Solitons in a Hamiltonian $\newcommand{\PT}{\mathcal{ PT}}{\boldsymbol \PT}$ -symmetric coupler

Zezyulin, Dmitry A.

doi:10.1088/1751-8121/aa96f4

Cited by 7 publications

(1 citation statement)

References 43 publications

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“…Non-Hermitian parity-time (PT ) symmetry physics has experienced rapid developments in the last two decades, especially in the field of optics, where the balanced optical gain and loss can be modeled by a PT -symmetric Hamiltonian, and it is found that gain and loss can serve as new engineering tools and also lead to abundant new and unexpected features [34][35][36][37][38]. These great developments inspired the interest in extending cold atom physics from Hermitian to non-Hermitian regime, with the prospect of exploring unidirectional transportation [39], non-Hermitian skin effect [40][41][42][43], soliton [44][45][46], double-well [47][48][49] and Hubbard model [50,51] in open environments, etc. In cold atom systems, controlled atomic loss can be realized by extracting atoms from the atomic gas via atom-light interaction [52]; while the atomic gain is proposed to be realized by injecting atoms into the atomic gas using an atom laser [53].…”

Section: Introductionmentioning

confidence: 99%

Phonon and maxon instability in Bose–Einstein condensates with parity-time symmetric spin–orbit coupling

Qin,

Zhou,

Dong

2023

New J. Phys.

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Parity-time ( P T ) symmetry has drawn great research interest in non-Hermitian physics. Recently, there is an emerging model of P T -symmetric spin–orbit coupling (SOC) which could be realized with spin-1/2 atomic Bose–Einstein condensates (BECs) when the two spin components are respectively subjected to momentum-dependent gain and loss (Qin et al 2022 New J. Phys. 24 063025). In this model, inter-atom interaction has no influence on the P T -symmetric plane waves. Thus, collective excitation playing the role of fingerprint of inter-atom interaction is investigated in this paper. For the phonon excitation, it is shown that the repulsive interaction between atoms in different spin states, which tends to drive the atoms to populate in only one spin component, can break the P T -symmetry, and leads to a phonon instability. Whereas, for the case of the phonon-maxon-roton collective excitation spectrum, the repulsive interaction between atoms in different spin states can lead to a maxon instability, which does not occur in Hermitian BEC systems (dipolar BECs or BECs with Raman induced SOC). Simulation of the time evolution of the plane wave solution against small noise shows that the maxon instability can result in the formation of a supersolid-like stripe pattern at the initial stage, but the non-Hermitian nature of the system finally destroys the pattern. The phase diagram of stability shows that the Rabi coupling and repulsive interaction between the atoms in the same spin state can stabilize the system.

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Section: Introductionmentioning

confidence: 99%

Phonon and maxon instability in Bose–Einstein condensates with parity-time symmetric spin–orbit coupling

Qin,

Zhou,

Dong

2023

New J. Phys.

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Coupled Nonlinear Schrödinger Equations with Gain and Loss: Modeling P T $$\mathcal {PT}$$ Symmetry

Konotop

2018

Springer Tracts in Modern Physics

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One-dimensional gap solitons in quintic and cubic–quintic fractional nonlinear Schrödinger equations with a periodically modulated linear potential

Zeng

2019

Nonlinear Dyn

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Competing nonlinearities, such as the cubic (Kerr) and quintic nonlinear terms whose strengths are of opposite signs (the coefficients in front of the nonlinearities), exist in various physical media (in particular, in optical and matter-wave media). A benign competition between self-focusing cubic and self-defocusing quintic nonlinear nonlinearities (known as cubic-quintic model) plays an important role in creating and stabilizing the self-trapping of D-dimensional localized structures, in the contexts of standard nonlinear Schrödinger equation. We incorporate an external periodic potential (linear lattice) into this model and extend it to the space-fractional scenario that begins to surface in very recent years-the nonlinear fractional Schrödinger equation (NLFSE), therefore obtaining the cubic-quintic or the purely quintic NLFSE, and investigate the propagation and stability properties of self-trapped modes therein. Two types of one-dimensional localized gap modes are found, including the fundamental and dipole-mode gap solitons. Employing the techniques based on the linear-stability analysis and direct numerical simulations, we get the stability regions of all the localized modes; and particularly, the anti-Vakhitov-Kolokolov criterion applies for the stable portions of soliton families generated in the frameworks of quintic-only nonlinearity and competing cubic-quintic nonlinear terms.

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Solitons in a Hamiltonian $\newcommand{\PT}{\mathcal{ PT}}{\boldsymbol \PT}$ -symmetric coupler

Cited by 7 publications

References 43 publications

Phonon and maxon instability in Bose–Einstein condensates with parity-time symmetric spin–orbit coupling

Phonon and maxon instability in Bose–Einstein condensates with parity-time symmetric spin–orbit coupling

Coupled Nonlinear Schrödinger Equations with Gain and Loss: Modeling P T $$\mathcal {PT}$$ Symmetry

One-dimensional gap solitons in quintic and cubic–quintic fractional nonlinear Schrödinger equations with a periodically modulated linear potential

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