Simulating sympathetic cooling of atomic mixtures in nonlinear traps

Jauffred, Francisco; Onofrio, Roberto; Sundaram, Bala

doi:10.1016/j.physleta.2017.06.046

Cited by 4 publications

(10 citation statements)

References 42 publications

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“…The scaling behaviors in other parameter regimes are more readily anticipated using simple analytic arguments. It should be noted that scaling is also expected to break down when using nonlinear trapping potentials, where thermalization itself is also more involved, as discussed in [8].…”

Section: Discussionmentioning

confidence: 99%

“…In order to compare these expectations with numerical simulations, one should add, on top of the request for a Maxwell-Boltzmann distribution (which implies a sort of weak-coupling limit, with small values of γ) also the ergodic theorem in which the ensemble averages evaluated above are matched by time-averaged quantities. This is a requirement for thermal equilibration, as discussed in [8].…”

Section: Analytical Considerationsmentioning

confidence: 99%

“…In previous work [6,7], we explored thermalization in the context of a model where the interaction, both in range and strength, appeared as a generalization of this more familiar Caldeira-Leggett model. Though the earlier context was the sympathetic cooling of atomic gas mixtures, our model was also intended to explore the realm of nonlinearities arising in either, or both, interaction and confining potentials [8]. In particular, plasma physics offers a phenomenological platform to discuss our model as scaling properties, turbulence, strong coupling, and exothermic reactions all play a crucial role.…”

Section: Introductionmentioning

confidence: 99%

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Scaling laws for harmonically trapped two-species mixtures at thermal equilibrium

2019

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We discuss the scaling of the interaction energy with particle numbers for a harmonically trapped two-species mixture at thermal equilibrium experiencing interactions of arbitrary strength and range. In the limit of long-range interactions and weak coupling, we recover known results for the integrable Caldeira-Leggett model in the classical limit. In the case of short-range interactions and for a balanced mixture, numerical simulations show scaling laws with exponents that depend on the interaction strength, its attractive or repulsive nature, and the dimensionality of the system. Simple analytic considerations based on equilibrium statistical mechanics and small interspecies coupling quantitatively recover the numerical results. The dependence of the scaling on interaction strength helps to identify a threshold between two distinct regimes. Our thermalization model covers both local and extended interactions allowing for interpolation between different systems such as fully ionized gases and neutral atoms, as well as parameters describing integrable and chaotic dynamics.

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Section: Discussionmentioning

confidence: 99%

Section: Analytical Considerationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Scaling laws for harmonically trapped two-species mixtures at thermal equilibrium

2019

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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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“…Power-law scaling was observed with an exponent quantitatively close to that associated with Kolmogorov scaling in turbulent fluid mixtures [15], suggestive of thermal homogenization. The model was also used to study the interplay of nonlinearities arising from both interaction and confining potentials [16].…”

Section: Introductionmentioning

confidence: 99%

Relationship between nonlinearities and thermalization in classical open systems: The role of the interaction range

Onofrio,

Sundaram

2022

Preprint

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We discuss results on the dynamics of thermalization for a model with Gaussian interactions between two classical many-body systems trapped in external harmonic potentials. Previous work showed an approximate, power-law scaling of the interaction energy with the number of particles, with particular focus on the dependence of the anomalous exponent on the interaction strength. Here we explore the role of the interaction range in determining anomalous exponents, showing that it is a more relevant parameter to differentiate distinct regimes of responses of the system. More specifically, on varying the interaction range from its largest values while keeping the interaction strength constant, we observe a crossover from an integrable system, approximating the Caldeira-Leggett interaction term in the long range limit, to an intermediate interaction range in which the system manifests anomalous scaling, and finally to a regime of local interactions in which anomalous scaling disappears. A Fourier analysis of the interaction energy shows that nonlinearities give rise to an effective bath with a broad band of frequencies, even when starting with only two distinct trapping frequencies, yielding efficient thermalization in the intermediate regime of interaction range. We provide qualitative arguments, based on an analogous Fourier analysis of the standard map, supporting the view that anomalous scaling and features of the Fourier spectrum may be used as proxies to identify the role of chaotic dynamics. Our work, that encompasses models developed in different contexts and unifies them in a common framework, may be relevant to the general understanding of the role of nonlinearities in a variety of many-body classical systems, ranging from plasmas to trapped atoms and ions.

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Simulating sympathetic cooling of atomic mixtures in nonlinear traps

Cited by 4 publications

References 42 publications

Scaling laws for harmonically trapped two-species mixtures at thermal equilibrium

Scaling laws for harmonically trapped two-species mixtures at thermal equilibrium

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

Relationship between nonlinearities and thermalization in classical open systems: The role of the interaction range

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