Supersymmetric Model of a Bose-Einstein Condensate in a 𝓟𝓣-Symmetric Double-delta Trap

Abstract

The most important properties of a Bose-Einstein condensate subject to balanced gain and loss can be modelled by a Gross-Pitaevskii equation with an external PT -symmetric double-delta potential. We study its linear variant with a supersymmetric extension. It is shown that both in the PT -symmetric as well as in the PT -broken phase arbitrary stationary states can be removed in a supersymmetric partner potential without changing the energy eigenvalues of the other state. The characteristic structure of the singular delta potential in the supersymmetry formalism is discussed, and the applicability of the formalism to the nonlinear Gross-Pitaevskii equation is analysed. In the latter case the formalism could be used to remove PT -broken states introducing an instability to the stationary PT -symmetric states.

Simple Models of Three Coupled Pt -Symmetric Wave Guides Allowing for Third-Order Exceptional Points

“…One speaks of broken PT symmetry, and the EP marks the position of the PT symmetry breaking. Since the occurrence of exceptional points is a generic feature of the PT phase transition a large number of works exists for PT -symmetric quantum mechanics [27,[34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49], quantum field theories [50,51], electromagnetic waves [52][53][54][55][56][57][58], and electronic devices [59].…”

State flip at exceptional points in atomic spectra

“…In quantum systems their existence has been proved in atomic [13][14][15][16] or molecular [17] spectra, in the scattering of particles at potential barriers [18], in atom waves [19][20][21][22], and in non-Hermitian Bose-Hubbard models [23]. Their relation to Fano resonances has been pointed out [24][25][26].…”

Population transfer at exceptional points in the spectra of the hydrogen atom in parallel electric and magnetic fields

“…Examples for theoretical treatments of EPs in quantum systems are atomic [5][6][7][8] and molecular [9,10] spectra, scattering of particles at potential barriers [11,12], atom waves [13][14][15][16], open Bose-Hubbard systems [17], unstable lasers [18], resonators [19], and optical waveguides [20,21]. Furthermore there exists experimental evidence of EPs.…”

“…or in SI unitsF EP ≡ 1.633 870 × 10 8 V/m, B EP ≡ 3.396 368 × 10 3 T,(15)which leads to coalescence at the eigenvalue E EP = −2.703 665 × 10 −2 − 4.171 979 × 10 −4 i (16). …”