Brownian motion of a matter-wave bright soliton moving through a thermal cloud of distinct atoms

McDonald, R. G.; Bradley, Ashton S.

doi:10.1103/physreva.93.063604

Cited by 11 publications

(11 citation statements)

References 61 publications

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“…For Γt 1, the soliton's position grows exponentially, indicative of the soliton rapidly reaching the speed of sound and disappearing. We examine equations (19) and (20) in the short-time limit Γt 1. The trap frequency ω also considerably affects the soliton dynamics.…”

Section: Dark Soliton Trajectorymentioning

confidence: 99%

“…However, they are also highly sensitive to dimensionality and background fluctuations [17]. Recent years have seen renewed theoretical interest in the effects of friction and dissipation on solitons, which can greatly affect their lifetime and stability [18][19][20][21][22][23][24][25]. Additionally, the diffusion coefficient of a soliton was recently measured experimentally for the first time [26].…”

Section: Introductionmentioning

confidence: 99%

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Kinetic theory of dark solitons with tunable friction

et al. 2017

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We study controllable friction in a system consisting of a dark soliton in a one-dimensional Bose-Einstein condensate coupled to a noninteracting Fermi gas. The fermions act as impurity atoms, not part of the original condensate, that scatter off of the soliton. We study semiclassical dynamics of the dark soliton, a particlelike object with negative mass, and calculate its friction coefficient. Surprisingly, it depends periodically on the ratio of interspecies (impurity-condensate) to intraspecies (condensate-condensate) interaction strengths. By tuning this ratio, one can access a regime where the friction coefficient vanishes. We develop a general theory of stochastic dynamics for negative-mass objects and find that their dynamics are drastically different from their positive-mass counterparts: they do not undergo Brownian motion. From the exact phase-space probability distribution function (i.e., in position and velocity), we find that both the trajectory and lifetime of the soliton are altered by friction, and the soliton can undergo Brownian motion only in the presence of friction and a confining potential. These results agree qualitatively with experimental observations by Aycock et al. [Proc. Natl. Acad. Sci. USA 114, 2503 (2017)] in a similar system with bosonic impurity scatterers.

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Section: Dark Soliton Trajectorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Kinetic theory of dark solitons with tunable friction

et al. 2017

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“…Future work will use this formalism to analytically explore experimentally accessible systems. The stochastic Ehrenfest relations provide a useful starting point for describing a range of dissipative dynamics in hot BEC including soliton evolution [37], phase-slip dynamics [38], sympathetic cooling [39,40], spinor BECs [41], and quantum turbulence [42][43][44][45].…”

Section: Discussionmentioning

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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“…The two-body problem [11] is an example but the separation can also be done for larger number of particles [12][13][14]26,27] at the cost of using more sophisticated methods of describing the relative motion [15,22]. In practice, the mentioned transformation of variables is difficult to perform straightforwardly, however it is a standard tool in a theoretical analysis of few-body problems [30][31][32]. In the following we will separate the the centre-of-mass motion within the scope of the second quantisation formalizm.…”

Section: The Centre-of-mass Framementioning

confidence: 99%

“…Unfortunately, in this case a lot of redundant information comes from trivial dynamics of the centre of mass of the system which is completely insensitive to interparticle interactions. This general problem can be overcome in the case of the harmonic confinement, where the centre-of-mass degree of freedom can be separated out from the relative motion [11][12][13][14][15]23,[25][26][27][28][29][30][31][32]. Here, we study one-dimensional fermionic mixtures and we show how to distillate the relevant information about relative excitations encoded in the full many-body wave functions.…”

mentioning

confidence: 99%

Experimentally Accessible Invariants Encoded in Interparticle Correlations of Harmonically Trapped Ultra-cold Few-Fermion Mixtures

Pęcak¹,

Gajda²,

Sowiński³

2017

Few-Body Syst

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A system of a two-flavour mixture of ultra-cold fermions confined in a one-dimensional harmonic trap is studied. Using the well-known properties of the centre-of-mass frame we present a numerical method of obtaining energetic spectra in this frame for an arbitrary mass ratio of fermionic species. We identify a specific invariant encoded in many-body correlations which may be helpful to determine an eigenstate of the Hamiltonian and to label excitations of the centre of mass. The tool presented can be easily applied and thus may be particularly useful in an experimental analysis of the interparticle interactions which do not affect the centre of mass excitations in a harmonic potential.

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Brownian motion of a matter-wave bright soliton moving through a thermal cloud of distinct atoms

Cited by 11 publications

References 61 publications

Kinetic theory of dark solitons with tunable friction

Kinetic theory of dark solitons with tunable friction

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

Experimentally Accessible Invariants Encoded in Interparticle Correlations of Harmonically Trapped Ultra-cold Few-Fermion Mixtures

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