Subrecoil laser cooling and Lévy flights

Bardou, F.; Bouchaud, J. P.; Émile, Olivier; Aspect, Alain; Cohen‐Tannoudji, Claude

doi:10.1103/physrevlett.72.203

Cited by 219 publications

(180 citation statements)

References 12 publications

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“…We study here the site occupation times T x (t) of a confined continuous-time random walk (CTRW) on a lattice, x ∈ Z. CTRWs and related models are a standard theoretical approach to describe dynamics where trapping mechanisms induce a variety of remarkable motion patterns; examples are the charge carrier transport in amorphous semiconductors [15], model glasses [10], subrecoil laser cooling [6,7], atomic transport in optical lattices [16] and diffusion in biological cells [17][18][19][20], to name a few [21][22][23][24][25][26]. We focus on a regime where the ergodic convergence (1) holds and the classical Boltzmann-Gibbs equilibrium and ergodicity ideas apply.…”

Section: Introductionmentioning

confidence: 99%

“…A submanifold of the complete phase space is considered in the problem of phase persistence [4,5]. The time a laser-cooled atom resides in the "dark" low-momentum state [6,7] determines the cooling efficiency. In a broader context, fluctuation theorems [8,9] describe deviations from equilibrium and refine our understanding of thermodynamic laws.…”

Section: Introductionmentioning

confidence: 99%

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Fluctuations around equilibrium laws in ergodic continuous-time random walks

Schulz

Barkai

2015

Phys. Rev. E

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We study occupation time statistics in ergodic continuous-time random walks. Under thermal detailed balance conditions, the average occupation time is given by the Boltzmann-Gibbs canonical law. But close to the non-ergodic phase, the finite-time fluctuations around this mean are large and nontrivial. They exhibit dual time scaling and distribution laws: the infinite density of large fluctuations complements the Lévy-stable density of bulk fluctuations. Neither of the two should be interpreted as a stand-alone limiting law, as each has its own deficiency: the infinite density has an infinite norm (despite particle conservation), while the stable distribution has an infinite variance (although occupation times are bounded). These unphysical divergences are remedied by consistent use and interpretation of both formulas. Interestingly, while the system's canonical equilibrium laws naturally determine the mean occupation time of the ergodic motion, they also control the infinite and Lévy-stable densities of fluctuations. The duality of stable and infinite densities is in fact ubiquitous for these dynamics, as it concerns the time averages of general physical observables.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fluctuations around equilibrium laws in ergodic continuous-time random walks

Schulz

Barkai

2015

Phys. Rev. E

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“…Many anomalous diffusion systems have a quantum nature, like for instance charge transport in anomalous solids [16], subrecoil laser cooling [17] and the aging effect in quantum dissipative systems [18].…”

Section: Introductionmentioning

confidence: 99%

Canonical quantization of nonlinear many-body systems

Scarfone

2005

Phys. Rev. E

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We study the quantization of a classical system of interacting particles obeying a recently proposed kinetic interaction principle (KIP) [G. Kaniadakis, Physica A 296, 405 (2001)]. The KIP fixes the expression of the Fokker-Planck equation describing the kinetic evolution of the system and imposes the form of its entropy. In the framework of canonical quantization, we introduce a class of nonlinear Schrödinger equations (NSEs) with complex nonlinearities, describing, in the mean field approximation, a system of collectively interacting particles whose underlying kinetics is governed by the KIP. We derive the Ehrenfest relations and discuss the main constants of motion arising in this model. By means of a nonlinear gauge transformation of third kind it is shown that in the case of constant diffusion and linear drift the class of NSEs obeying the KIP is gauge-equivalent to another class of NSEs containing purely real nonlinearities depending only on the field ρ = |ψ| 2 .

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“…However there are good reasons to believe that the peak of cold atoms at the center of the final distribution is isotropic (in two dimensions). As indicated in [10], the dynamics of each individual atom is dominated by fairly distinct phases, where it either performs a random walk in velocity space outside the subrecoil range, or stays close to the dark state, in the subrecoil range, until it gets excited and resumes the random walk. The argument for a final isotropic velocity distribution relies on two considerations.…”

Section: Resultsmentioning

confidence: 99%

“…It is also expected to be better in the two-dimensional case [5,9]. The dynamics of Raman cooling, as well as that of VSCPT, are related to non Gaussian statistics called Lévy flights [9,10]. More precisely, for an excitation spectrum varying as v α around v = 0, the width of the velocity distribution scales with the cooling time Θ as Θ −1/α .…”

Section: Raman Cooling Theorymentioning

confidence: 99%

Deeply subrecoil two-dimensional Raman cooling

et al. 2004

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We report the implementation of a two-dimensional Raman cooling scheme using sequential excitations along the orthogonal axes. Using square pulses, we have cooled a cloud of ultracold Cesium atoms down to an RMS velocity spread of 0.39(5) recoil velocities, corresponding to an effective temperature of 30 nK (0.15 Trec). This technique can be useful to improve cold-atom atomic clocks, and is particularly relevant for clocks in microgravity.

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Subrecoil laser cooling and Lévy flights

Cited by 219 publications

References 12 publications

Fluctuations around equilibrium laws in ergodic continuous-time random walks

Fluctuations around equilibrium laws in ergodic continuous-time random walks

Canonical quantization of nonlinear many-body systems

Deeply subrecoil two-dimensional Raman cooling

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