Stochastic Projected Gross-Pitaevskii equation for spinor and multi-component condensates

Abstract

A stochastic Gross-Pitaevskii equation is derived for partially condensed Bose gas systems subject to binary contact interactions. The theory we present provides a classical-field theory suitable for describing dissipative dynamics and phase transitions of spinor and multi-component Bose gas systems comprised of an arbitrary number of distinct interacting Bose fields. A new class of dissipative processes involving distinguishable particle interchange between coherent and incoherent regions of phase-space is identified. The formalism and its implications are illustrated for two-component mixtures and spin-1 Bose-Einstein condensates. For systems comprised of atoms of equal mass, with thermal reservoirs that are close to equilibrium, the dissipation rates of the theory are reduced to analytical expressions that may be readily evaluated. The unified treatment of binary contact interactions presented here provides a theory with broad relevance for quasi-equilibrium and far-from-equilibrium Bose-Einstein condensates.

arXiv comment19 pages, 2 figures

References in corpus (65)

• Vortices in a Bose-Einstein Condensate
• Spin domains in ground state spinor Bose-Einstein condensates
• The dynamics of component separation in a binary mixture of Bose-Einstein condensates
• Spinor Bose-Einstein condensates
• Spontaneous vortices in the formation of Bose-Einstein condensates
• Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques
• A two atomic species superfluid
• Observation of metastable states in spinor Bose-Einstein condensates
• Vortex lattice formation in a rotating Bose-Einstein condensate
• Finite Temperature Models of Bose-Einstein Condensation
• Dual-Species Bose-Einstein Condensate of ${}^{87}$Rb and ${}^{133}$Cs
• Vortex Lattice Dynamics in Rotating Spinor Bose-Einstein Condensates
• Persistent currents in spinor condensates
• Characteristics of Two-Dimensional Quantum Turbulence in a Compressible Superfluid
• The stochastic Gross-Pitaevskii equation II
• Einstein--de Haas Effect in Dipolar Bose-Einstein Condensates
• Soliton creation during a Bose-Einstein condensation
• The nucleation, growth and stabilization of vortex lattices
• Magnetic control of the interaction in ultracold K-Rb mixtures
• Observation of interspecies Feshbach resonances in an ultracold Rb-Cs mixture
• Bose-Einstein Condensation from a Rotating Thermal Cloud: Vortex Nucleation and Lattice Formation
• The Projected Gross-Pitaevskii Equation for harmonically confined Bose gases
• Phase separation and pattern formation in a binary Bose-Einstein condensate
• Condensate growth in trapped Bose gases
• Long timescale dynamics of spin textures in a degenerate F=1 ${}^{87}$ Rb spinor Bose gas
• Finite temperature vortex dynamics in Bose Einstein condensates
• Dynamics in spinor condensates controlled by a microwave dressing field
• Critical temperature of a trapped Bose gas: comparison of theory and experiment
• Periodic spin textures in a degenerate F=1 ${}^{87}$Rb spinor Bose gas
• Modelling Bose-condensed gases at finite temperatures with $N$-body simulations
• Decay of a quantum vortex: test of non-equilibrium theories for warm Bose-Einstein condensates
• Dynamics of thermal Bose fields in the classical limit
• Dark soliton dynamics in Bose-Einstein condensates at finite temperature
• Crystallized merons and inverted merons in the condensation of spin-1 Bose gases with spin-orbit coupling
• Matter-wave dark solitons: stochastic vs. analytical results
• A number-conserving approach to a minimal self-consistent treatment of condensate and non-condensate dynamics in a degenerate Bose gas
• The Stochastic Gross-Pitaevskii Equation and some Applications
• Suppression of Kelvon-induced decay of quantized vortices in oblate Bose-Einstein Condensates
• Kibble-Zurek scaling and its breakdown for spontaneous generation of Josephson vortices in Bose-Einstein condensates
• Finite-temperature simulations of the scissors mode in Bose-Einstein condensed gases
• Yang-Yang thermometry and momentum distribution of a trapped one-dimensional Bose gas
• The stochastic projected Gross-Pitaevskii equation
• A comparison between microscopic methods for finite temperature Bose gases
• Number Fluctuations and Energy Dissipation in Sodium Spinor Condensates
• Quasi-condensate growth on an atom chip
• Properties of the stochastic Gross-Pitaevskii equation: Projected Ehrenfest relations and the optimal plane wave basis
• Persistent current formation in a high-temperature Bose-Einstein condensate: an experimental test for c-field theory
• Noisy Dynamics of a Vortex in a Partially Bose-Einstein Condensed Gas
• Ab initio methods for finite temperature two-dimensional Bose gases
• Feshbach spectroscopy of an ultracold mixture of ${}^{85}$Rb and ${}^{133}$Cs
• Dynamical thermalization and vortex formation in stirred 2D Bose-Einstein condensates
• Critical properties of a trapped interacting Bose gas
• Numerical method for the stochastic projected Gross-Pitaevskii equation
• Many-body physics in the classical-field description of a degenerate Bose gas
• Decoherence-driven Cooling of a Degenerate Spinor Bose Gas
• Fluctuating and dissipative dynamics of dark solitons in quasi-condensates
• Second-order, number-conserving description of non-equilibrium dynamics in finite-temperature Bose-Einstein condensates
• PGPE theory of finite temperature collective modes for a trapped Bose gas
• Finite-temperature dynamics of a single vortex in a Bose-Einstein condensate: Equilibrium precession and rotational symmetry breaking
• Condensation and quasicondensation in an elongated three-dimensional Bose gas
• Coherence properties of spinor condensates at finite temperatures
• Finite-temperature phase transitions in quasi-two-dimensional spin-1 Bose gases
• Temporal coherence, anomalous moments, and pairing correlations in the classical-field description of a degenerate Bose gas
• Nonequilibrium dynamics of vortex arrest in a finite-temperature Bose-Einstein condensate
• Number-conserving approaches to $n$-component Bose-Einstein condensates

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• 3D quaternionic condensations, Hopf invariants, and skyrmion lattices with synthetic spin-orbit coupling
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• Reservoir interactions during Bose-Einstein condensation: modified critical scaling in the Kibble-Zurek mechanism of defect formation
• Reservoir interactions of a vortex in a trapped 3D Bose-Einstein condensate
• Dynamics of a quenched spin-1 antiferromagnetic condensate in a harmonic trap
• Brownian motion of a matter-wave bright soliton: realizing a quantum pollen grain
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• Extracting work from coherence in a two-mode Bose-Einstein condensate
• Bubble nucleation in a cold spin 1 gas
• Stoner-Wohlfarth switching of the condensate magnetization in a dipolar spinor gas and the metrology of excitation damping
• Complex wave fields in the interacting one-dimensional Bose gas
• A Non-Equilibrium Kinetic Theory for Trapped Binary Condensates
• Finite temperature ferromagnetic transition in coherently coupled Bose gases
• Berezinskii-Kosterlitz-Thouless transitions in an easy-plane ferromagnetic superfluid
• Dynamics of Hot Bose-Einstein Condensates: stochastic Ehrenfest relations for number and energy damping
• Berezinskii-Kosterlitz-Thouless transitions in a ferromagnetic superfluid: effects of axial magnetization
• Stochastic Gross-Pitaevskii theory for a spin-1 Bose gas: Application to superfluidity in two dimensions
• Equilibration of a finite temperature binary Bose gas formed by population transfer
• Equilibrium, Relaxation and Fluctuations in homogeneous Bose-Einstein Condensates: Linearized Classical Field Analysis
• Temperature driven false vacuum decay in coherently coupled Bose superfluids