Dark soliton decay in a Bose-Einstein condensate

We consider the decay of a dark soliton in a homogeneous BEC at finite temperature, with a particular emphasis on the effect of thermal noise on the stability of the soliton. We present an analytical treatment of a damped soliton in an unbounded system, comparing the predicted dynamics with numerical stochastic simulations of a spatially confined system. By varying the system temperature we study the relative importance of noise on the motion of the soliton. In the regime of low temperature the soliton is largely immune to thermal fluctuations, and is well described by the damped Gross-Pitaevskii equation. In this regime our analytical treatment is in close agreement with numerical simulations. For sufficiently high temperature, the thermal fluctuations have the interesting effect of increasing the stability of the soliton, extending its lifetime beyond the predictions of damped Gross-Pitaevskii theory.We consider the decay of a dark soliton in a homogeneous BEC at finite temperature, with a particular emphasis on the effect of thermal noise on the stability of the soliton. We present an analytical treatment of a damped soliton in an unbounded system, comparing the predicted dynamics with numerical stochastic simulations of a spatially confined system. By varying the system temperature we study the relative importance of noise on the motion of the soliton. In the regime of low temperature the soliton is largely immune to thermal fluctuations, and is well described by the damped Gross-Pitaevskii equation. In this regime our analytical treatment is in close agreement with numerical simulations. For sufficiently high temperature, the thermal fluctuations have the interesting effect of increasing the stability of the soliton, extending its lifetime beyond the predictions of damped Gross-Pitaevskii theory.

Aug 1, 20110 citations

Stochastic longevity of a dark soliton in a finite-temperature Bose-Einstein condensate

Karen Wright, Ashton S. Bradley

We study the decay of a dark soliton in a homogeneous Bose-Einstein condensate. We give an analytical treatment of a decaying soliton, deriving an expression for the soliton velocity and decay time in the absence of thermal noise. We test the result against numerical simulations of a spatially confined system and find good agreement in the regime of low temperature ( $k_BT\ll μ$ ). Thermal fluctuations are found to slow the escape of the soliton, extending its lifetime beyond the predictions of the noise-free theory; the effect becomes significant at a characteristic temperature $k_BT\sim μ$ . This stabilization by noise allows us to infer an analytical lower bound for the dark soliton decay time.We study the decay of a dark soliton in a homogeneous Bose-Einstein condensate. We give an analytical treatment of a decaying soliton, deriving an expression for the soliton velocity and decay time in the absence of thermal noise. We test the result against numerical simulations of a spatially confined system and find good agreement in the regime of low temperature ($k_BT\ll μ$). Thermal fluctuations are found to slow the escape of the soliton, extending its lifetime beyond the predictions of the noise-free theory; the effect becomes significant at a characteristic temperature $k_BT\sim μ$. This stabilization by noise allows us to infer an analytical lower bound for the dark soliton decay time.

arXiv:1104.2691Apr 14, 20111 citation

Fluctuating and dissipative dynamics of dark solitons in quasicondensates

S. P. Cockburn, Hector E. Nistazakis, Theodoros P. Horikis +3 more

The fluctuating and dissipative dynamics of matter-wave dark solitons within harmonically trapped, partially condensed Bose gases is studied both numerically and analytically. A study of the stochastic Gross-Pitaevskii equation, which correctly accounts for density and phase fluctuations at finite temperatures, reveals dark-soliton decay times to be lognormally distributed at each temperature, thereby characterizing the previously predicted long-lived soliton trajectories within each ensemble of numerical realizations [S. P. Cockburn et al., Phys. Rev. Lett. 104, 174101 (2010)]. Expectation values for the average soliton lifetimes extracted from these distributions are found to agree well with both numerical and analytic predictions based upon the dissipative Gross-Pitaevskii model (with the same ab initio damping). Probing the regime for which 0.8 ${k}_{B}T<\ensuremath{\mu}<1.6$ ${k}_{B}T$ , we find average soliton lifetimes to scale with temperature as $\ensuremath{\tau}\ensuremath{\sim}{T}^{\ensuremath{-}4}$, in agreement with predictions previously made for the low-temperature regime ${k}_{B}T\ensuremath{\ll}\ensuremath{\mu}$. The model is also shown to capture the experimentally relevant decrease in the visibility of an oscillating soliton due to the presence of background fluctuations.The fluctuating and dissipative dynamics of matter-wave dark solitons within harmonically trapped, partially condensed Bose gases is studied both numerically and analytically. A study of the stochastic Gross-Pitaevskii equation, which correctly accounts for density and phase fluctuations at finite temperatures, reveals dark-soliton decay times to be lognormally distributed at each temperature, thereby characterizing the previously predicted long-lived soliton trajectories within each ensemble of numerical realizations [S. P. Cockburn et al., Phys. Rev. Lett. 104, 174101 (2010)]. Expectation values for the average soliton lifetimes extracted from these distributions are found to agree well with both numerical and analytic predictions based upon the dissipative Gross-Pitaevskii model (with the same ab initio damping). Probing the regime for which 0.8 ${k}_{B}T<\ensuremath{\mu}<1.6$ ${k}_{B}T$, we find average soliton lifetimes to scale with temperature as $\ensuremath{\tau}\ensuremath{\sim}{T}^{\ensuremath{-}4}$, in agreement with predictions previously made for the low-temperature regime ${k}_{B}T\ensuremath{\ll}\ensuremath{\mu}$. The model is also shown to capture the experimentally relevant decrease in the visibility of an oscillating soliton due to the presence of background fluctuations.

arXiv:1107.3855Physical Review AOct 28, 201129 citations

Dissipation of a dark soliton in a trapped BEC

Eric Xu

The stochastic projected Gross-Pitaevskii equation (SPGPE) is a finite temperature theory of Bose-Einstein condensate (BEC) dynamics. It utilizes C-field techniques, which describe the dynamics of a low-energy coherent subspace in contact with a thermal reservoir [1]. There are two distinct mechanisms when interactions between the coherent field and the incoherent field are taken into account, known as number-damping and energy-damping. Number-damping has been treated extensively, while energy-damping has had less attention due to the lack of an accurate and efficient numerical method for solving it. However, Rooney et al. [2] developed a numerical technique allowing opportunities for the investigation of the energy-damping process. Bradley and McDonald examined the analytic treatment of the energy-damping process using functional Ito calculus for a range of systems, except for dark soliton. They found there is usually a regime where energy-damping dominates number-damping. Wright [3] has done analytical work on the dissipation of dark soliton in a homogenous system via a Lagrangian approach (where the number-damping term is treated as the perturbation to GPE). Still, the effect of the energy-damping process was not considered. In this thesis, we present an analytic investigation of the dissipation effects of number-damping and energy-damping on dark solitons. This is done through the framework of the one-dimensional Damped Gross-Pitaevskii equation (1D-DGPE). We take a Lagrangian variational approach and treat the number-damping and energy-damping as perturbations to the GPE. Dynamics of the soliton position are obtained, and anti-damping of the dark soliton in a harmonically trapped prolate BEC is observed in the perturbation regime. Our analytic work shows that dissipation effects of energy- damping becomes more dominant as the chemical potential of the system increases; for even modest chemical potential, energy-damping dominates number-damping. We compare our analytic results against numerical simulations and find good agreement for dark soliton position dynamics, kinetic energy, potential energy, and interaction energy dynamics in the regime where the dark soliton is near to the trap center and moving slowly relative to the speed of sound.The stochastic projected Gross-Pitaevskii equation (SPGPE) is a finite temperature theory of Bose-Einstein condensate (BEC) dynamics. It utilizes C-field techniques, which describe the dynamics of a low-energy coherent subspace in contact with a thermal reservoir [1]. There are two distinct mechanisms when interactions between the coherent field and the incoherent field are taken into account, known as number-damping and energy-damping. Number-damping has been treated extensively, while energy-damping has had less attention due to the lack of an accurate and efficient numerical method for solving it. However, Rooney et al. [2] developed a numerical technique allowing opportunities for the investigation of the energy-damping process. Bradley and McDonald examined the analytic treatment of the energy-damping process using functional Ito calculus for a range of systems, except for dark soliton. They found there is usually a regime where energy-damping dominates number-damping. Wright [3] has done analytical work on the dissipation of dark soliton in a homogenous system via a Lagrangian approach (where the number-damping term is treated as the perturbation to GPE). Still, the effect of the energy-damping process was not considered. In this thesis, we present an analytic investigation of the dissipation effects of number-damping and energy-damping on dark solitons. This is done through the framework of the one-dimensional Damped Gross-Pitaevskii equation (1D-DGPE). We take a Lagrangian variational approach and treat the number-damping and energy-damping as perturbations to the GPE. Dynamics of the soliton position are obtained, and anti-damping of the dark soliton in a harmonically trapped prolate BEC is observed in the perturbation regime. Our analytic work shows that dissipation effects of energy- damping becomes more dominant as the chemical potential of the system increases; for even modest chemical potential, energy-damping dominates number-damping. We compare our analytic results against numerical simulations and find good agreement for dark soliton position dynamics, kinetic energy, potential energy, and interaction energy dynamics in the regime where the dark soliton is near to the trap center and moving slowly relative to the speed of sound.

Jan 1, 20220 citations

Dark-bright solitons in Bose–Einstein condensates at finite temperatures

Vassos Achilleos, D Yan, P G Kevrekidis +1 more

We study the dynamics of dark-bright (DB) solitons in binary mixtures of Bose gases at finite temperature using a system of two coupled dissipative Gross–Pitaevskii equations. We develop a perturbation theory for the two-component system to derive an equation of motion for the soliton centers and identify different temperature-dependent damping regimes. We show that the effect of the bright ('filling') soliton component is to partially stabilize 'bare' dark solitons against temperature-induced dissipation, thus providing longer lifetimes. We also study analytically thermal effects on DB soliton 'molecules' (i.e. two in-phase and out-of-phase DB solitons), showing that they undergo expanding oscillations while interacting. Our analytical findings are in good agreement with results obtained via a Bogoliubov–de Gennes analysis and direct numerical simulations.We study the dynamics of dark-bright (DB) solitons in binary mixtures of Bose gases at finite temperature using a system of two coupled dissipative Gross–Pitaevskii equations. We develop a perturbation theory for the two-component system to derive an equation of motion for the soliton centers and identify different temperature-dependent damping regimes. We show that the effect of the bright ('filling') soliton component is to partially stabilize 'bare' dark solitons against temperature-induced dissipation, thus providing longer lifetimes. We also study analytically thermal effects on DB soliton 'molecules' (i.e. two in-phase and out-of-phase DB solitons), showing that they undergo expanding oscillations while interacting. Our analytical findings are in good agreement with results obtained via a Bogoliubov–de Gennes analysis and direct numerical simulations.

arXiv:1110.3173New Journal of PhysicsMay 1, 201238 citations

Multiple dark solitons in Bose-Einstein condensates at finite temperatures

P. G. Kevrekidis, D. J. Frantzeskakis

We study analytically, as well as numerically, single- and multiple-dark matter-wave solitons in atomic Bose-Einstein condensates at finite temperatures. Our analysis is based on the study of the dissipative Gross-Pitaevskii equation, which incorporates a phenomenological damping term accounting for the interaction of the condensate with the thermal cloud. We illustrate how the negative Krein sign eigenmodes (associated with the the single- or multiple-dark soliton states) can give rise to Hopf bifurcations and oscillatory instabilities, whose ensuing dynamics is also elucidated. In all cases, the finite-temperature induced dynamics results in soliton decay, and the system eventually asymptotes to the ground state.We study analytically, as well as numerically, single- and multiple-dark matter-wave solitons in atomic Bose-Einstein condensates at finite temperatures. Our analysis is based on the study of the dissipative Gross-Pitaevskii equation, which incorporates a phenomenological damping term accounting for the interaction of the condensate with the thermal cloud. We illustrate how the negative Krein sign eigenmodes (associated with the the single- or multiple-dark soliton states) can give rise to Hopf bifurcations and oscillatory instabilities, whose ensuing dynamics is also elucidated. In all cases, the finite-temperature induced dynamics results in soliton decay, and the system eventually asymptotes to the ground state.

Discrete and Continuous Dynamical Systems - SDec 29, 20107 citations

k_BT\ll μ

). Thermal fluctuations are found to slow the escape of the soliton, extending its lifetime beyond the predictions of the noise-free theory; the effect becomes significant at a characteristic temperature

k_BT\sim μ

. This stabilization by noise allows us to infer an analytical lower bound for the dark soliton decay time.

{k}_{B}T

, we find average soliton lifetimes to scale with temperature as $\ensuremath{\tau}\ensuremath{\sim}{T}^{\ensuremath{-}4}$, in agreement with predictions previously made for the low-temperature regime ${k}_{B}T\ensuremath{\ll}\ensuremath{\mu}$. The model is also shown to capture the experimentally relevant decrease in the visibility of an oscillating soliton due to the presence of background fluctuations.