a critical drive amplitude. Unlike other phase transitions reported in the literature, the degeneracy prepares the system in a superposition of incompatible states upon detection of the electromagnetic field. Probing the field hints at an order above the transition point that, due to state masking, allows for atomic coherence to survive at long times. *

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“…Because of these properties, different classes of QWs have been explored in the past decade, including walks with multiple [20] or decoherent coins [21], aperiodic walks [22], walks in two and more dimensions [23] or with multiple walkers [24]. Moreover, the concept of QWs have been applied to position-dependent walks [25], to time-dependent walks that remember their history [26][27][28][29] as well as to (so-called) spinor Bose-Einstein condensate [30,31].…”

Section: Introductionmentioning

confidence: 99%

Controlling quantum random walk with a step-dependent coin

Panahiyan

Fritzsche

2018

New J. Phys.

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We report on the possibility of controlling quantum random walks (QWs) with a step-dependent coin (SDC). The coin is characterized by a (single) rotation angle. Considering different rotation angles, one can find diverse probability distributions for this walk including: complete localization, Gaussian and asymmetric likes. In addition, we explore the entropy of walk in two contexts; for probability density distributions over position space and walkerʼs internal degrees of freedom space (coin space). We show that entropy of position space can decrease for a SDC with the step-number, quite in contrast to a walk with step-independent coin (SIC). For entropy of coin space, a damped oscillation is found for walk with SIC while for a SDC case, the behavior of entropy depends on rotation angle. In general, we demonstrate that quantum walks with simple initiatives may exhibit a quite complex and varying behavior if SDCs are applied. This provides the possibility of controlling QW with a SDC.

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Quantum random walk of a Bose-Einstein condensate in momentum space

Cited by 36 publications

References 34 publications

Directed momentum current induced by the PT -symmetric driving

Directed momentum current induced by the PT -symmetric driving

Masked states of an atom coupled to a standing-wave cavity mode

Controlling quantum random walk with a step-dependent coin

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