A Vlasov approach to bunching and selfordering of particles in optical resonators

Grießer, Tobias; Ritsch, Helmut; Hemmerling, M.; Robb, G. R. M.

doi:10.1140/epjd/e2010-00113-9

Cited by 17 publications

(42 citation statements)

References 30 publications

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“…In the case of no pump asymmetry the two setups are fully equivalent [18]. However, the system considered in this work is more versatile, because, in principle, by the choice of the pump asymmetry, ordered particle distributions with any prescribed centre of mass velocity can be generated.…”

Section: Discussionmentioning

confidence: 99%

“…Obviously there exists a close analogy between the present setup with equal pump strengths and a transversally pumped ring-cavity. As in the latter case there appear stable selforganized solutions beyond an instability threshold [18], which is given by…”

Section: Stability Analysismentioning

confidence: 91%

“…However, in the limit N → ∞ the dynamics of the gas can, for sufficiently short times be reliably approximated by a Vlasov equation (in 1D) [18,19] …”

Section: Modelmentioning

confidence: 99%

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Atomic self-ordering in a ring cavity with counterpropagating pump fields

Ostermann

Grießer

Ritsch

2015

EPL

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The collective dynamics of mobile scatterers and light in optical resonators generates complex behaviour. For strong transverse illumination a phase transition from homogeneous to crystalline particle order appears. In contrast, a gas inside a single-side pumped ring cavity exhibits an instability towards bunching and collective acceleration called collective atomic recoil lasing (CARL). We demonstrate that by driving two orthogonally polarized counter propagating modes of a ring resonator one realises both cases within one system. The corresponding phase diagram depending on the two pump intensities exhibits regions in which either a generalized form of self-ordering towards a travelling density wave with constant centre of mass velocity or a CARL instability is formed. Controlling the cavity driving then allows to accelerate or slow down and trap a sufficiently dense beam of linearly polarizable particles.

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Section: Discussionmentioning

confidence: 99%

Section: Stability Analysismentioning

confidence: 91%

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Atomic self-ordering in a ring cavity with counterpropagating pump fields

Ostermann

Grießer

Ritsch

2015

EPL

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“…In order to do so, we use a standard procedure, which is also detailed in Ref. [19,40]. For short times t after the quench, we write the distribution as…”

Section: B Stability Analysis Of Spatially Homogeneous Distributionsmentioning

confidence: 99%

Mean-field theory of atomic self-organization in optical cavities

2016

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Photons mediate long-range optomechanical forces between atoms in high finesse resonators, which can induce the formation of ordered spatial patterns. When a transverse laser drives the atoms, the system undergoes a second order phase transition, that separates a uniform spatial density from a Bragg grating maximizing scattering into the cavity and is controlled by the laser intensity. Starting from a Fokker-Planck equation describing the semiclassical dynamics of the N -atom distribution function, we systematically develop a mean-field model and analyse its predictions for the equilibrium and out-of-equilibrium dynamics. The validity of the mean-field model is tested by comparison with the numerical simulations of the N -body Fokker-Planck equation and by means of a BBGKY hierarchy. The mean-field theory predictions well reproduce several results of the N -body FokkerPlanck equation for sufficiently short times, and are in good agreement with existing theoretical approaches based on field-theoretical models. Mean-field, on the other hand, predicts thermalization time scales which are at least one order of magnitude shorter than the ones predicted by the N -body dynamics. We attribute this discrepancy to the fact that the mean-field ansatz discards the effects of the long-range incoherent forces due to cavity losses.

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“…Thus, even in an ensemble, recoil heating sets a limit for the temperature of individual atoms n i n 0 + 1/η that depends on the single-atom cooperativity η: ground-state cooling requires η > 1 [3]. Whether the same result holds in other cooling geometries, e.g., with transverse pumping [5,6,23], is under investigation [23].…”

Section: (Gxmentioning

confidence: 99%

Optomechanical Cavity Cooling of an Atomic Ensemble

et al. 2011

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We demonstrate cavity sideband cooling of a single collective motional mode of an atomic ensemble down to a mean phonon occupation number n min = 2.0 +0.9 −0.3 . Both n min and the observed cooling rate are in good agreement with an optomechanical model. The cooling rate constant is proportional to the total photon scattering rate by the ensemble, demonstrating the cooperative character of the light-emission-induced cooling process. We deduce fundamental limits to cavity-cooling either the collective mode or, sympathetically, the single-atom degrees of freedom.

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A Vlasov approach to bunching and selfordering of particles in optical resonators

Cited by 17 publications

References 30 publications

Atomic self-ordering in a ring cavity with counterpropagating pump fields

Atomic self-ordering in a ring cavity with counterpropagating pump fields

Mean-field theory of atomic self-organization in optical cavities

Optomechanical Cavity Cooling of an Atomic Ensemble

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