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arXiv:2204.01878 · Physical Review Research

Core structure of static ferrodark solitons in a spin-1 Bose-Einstein condensate

Xiaoquan Yu, P. B. Blakie

Published Jul 18, 2022• 4 citations
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Abstract

We develop an analytical description of static ferrodark solitons, the ${\mathbb{Z}}_{2}$ topological defects in the magnetic order, in the easy-plane phase of ferromagnetic spin-1 Bose-Einstein condensates. We find that the type-I ferrodark soliton has a single width while the type-II ferrodark soliton exhibits two characteristic length scales. The proposed Ans\"atze show excellent agreement with numerical results. Spin-singlet amplitudes, nematic tensor densities, and nematic currents of ferrodark solitons are also discussed. The ${\mathbb{Z}}_{2}$ topological defects in the mass superfluid order, dark-dark-dark vector solitons, are obtained exactly in the parameter regime where exact ferrodark solitons exist. The dark-dark-dark vector soliton has higher excitation energy than ferrodark solitons.

DOI
10.1103/physrevresearch.4.033056

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We develop an analytical description of static ferrodark solitons, the Z2{\mathbb{Z}}_{2}Z2​ topological defects in the magnetic order, in the easy-plane phase of ferromagnetic spin-1 Bose-Einstein condensates. We find that the type-I ferrodark soliton has a single width while the type-II ferrodark soliton exhibits two characteristic length scales. The proposed Ans"atze show excellent agreement with numerical results. Spin-singlet amplitudes, nematic tensor densities, and nematic currents of ferrodark solitons are also discussed. The Z2{\mathbb{Z}}_{2}Z2​ topological defects in the mass superfluid order, dark-dark-dark vector solitons, are obtained exactly in the parameter regime where exact ferrodark solitons exist. The dark-dark-dark vector soliton has higher excitation energy than ferrodark solitons.
Exact propagating topological solitons are found in the easy-plane phase of ferromagnetic spin-1 Bose-Einstein condensates, manifesting themselves as kinks in the transverse magnetization. Propagation is only possible when the symmetry-breaking longitudinal magnetic field is applied. Such solitons have two types: a low energy branch with positive inertial mass and a higher energy branch with negative inertial mass. Both types become identical at the maximum speed, a new speed bound that is different from speed limits set by the elementary excitations. The physical mass, which accounts for the number density dip, is negative for both types. In a finite one-dimensional system subject to a linear potential, the soliton undergoes oscillations caused by transitions between the two types occurring at the maximum speed.
Exact solutions of magnetic field-driven propagating topological solitons are found in the easy-plane phase of ferromagnetic spin-1 Bose-Einstein condensates, manifesting themselves as dark-soliton-like magnetic domain walls. Such solitons have two types: a low energy solution with positive inertial mass and a higher energy solution with negative inertial mass. Both types become identical at the maximum speed, a new speed bound that is different from speed limits set by the elementary excitations. The physical mass, which accounts for the number density dip, is negative for both types. In a finite one-dimensional system subject to a linear potential, the soliton undergoes oscillations, and transitions between the two types occurring at the maximum speed.
Spinor Bose-Einstein condensates exhibit both superfluid and magnetic order, and accommodate phases with rich symmetry properties and topological defects. Transitions between these phases can be induced by tuning external fields. In this thesis we explore the dynamics of order formation in a quasi-2D spin-1 ferromagnetic condensate following a quench from an unmagnetised phase to one of three ferromagnetic phases. The ferromagnetic phases exhibit distinct symmetry properties (easy-plane, easy-axis or isotropic) and support distinct topological defects. In each phase we observe scale invariant ordering and identify the relevant topological defect affecting the order parameter growth. We find that each phase is characterised by a distinct dynamic critical exponent. In the easy-plane phase we identify a persistent turbulent cascade that affects spin ordering long after all topological defects have annihilated. In addition to our exploration of phase ordering dynamics, we study a microscopic model of spin vortex dynamics in the easy-plane phase. Our work provides a comprehensive theoretical study of phase ordering in a conservative system, provides a thorough foundation for studies of phase ordering in antiferromagnetic and higher spin condensates, and offers prospects for further research into fundamental questions regarding the ordering properties of spin systems. Our work is pertinent to current experiments, which have explored the initial stages of phase ordering in both ferromagnetic and antiferromagnetic spin-1 condensates.
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.
We study collisions between a ferrodark soliton (FDS) and an antiFDS (Z2\mathbb{Z}_2Z2​ kinks in the spin order) in the easy-plane phase of spin-1 Bose-Einstein condensates (BECs). For a type-I pair (type-I FDS-antiFDS pair) at low incoming velocities, the pair annihilates followed by the formation of an extremely long-lived dissipative breather on a stable background, a spatially localized wave packet with out-of-phase oscillating magnetization and mass superfluid densities. Periodic emissions of spin and density waves cause breather energy dissipation and we find that the breather energy decays logarithmically in time. When the incoming velocity is larger than a critical velocity at which a stationary FDS-antiFDS pair forms, a pair with finite separating velocity is reproduced. When approaching the critical velocity from below, we find that the lifetime of the stationary type-I pair shows a power-law divergence, resembling a critical behavior. In contrast, a type-II pair (type-II FDS-antiFDS pair) never annihilates and only exhibits reflection. For collisions of a mixed type FDS-antiFDS pair, as Z2\mathbb{Z}_2Z2​ kinks in the spin order, reflection occurs in the topological structure of the magnetization while the mass superfluid density profiles pass through each other, manifesting spin-mass separation.