Vortices in Bose-Einstein condensates with 
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-symmetric gain and loss

Schwarz, Lukas; Cartarius, Holger; Musslimani, Ziad H.; Main, Jörg

doi:10.1103/physreva.95.053613

Cited by 27 publications

(22 citation statements)

References 73 publications

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“…If we assume that the dot is nearly closed, i.e., the interaction between the dot and reservoirs is weak and hence the current is small, we may emulate the system in the following way. Thus, we do away with the reservoirs and replace them by imaginary potentials in the regions of leads (see recent work on interacting Bose-Einstein condensates [34]). Effectively, there will thus be gain and loss in the system, i.e., input and output of particles, as an imaginary potential is used [35].…”

Section: A Model Of An Electron Dotmentioning

confidence: 99%

Spectra, current flow, and wave-function morphology in a modelPT-symmetric quantum dot with external interactions

Tellander

Berggren

2017

Phys. Rev. A

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In this paper we use numerical simulations to study a two-dimensional (2D) quantum dot (cavity) with two leads for passing currents (electrons, photons, etc.) through the system. By introducing an imaginary potential in each lead the system is made symmetric under parity-time inversion (PT symmetric). This system is experimentally realizable in the form of, e.g., quantum dots in low-dimensional semiconductors, optical and electromagnetic cavities, and other classical wave analogs. The computational model introduced here for studying spectra, exceptional points (EPs), wave-function symmetries and morphology, and current flow includes thousands of interacting states. This supplements previous analytic studies of few interacting states by providing more detail and higher resolution. The Hamiltonian describing the system is non-Hermitian; thus, the eigenvalues are, in general, complex. The structure of the wave functions and probability current densities are studied in detail at and in between EPs. The statistics for EPs is evaluated, and reasons for a gradual dynamical crossover are identified.

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Section: A Model Of An Electron Dotmentioning

confidence: 99%

Spectra, current flow, and wave-function morphology in a modelPT-symmetric quantum dot with external interactions

Tellander

Berggren

2017

Phys. Rev. A

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“…One of prominent experimentally demonstrated applications of the PT symmetry in optics is unidirectional transmission of light [39].Other classical waveguiding settings also admit emulation of the PT symmetry, as demonstrated in acoustics [40] and predicted in optomechanical systems [41]. Also predicted were realizations of this symmetry in atomic Bose-Einstein condensates [42], magnetism [43], mechanical chains of coupled pendula [44], and electronic circuits [45] (in the latter case, the prediction was also demonstrated experimentally). In terms of the theoretical analysis, PT -symmetric extensions were also elaborated for 47], Burgers [48], and sine-Gordon [49] equations, as well as in a system combining the PT symmetry with the optical emulation of the spin-orbit coupling [50].While the PT symmetry is a linear property of the system, it may be naturally combined with intrinsic nonlinearity of the medium in which the symmetry is realized, such as the ubiquitous Kerr nonlinearity of optical waveguides.…”

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confidence: 77%

Making the P T $$\mathbb {PT}$$ Symmetry Unbreakable

Lutsky

Luz

Granot

et al. 2018

Springer Tracts in Modern Physics

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It is well known that typical PT -symmetric systems suffer symmetry breaking when the strength of the gain-loss terms, i.e., the coefficient in front of the non-Hermitian part of the underlying Hamiltonian, exceeds a certain critical value. In this article, we present a summary of recently published and newly produced results which demonstrate various possibilities of extending the PT symmetry to arbitrarily large values of the gain-loss coefficient. First, we recapitulate the analysis which demonstrates a possibility of the restoration of the PT symmetry and, moreover, complete avoidance of the breaking in a photonic waveguiding channel of a subwavelength width. The analysis is necessarily based on the system of Maxwell's equations, instead of the usual paraxial approximation. Full elimination of the PT -symmetry-breaking transition is found in a deeply subwavelength region. Next, we review a recently proposed possibility to construct stable one-dimensional (1D) PT -symmetric solitons in a paraxial model with arbitrarily large values of the gain-loss coefficient, provided that the self-trapping of the solitons is induced by self-defocusing cubic nonlinearity, whose local strength grows sufficiently fast from the center to periphery. The model admits a particular analytical solution for the fundamental soliton, and provides full stability for families of fundamental and dipole solitons. It is relevant to stress that this model is nonlinearizable, hence the concept of the PT symmetry in it is also an essentially nonlinear one. Finally, we report new results for unbreakable PT -symmetric solitons in 2D extensions of the 1D model: one with a quasi-1D modulation profile of the local gain-loss coefficient, and another with the fully-2D modulation. These settings admit particular analytical solutions for 2D solitons, while generic soliton families are found in a numerical form. The quasi-1D modulation profile gives rise to a stable family of single-peak 2D solitons, while their dual-peak counterparts tend to be unstable. The soliton stability in the full 2D model is possible if the local gain-loss term is subject to spatial confinement.2 exciton-polariton condensates [36]- [38], and in other physically relevant contexts. In particular, the transitions from unbroken to broken PT symmetry was observed in many experiments. One of prominent experimentally demonstrated applications of the PT symmetry in optics is unidirectional transmission of light [39].Other classical waveguiding settings also admit emulation of the PT symmetry, as demonstrated in acoustics [40] and predicted in optomechanical systems [41]. Also predicted were realizations of this symmetry in atomic Bose-Einstein condensates [42], magnetism [43], mechanical chains of coupled pendula [44], and electronic circuits [45] (in the latter case, the prediction was also demonstrated experimentally). In terms of the theoretical analysis, PT -symmetric extensions were also elaborated for 47], Burgers [48], and sine-Gordon [49] equations, as well as in a system combi...

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“…In these contexts, breaking of the symmetry was observed experimentally too. Emulation of the symmetry was also demonstrated in acoustics 42 and electronic circuits 43 , and predicted in atomic Bose-Einstein condensates 44 , magnetism 45 , and chains of coupled pendula 46 .…”

Section: Introductionmentioning

confidence: 83%

Robust $${\bf{P}}{\bf{T}}$$ symmetry of two-dimensional fundamental and vortex solitons supported by spatially modulated nonlinearity

Luz

Lutsky

Granot

et al. 2019

Sci Rep

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The real spectrum of bound states produced by -symmetric Hamiltonians usually suffers breakup at a critical value of the strength of gain-loss terms, i.e., imaginary part of the complex potential. The breakup essentially impedes the use of -symmetric systems for various applications. On the other hand, it is known that the symmetry can be made unbreakable in a one-dimensional (1D) model with self-defocusing nonlinearity whose strength grows fast enough from the center to periphery. The model is nonlinearizable, i.e., it does not have a linear spectrum, while the (unbreakable) symmetry in it is defined by spectra of continuous families of nonlinear self-trapped states (solitons). Here we report results for a 2D nonlinearizable model whose symmetry remains unbroken for arbitrarily large values of the gain-loss coefficient. Further, we introduce an extended 2D model with the imaginary part of potential ~xy in the Cartesian coordinates. The latter model is not a -symmetric one, but it also supports continuous families of self-trapped states, thus suggesting an extension of the concept of the symmetry. For both models, universal analytical forms are found for nonlinearizable tails of the 2D modes, and full exact solutions are produced for particular solitons, including ones with the unbreakable symmetry, while generic soliton families are found in a numerical form. The -symmetric system gives rise to generic families of stable single- and double-peak 2D solitons (including higher-order radial states of the single-peak solitons), as well as families of stable vortex solitons with m = 1, 2, and 3. In the model with imaginary potential ~xy, families of single- and multi-peak solitons and vortices are stable if the imaginary potential is subject to spatial confinement. In an elliptically deformed version of the latter model, an exact solution is found for vortex solitons with m = 1.

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Vortices in Bose-Einstein condensates with PT -symmetric gain and loss

Cited by 27 publications

References 73 publications

Spectra, current flow, and wave-function morphology in a modelPT-symmetric quantum dot with external interactions

Spectra, current flow, and wave-function morphology in a modelPT-symmetric quantum dot with external interactions

Making the P T $$\mathbb {PT}$$ Symmetry Unbreakable

Robust $${\bf{P}}{\bf{T}}$$ symmetry of two-dimensional fundamental and vortex solitons supported by spatially modulated nonlinearity

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