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arXiv:1801.00590 · Journal of Physics B Atomic Molecular and Optical Physics

Continuous-wave solutions and modulational instability in spinor condensates of positronium

Ishfaq Ahmad Bhat, Thudiyangal Mithun, Boris A. Malomed, K Porsezian

Published Dec 21, 2017• 2 citations
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Abstract

Abstract We obtain general continuous-wave (CW) solutions in the model of a spinor positronium condensate in the absence of magnetic field. The CW solutions with both in-phase ( n = 0) and out-of-phase ( n = 1) spin components exist, with their ranges limited by the total particle density, ρ . In the limit of negligible population exchange between the spin components, the CW solutions are found to be stable or unstable, depending on the particle density of the para-positronium. Ortho-positronium, in the F = 1 spinor state, forms a ferromagnetic condensate with stable in-phase CW solutions only. Subsequent examination of the modulational instability is carried out both in the limit case of identical wavenumbers in the spin components, Δ k ≡ k 1 − k − 1 = 0 , and in the more general case of Δ k ≠ 0 too. The CW solutions with n = 0 and 1 solutions, which are stable in the case of Δ k = 0 , are unstable for Δ k ≠ 0 , for the natural repulsive sign of the nonlinearities. The total particle density, ρ , in the limit of Δ k = 0 is found to have a significant role in the stability of the condensate, which is determined by the sign of the self-interaction nonlinearity.

DOI
10.1088/1361-6455/aaa399

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Abstract We obtain general continuous-wave (CW) solutions in the model of a spinor positronium condensate in the absence of magnetic field. The CW solutions with both in-phase ( n = 0) and out-of-phase ( n = 1) spin components exist, with their ranges limited by the total particle density, ρ . In the limit of negligible population exchange between the spin components, the CW solutions are found to be stable or unstable, depending on the particle density of the para-positronium. Ortho-positronium, in the F = 1 spinor state, forms a ferromagnetic condensate with stable in-phase CW solutions only. Subsequent examination of the modulational instability is carried out both in the limit case of identical wavenumbers in the spin components, Δ k ≡ k 1 − k − 1 = 0 , and in the more general case of Δ k ≠ 0 too. The CW solutions with n = 0 and 1 solutions, which are stable in the case of Δ k = 0 , are unstable for Δ k ≠ 0 , for the natural repulsive sign of the nonlinearities. The total particle density, ρ , in the limit of Δ k = 0 is found to have a significant role in the stability of the condensate, which is determined by the sign of the self-interaction nonlinearity.
We analyze sound waves (phonons, i.e. Bogoliubov excitations) propagating on continuous-wave (cw) solutions of repulsive F=1F=1F=1 spinor Bose-Einstein condensates (BECs) such as 23Na^{23}\mathrm{Na}23Na (which is antiferromagnetic or polar) and 87Rb^{87}\mathrm{Rb}87Rb (which is ferromagnetic). Zeeman splitting by a uniform magnetic field is included. All cw solutions to ferromagnetic BECs with vanishing MF=0{M}_{F}=0MF​=0 particle density and nonzero components in both ${M}_{F}=\ifmmode\pm\else\textpm\fi{}1$ fields are subject to modulational instability (MI). Modulational instability increases with increasing particle density. Modulational instability also increases with differences in the components' wave numbers; this effect is larger at lower densities but becomes insignificant at higher particle densities. Continuous-wave solutions to antiferromagnetic (polar) BECs with vanishing MF=0{M}_{F}=0MF​=0 particle density and nonzero components in both ${M}_{F}=\ifmmode\pm\else\textpm\fi{}1$ fields do not suffer MI if the wave numbers of the components are the same. If there is a wave-number difference, MI initially increases with increasing particle density and then peaks before dropping to zero beyond a given particle density. The cw solutions with particles in both ${M}_{F}=\ifmmode\pm\else\textpm\fi{}1$ components and nonvanishing MF=0{M}_{F}=0MF​=0 components do not have MI if the wave numbers of the components are the same, but do exhibit MI when the wave numbers are different. Direct numerical simulations of a continuous wave with weak white noise confirm that weak noise grows fastest at wave numbers with the largest MI and show some of the results beyond small-amplitude perturbations. Phonon dispersion curves are computed numerically; we find analytic solutions for the phonon dispersion in a variety of limiting cases.
We find analytic continuous-wave (cw) solutions for spinor Bose-Einstein condensates in a magnetic field that are more general than other published solutions. For particles with spin F=1F=1F=1 in a homogeneous one-dimensional trap, there exist cw states in which the chemical potential and wave vectors of the different spin components are different from each other. We include linear and quadratic Zeeman splitting. Linear Zeeman splitting, if the magnetic field is constant and uniform, can be mathematically eliminated by a gauge transformation, but quadratic Zeeman effects modify the cw solutions in a way similar to nonzero differences in the wave numbers between the different spin states. The solutions are stable fixed points within the continuous-wave framework, and the coherent spin mixing frequencies are obtained.
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Abstract We present the phase diagram, the underlying stability and magnetic properties as well as the dynamics of nonlinear solitary wave excitations arising in the distinct phases of a harmonically confined spinor F = 1 Bose–Einstein condensate. Particularly, it is found that nonlinear excitations in the form of dark–dark–bright solitons exist in the antiferromagnetic and in the easy-axis phase of a spinor gas, being generally unstable in the former while possessing stability intervals in the latter phase. Dark–bright–bright solitons can be realized in the polar and the easy-plane phases as unstable and stable configurations respectively; the latter phase can also feature stable dark–dark–dark solitons. Importantly, the persistence of these types of states upon transitioning, by means of tuning the quadratic Zeeman coefficient from one phase to the other is unravelled. Additionally, the spin-mixing dynamics of stable and unstable matter waves is analyzed, revealing among others the coherent evolution of magnetic dark–bright, nematic dark–bright–bright and dark–dark–dark solitons. Moreover, for the unstable cases unmagnetized or magnetic droplet-like configurations and spin-waves consisting of regular and magnetic solitons are seen to dynamically emerge remaining thereafter robust while propagating for extremely large evolution times. Interestingly, exposing spinorial solitons to finite temperatures, their anti-damping in trap oscillation is showcased. It is found that the latter is suppressed for stronger bright soliton component ‘fillings’. Our investigations pave the wave for a systematic production and analysis involving spin transfer processes of such waveforms which have been recently realized in ultracold experiments.
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