Realizing<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="script">PT</mml:mi></mml:math>-symmetric non-Hermiticity with ultracold atoms and Hermitian multiwell potentials

Kreibich, Manuel; Main, Jörg; Cartarius, Holger; Wunner, Günter

doi:10.1103/physreva.90.033630

Cited by 64 publications

(66 citation statements)

References 23 publications

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“…A unique property of PT symmetric quantum systems is a spontaneous transition that is the real energy eigenvalues become to be complex * zwlphys@aliyun.com † wangjz@ustc.edu.cn ‡ pqtong@njnu.edu.cn when the strength of the imaginary part of the complex potential exceeds a threshold value. Interestingly, the experimental progress has realized the ultracold atoms in complex optics lattices [23][24][25][26][27][28][29], which opens the opportunity for investigating the transport behavior in the PT symmetric potential. Previous studies on wavepackets dynamics of these system show that, with the PT symmetry being broken, the energy band merging leads to peculiar transport behavior of optic wave and matter wave, such as double refraction, nonreciprocal diffraction, bifurcation, and many others [30,31].…”

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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“…The approach provides an alternative to that suggested in Ref. [51,52] where the PTsymmetric double-well was considered to be embedded in a four-well structure. The results presented here are very encouraging since they demonstrate the applicability of the approach.…”

Section: Discussion and Outlookmentioning

confidence: 99%

Coupling approach for the realization of aPT-symmetric potential for a Bose-Einstein condensate in a double well

et al. 2014

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We show how non-Hermitian potentials used to describe probability gain and loss in effective theories of open quantum systems can be achieved by a coupling of the system to an environment. We do this by coupling a Bose-Einstein condensate (BEC) trapped in an attractive double-δ potential to a condensate fraction outside the double well. We investigate which requirements have to be imposed on possible environments with a linear coupling to the system. This information is used to determine an environment required for stationary states of the BEC. To investigate the stability of the system we use fully numerical simulations of the dynamics. It turns out that the approach is viable and possible setups for the realization of a PT -symmetric potential for a BEC are accessible. Vulnerabilities of the whole system to small perturbations can be attributed to the singular character of the simplified δ-shaped potential used in our model.

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“…This behaviour already arose in investigations concerning the MF properties of the four-well system of Kreibich et al [21], which was the reason for introducing an additional time-dependent degree of freedom d(t). This additional degree of freedom can lead to several difficulties and different possibilities for choosing d(t) were already investigated [23].…”

Section: Time Dependence Of Parametersmentioning

confidence: 99%

Using mixed many-body particle states to generate exact $\mathcal{PT} $ -symmetry in a time-dependent four-well system

Mathea

Dast

Dizdarevic

et al. 2018

J. Phys. A: Math. Theor.

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Bose-Einstein condensates with balanced gain and loss in a double-well potential have been shown to exhibit PT -symmetric states. As proposed by Kreibich et al [Phys. Rev. A 87, 051601(R) (2013)], in the mean-field limit the dynamical behaviour of this system, especially that of the PT -symmetric states, can be simulated by embedding it into a Hermitian four-well system with time-dependent parameters. In this paper we go beyond the mean-field approximation and investigate manybody effects in this system, which are in lowest order described by the single-particle density matrix. The conditions for PT symmetry in the single-particle density matrix cannot be completely fulfilled by using pure initial states. Here we show that it is mathematically possible to achieve exact PT symmetry in the four-well many-body system in the sense of the dynamical behaviour of the single-particle density matrix. In contrast to previous work, for this purpose, we use mixed initial states fulfilling certain constraints and use them to calculate the dynamics.

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RealizingPT-symmetric non-Hermiticity with ultracold atoms and Hermitian multiwell potentials

Cited by 64 publications

References 23 publications

Directed momentum current induced by the PT -symmetric driving

Directed momentum current induced by the PT -symmetric driving

Coupling approach for the realization of aPT-symmetric potential for a Bose-Einstein condensate in a double well

Using mixed many-body particle states to generate exact $\mathcal{PT} $ -symmetry in a time-dependent four-well system

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