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Stability and dynamics across magnetic phases of nonlinear excitations in two-dimensional spinor Bose-Einstein condensates.

G. C. Katsimiga, S. I. Mistakidis, K. Mukherjee, P. G. Kevrekidis, Peter Schmelcher

Published Sep 15, 2021• 0 citations
OpenAlex

Abstract

The static properties, i.e., existence and stability, as well as the quench-induced dynamics of nonlinear excitations of the vortex-bright type appearing in two-dimensional harmonically confined spin-1 Bose-Einstein condensates are investigated. Linearly stable vortex-bright-vortex and bright-vortex-bright solutions arise in both antiferromagnetic and ferromagnetic spinor gases upon quadratic Zeeman energy shift variations. The precessional motion of such coherent structures is subsequently monitored dynamically. Deformations of the above configurations across the relevant transitions are exposed and discussed in detail. It is further found that stationary states involving highly quantized vortices can be realized in both settings. Spatial elongations, precessional motion and spiraling of the nonlinear excitations when exposed to finite temperatures and upon crossing the distinct phase boundaries, via quenching of the quadratic Zeeman coefficient, are unveiled. Spin-mixing processes triggered by the quench lead, among others, to changes in the waveform of the ensuing configurations. Our findings reveal an interplay between pattern formation and spin-mixing processes being accessible in contemporary cold atom experiments.

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Stability and dynamics across magnetic phases of vortex-bright type excitations in spinor Bose-Einstein condensates

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The static properties, i.e., existence and stability, as well as the quench-induced dynamics of vortex-bright type excitations in two-dimensional harmonically confined spin-1 Bose-Einstein condensates are investigated. Linearly stable vortex-bright-vortex and bright-vortex-bright solutions arise in both antiferromagnetic and ferromagnetic spinor gases upon quadratic Zeeman energy shift variations. Their deformations across the relevant transitions are exposed and discussed in detail, evincing also that emergent instabilities can lead to pattern formation. Spatial elongations, precessional motion, and spiraling of the nonlinear excitations when exposed to finite temperatures and upon crossing the distinct phase boundaries, via quenching of the quadratic Zeeman coefficient, are unveiled. Spin-mixing processes triggered by the quench lead, among others, to changes in the waveform of the ensuing configurations. Our findings reveal an interplay between pattern formation and spin-mixing processes accessible in contemporary cold atom experiments.

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Phase diagram, stability and magnetic properties of nonlinear excitations in spinor Bose–Einstein condensates

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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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This thesis discusses non-equilibrium phenomena in antiferromagnetic spinor quantum gases. We investigate, both experimentally and theoretically, the quench dynamics of antiferromagnetic spinor Bose-Einstein condensates in the vicinity of a zero temperature quantum phase transition. A microwave dressing field was used as a novel tool to access the polar to antiferrmagnetic quantum phase transition at the quadratic Zeeman shift, q=0. By performing instantaneous quenches across the phase transition,a dynamical instability was induced in the atomic cloud. This lead to pair formation and rapid amplification of spin +/-1 atoms through spin-mixing collisions. The spatial ordering kinetics in the vicinity of the phase transition was quantified by performing the local spin measurement. The coarsening dynamics was observed for the instability for q < 0, as it nucleated small domains that grew to the axial size of the cloud. Rich nonequilibrium behavior was observed in the form of growth and decay of both nematic and magnetic spin waves, following the quench. The spatiotemporal evolution was characterized through two particle correlations between atoms in each pair of spin states, which revealed dramatic differences between the dynamics of the spin correlations and those of the spin populations. \nFinally, we demonstrate the remarkable influence of linear Zeeman term on non-equilibrium dynamics of spinor Bose-Einstein condensates. We show that contrary to prior understanding magnetic field gradient actually suppresses the tendency of spin 0 state to separate into spin +/-1 state. This reconciles the Bogoliubov discrepancies and leads to a dramatic sharpening of the transition point, resulting in a resolution at the 1 Hz level. Our results point to the use of dynamics, rather than equilibrium quantities for high precision measurements of phase transitions in quantum gases.

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Bose-Einstein condensation (BEC) is a phenomenon in which identical bosons occupy the same quantum state below a certain critical temperature. A hallmark of BEC is the coherence between particles every particle shares the same quantum wavefunction and phase. This coherence has been demonstrated for the external (motional) degrees of freedom of the atomic condensates by interfering two condensates. In this thesis, the coherence is shown to extend to the internal spin degrees of freedom of a spin-1 Bose gas evidenced by the observed coherent and reversible spin-changing collisions. The observed coherent dynamics are analogous to Josephson oscillations in weakly connected superconductors and represent a type of matter-wave four-wave mixing. Control of the coherent evolution of the system using magnetic fields is also demonstrated. The studies on spinor condensates begin by creating spinor condensates directly using all-optical approaches that were first developed in our laboratory. All-optical formation of Bose-Einstein condensates (BEC) in 1D optical lattice and single focus trap geometries are developed and presented. These techniques offer considerable flexibility and speed compared to magnetic trap approaches, and the trapping potential can be essentially spin-independent and are ideally suited for studying spinor condensates. Using condensates with well-defined initial non-equilibrium spin configuration, spin mixing of F = 1 and F = 2 spinor condensates of rubidium-87 atoms confined in an optical trap is observed. The equilibrium spin configuration in the F = 1 manifold confirms that 87Rb is ferromagnetic. The coherent spinor dynamics are demonstrated by initiating spin mixing deterministically with a non-stationary spin population configuration. Finally, the interplay between the coherent spin mixing and spatial dynamics in spin-1 condensates with ferromagnetic interactions is investigated.

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In this thesis we investigate the static, dynamic, and thermodynamic properties\nof atomic spin-1 Bose gases in external magnetic fields. At low magnetic fields\nthe properties of single-component, or scalar condensates, are essentially\nunaffected but can become significantly altered for spinor Bose condensates as\nshown by our studies.\n\nWe first study the Bose-Einstein condensation of trapped spin-1 Bose gases by\nemploying the Hartree-Fock approximation and the two-fluid model within a mean\nfield approximation. Our detailed investigation reveals that the\nferromagnetically interacting spin-1 condensates exhibit triple condensations\nwhile the antiferromagnetically interacting ones show double condensations.\n\nThe ground state structure of homogeneous and trapped spin-1 Bose condensates\nwith ferromagnetic and antiferromagnetic interactions at zero temperature in\nmagnetic fields are then investigated systematically. We further illuminate the\nimportant effect of quadratic Zeeman shift which causes a preferred occupation\nof the $|m_F=0\nangle$ state through spin exchange collisions, $2|m_F=0\nangle\nleftrightarrow |m_F=1\nangle + |m_F=-1\nangle$.\n\nWe also present detailed studies of the off-equilibrium coherent dynamics of\nspin-1 Bose condensates in magnetic fields within the single spatial mode\napproximation. Dynamical instabilities of the off-equilibrium oscillations are\nshown to be responsible for the formation of multiple domains as recently\nobserved in several $^{87}$Rb experiments.\n\nFinally, we discuss briefly excited condensate states, or soliton-like states,\nin cigar-shaped spin-1 Bose condensates with an effective quasi-1D description,\nusing the developed nonpolynomial Schr"odinger equation.

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Properties of a nematic spin vortex in an antiferromagnetic spin-1 Bose-Einstein condensate

Andrew P. C. Underwood, D. Baillie, P. B. Blakie +1 more

A spin-1 condensate with antiferromagnetic interactions supports nematic spin vortices in the easy-plane polar phase. These vortices have a $2\ensuremath{\pi}$ winding of the nematic director with a core structure that depends on the quadratic Zeeman energy. We characterize the properties of the nematic spin vortex in a uniform quasi-two-dimensional system. We also obtain the vortex excitation spectrum and use it to quantify its stability against dissociating into two half-quantum vortices, finding a parameter regime where the nematic spin vortex is dynamically stable. These results are supported by full dynamical simulations.

arXiv:2005.09203•Physical Review A•Aug 26, 2020•10 citations
The static properties, i.e., existence and stability, as well as the quench-induced dynamics of nonlinear excitations of the vortex-bright type appearing in two-dimensional harmonically confined spin-1 Bose-Einstein condensates are investigated. Linearly stable vortex-bright-vortex and bright-vortex-bright solutions arise in both antiferromagnetic and ferromagnetic spinor gases upon quadratic Zeeman energy shift variations. The precessional motion of such coherent structures is subsequently monitored dynamically. Deformations of the above configurations across the relevant transitions are exposed and discussed in detail. It is further found that stationary states involving highly quantized vortices can be realized in both settings. Spatial elongations, precessional motion and spiraling of the nonlinear excitations when exposed to finite temperatures and upon crossing the distinct phase boundaries, via quenching of the quadratic Zeeman coefficient, are unveiled. Spin-mixing processes triggered by the quench lead, among others, to changes in the waveform of the ensuing configurations. Our findings reveal an interplay between pattern formation and spin-mixing processes being accessible in contemporary cold atom experiments.
The static properties, i.e., existence and stability, as well as the quench-induced dynamics of vortex-bright type excitations in two-dimensional harmonically confined spin-1 Bose-Einstein condensates are investigated. Linearly stable vortex-bright-vortex and bright-vortex-bright solutions arise in both antiferromagnetic and ferromagnetic spinor gases upon quadratic Zeeman energy shift variations. Their deformations across the relevant transitions are exposed and discussed in detail, evincing also that emergent instabilities can lead to pattern formation. Spatial elongations, precessional motion, and spiraling of the nonlinear excitations when exposed to finite temperatures and upon crossing the distinct phase boundaries, via quenching of the quadratic Zeeman coefficient, are unveiled. Spin-mixing processes triggered by the quench lead, among others, to changes in the waveform of the ensuing configurations. Our findings reveal an interplay between pattern formation and spin-mixing processes accessible in contemporary cold atom experiments.
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.
This thesis discusses non-equilibrium phenomena in antiferromagnetic spinor quantum gases. We investigate, both experimentally and theoretically, the quench dynamics of antiferromagnetic spinor Bose-Einstein condensates in the vicinity of a zero temperature quantum phase transition. A microwave dressing field was used as a novel tool to access the polar to antiferrmagnetic quantum phase transition at the quadratic Zeeman shift, q=0. By performing instantaneous quenches across the phase transition,a dynamical instability was induced in the atomic cloud. This lead to pair formation and rapid amplification of spin +/-1 atoms through spin-mixing collisions. The spatial ordering kinetics in the vicinity of the phase transition was quantified by performing the local spin measurement. The coarsening dynamics was observed for the instability for q < 0, as it nucleated small domains that grew to the axial size of the cloud. Rich nonequilibrium behavior was observed in the form of growth and decay of both nematic and magnetic spin waves, following the quench. The spatiotemporal evolution was characterized through two particle correlations between atoms in each pair of spin states, which revealed dramatic differences between the dynamics of the spin correlations and those of the spin populations. \nFinally, we demonstrate the remarkable influence of linear Zeeman term on non-equilibrium dynamics of spinor Bose-Einstein condensates. We show that contrary to prior understanding magnetic field gradient actually suppresses the tendency of spin 0 state to separate into spin +/-1 state. This reconciles the Bogoliubov discrepancies and leads to a dramatic sharpening of the transition point, resulting in a resolution at the 1 Hz level. Our results point to the use of dynamics, rather than equilibrium quantities for high precision measurements of phase transitions in quantum gases.
Bose-Einstein condensation (BEC) is a phenomenon in which identical bosons occupy the same quantum state below a certain critical temperature. A hallmark of BEC is the coherence between particles every particle shares the same quantum wavefunction and phase. This coherence has been demonstrated for the external (motional) degrees of freedom of the atomic condensates by interfering two condensates. In this thesis, the coherence is shown to extend to the internal spin degrees of freedom of a spin-1 Bose gas evidenced by the observed coherent and reversible spin-changing collisions. The observed coherent dynamics are analogous to Josephson oscillations in weakly connected superconductors and represent a type of matter-wave four-wave mixing. Control of the coherent evolution of the system using magnetic fields is also demonstrated. The studies on spinor condensates begin by creating spinor condensates directly using all-optical approaches that were first developed in our laboratory. All-optical formation of Bose-Einstein condensates (BEC) in 1D optical lattice and single focus trap geometries are developed and presented. These techniques offer considerable flexibility and speed compared to magnetic trap approaches, and the trapping potential can be essentially spin-independent and are ideally suited for studying spinor condensates. Using condensates with well-defined initial non-equilibrium spin configuration, spin mixing of F = 1 and F = 2 spinor condensates of rubidium-87 atoms confined in an optical trap is observed. The equilibrium spin configuration in the F = 1 manifold confirms that 87Rb is ferromagnetic. The coherent spinor dynamics are demonstrated by initiating spin mixing deterministically with a non-stationary spin population configuration. Finally, the interplay between the coherent spin mixing and spatial dynamics in spin-1 condensates with ferromagnetic interactions is investigated.
In this thesis we investigate the static, dynamic, and thermodynamic properties\nof atomic spin-1 Bose gases in external magnetic fields. At low magnetic fields\nthe properties of single-component, or scalar condensates, are essentially\nunaffected but can become significantly altered for spinor Bose condensates as\nshown by our studies.\n\nWe first study the Bose-Einstein condensation of trapped spin-1 Bose gases by\nemploying the Hartree-Fock approximation and the two-fluid model within a mean\nfield approximation. Our detailed investigation reveals that the\nferromagnetically interacting spin-1 condensates exhibit triple condensations\nwhile the antiferromagnetically interacting ones show double condensations.\n\nThe ground state structure of homogeneous and trapped spin-1 Bose condensates\nwith ferromagnetic and antiferromagnetic interactions at zero temperature in\nmagnetic fields are then investigated systematically. We further illuminate the\nimportant effect of quadratic Zeeman shift which causes a preferred occupation\nof the $|m_F=0\nangle$ state through spin exchange collisions, $2|m_F=0\nangle\nleftrightarrow |m_F=1\nangle + |m_F=-1\nangle$.\n\nWe also present detailed studies of the off-equilibrium coherent dynamics of\nspin-1 Bose condensates in magnetic fields within the single spatial mode\napproximation. Dynamical instabilities of the off-equilibrium oscillations are\nshown to be responsible for the formation of multiple domains as recently\nobserved in several 87^{87}87Rb experiments.\n\nFinally, we discuss briefly excited condensate states, or soliton-like states,\nin cigar-shaped spin-1 Bose condensates with an effective quasi-1D description,\nusing the developed nonpolynomial Schr"odinger equation.
A spin-1 condensate with antiferromagnetic interactions supports nematic spin vortices in the easy-plane polar phase. These vortices have a $2\ensuremath{\pi}$ winding of the nematic director with a core structure that depends on the quadratic Zeeman energy. We characterize the properties of the nematic spin vortex in a uniform quasi-two-dimensional system. We also obtain the vortex excitation spectrum and use it to quantify its stability against dissociating into two half-quantum vortices, finding a parameter regime where the nematic spin vortex is dynamically stable. These results are supported by full dynamical simulations.