Stochastic projected Gross-Pitaevskii equation for spinor and multicomponent condensates

Bradley, Ashton S.; Blakie, P. B.

doi:10.1103/physreva.90.023631

Cited by 30 publications

(64 citation statements)

References 79 publications

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“…We use γ = 10 −2 , which gives |dW | q 0 |ψ m |dt, and therefore reservoir scattering events occur within the time scale of spin interactions. The microscopically derived value for γ will be considerably smaller than this [53], resulting in the GPE dynamics overwhelming the reservoir interactions. We evolve Eq.…”

Section: A5 Open System Simulationsmentioning

confidence: 91%

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Anomalous phase ordering of a quenched ferromagnetic superfluid

Williamson

Blackie

2019

SciPost Phys.

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Coarsening dynamics, the canonical theory of phase ordering following a quench across a symmetry breaking phase transition, is thought to be driven by the annihilation of topological defects. Here we show that this understanding is incomplete. We simulate the dynamics of an isolated spin-1 condensate quenched into the easy-plane ferromagnetic phase and find that the mutual annihilation of spin vortices does not take the system to the equilibrium state. A nonequilibrium background of long wavelength spin waves remain at the Berezinskii-Kosterlitz-Thouless temperature, an order of magnitude hotter than the equilibrium temperature. The coarsening continues through a second much slower scale invariant process with a length scale that grows with time as t 1/3 . This second regime of coarsening is associated with spin wave energy transport from low to high wavevectors, bringing about the the eventual equilibrium state. Because the relevant spin waves are noninteracting, the transport occurs through a dynamic coupling to other degrees of freedom of the system. The transport displays features of a spin wave energy cascade, providing a potential profitable connection with the emerging field of spin wave turbulence. Strongly coupling the system to a reservoir destroys the second regime of coarsening, allowing the system to thermalise following the annihilation of vortices.

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Section: A5 Open System Simulationsmentioning

confidence: 91%

“…To model open system evolution we couple our condensate to a reservoir of energy and particles with fixed temperature T and chemical potential µ. The dynamics is simulated using the simple growth stochastic Gross-Pitaevskii equations (SGPEs) [53,[57][58][59],…”

Section: A5 Open System Simulationsmentioning

confidence: 99%

Anomalous phase ordering of a quenched ferromagnetic superfluid

Williamson

Blackie

2019

SciPost Phys.

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“…The derivation of the complete SPGPE for scalar BEC appeared in [9]. A later generalization allows for the possibility of multiple components and spins [13]. The derivation involves finding a master equation for the coherent region density operator.…”

Section: Stochastic Projected Gross-pitaevskii Equationmentioning

confidence: 99%

“…Indeed, various generalized Gross-Pitaevskii theories have been developed for the high temperature regime, describing many modes that are weakly occupied, interacting, and partially coherent [7,8]. Devoid of the symmetry-breaking ansatz, these approaches have advantages for high-temperature work.One approach capable of describing experiments across the phase transition is known as the stochastic projected Gross-Pitaevskii equation (SPGPE) [9][10][11][12][13]. The SPGPE was developed as a synthesis of quantum kinetic theory [14] and the projected Gross-Pitaevskii equation [15], and provides a…”

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confidence: 99%

Dynamics of hot Bose-Einstein condensates: stochastic Ehrenfest relations for number and energy damping

et al. 2020

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Describing high-temperature Bose gases poses a long-standing theoretical challenge. We present exact stochastic Ehrenfest relations for the stochastic projected Gross-Pitaevskii equation, including both number and energy damping mechanisms, and all projector terms that arise from the energy cutoff separating system from reservoir. Analytic solutions for the center of mass position, momentum, and their two-time correlators are in close agreement with simulations of a harmonically trapped prolate system. The formalism lays the foundation to analytically explore experimentally accessible hot Bose-Einstein condensates. Contents arXiv:1908.05809v1 [cond-mat.quant-gas] B Kohn mode projector terms 21 B.1 Position and momentum 22 B.2 Dimensionless variable z(t) 23 B.3 Numerical evaluation of projector terms 23 References 24 IntroductionA system of Bose atoms with temperature T undergoes a dramatic change in behavior at the critical temperature for the formation of a Bose-Einstein condensate (BEC), T c . Far below the BEC transition T T c , a nearly pure BEC forms, consisting of a highly occupied many-body quantum state; in this regime dilute gas BEC are renowned both for their high experimental control, and precise theoretical description [1]. At temperatures T T c thermal energy dominates, the quantum statistics are unimportant, and a Boltzman description captures the physical properties of the atoms. When T ∼ T c the quantum statistics of the atoms are decisive, despite appreciable thermal energy. In a hot BEC T T c , competition between thermal and interaction effects leads to fragmentation of the condensate, and formation of vortices, solitons, and phononic excitations. A cooling quench across the transition can inject interesting excitations into the BEC that form as remnants of the broken U(1) symmetry [2, 3], and rich turbulent dynamics develop from the competition between thermal, quantum, and interaction effects, posing a challenge for theory.At low temperatures T T c , mean field theory provides a useful description, upon which the GPE and its generalizations are based. The Zaremba-Nikuni-Griffin U(1) symmetry breaking approach has proven well suited for practical calculations in the low-temperature regime [4], having the virtue that the interactions between condensate and thermal cloud, and their respective dynamics, are all included in the dynamical description. However, it's strength for low temperatures presents a limitation at high temperatures: the symmetry-breaking ansatz cannot describe strongly fluctuating systems containing large non-condensate fraction. Fortunately, the scope of the Gross-Pitaevskii equation (GPE) upon which ZNG is based goes much further than mean-field theory: GPE-like field equations appear naturally in phase-space representations of Bose gases [5], suggesting a generalization of quantum optical open systems theory [6] for describing hot Bose gases. Indeed, various generalized Gross-Pitaevskii theories have been developed for the high temperature regime, describing many modes that...

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“…This leads to a multimode description of the system in which the classical field also obeys the GPE, but now encompassing both the condensate and the low-lying excitations in a unified manner [34][35][36][37][38][39][40][41][42][43][44][45][46]. In order to make use of such a classical field description, one needs to have populations initially distributed in modes other than the condensate mode (see also variants of this method [30,[47][48][49] based on slightly different initial mode seedings). This can be facilitated by an initial (nonzero) condition across all classical modes, which thus enables mode mixing during the numerical evolution.…”

Section: Introductionmentioning

confidence: 99%

Equilibration of a finite-temperature binary Bose gas formed by population transfer

2014

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We consider an equilibrium single-species homogeneous Bose gas from which a proportion of the atoms are instantaneously and coherently transferred to a second species, thereby forming a binary Bose gas in a non-equilibrium initial state. We study the ensuing evolution towards a new equilibrium, mapping the dynamics and final equilibrium state out as a function of the population transfer and the interspecies interactions by means of classical field methods. While in certain regimes, the condensate fractions are largely unaffected by the population transfer process, in others, particularly for immiscible interactions, one or both condensate fractions are vastly reduced to a new equilibrium value.

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Stochastic projected Gross-Pitaevskii equation for spinor and multicomponent condensates

Cited by 30 publications

References 79 publications

Anomalous phase ordering of a quenched ferromagnetic superfluid

Anomalous phase ordering of a quenched ferromagnetic superfluid

Dynamics of hot Bose-Einstein condensates: stochastic Ehrenfest relations for number and energy damping

Equilibration of a finite-temperature binary Bose gas formed by population transfer

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