Kinetic theory of cavity cooling and self-organisation of a cold gas

Niedenzu, Wolfgang; Grießer, Tobias; Ritsch, Helmut

doi:10.1209/0295-5075/96/43001

Cited by 35 publications

(75 citation statements)

References 24 publications

(51 reference statements)

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“…It implies that cavity-cooling of a large sample of atoms into the self-organized phase, corresponding to a sudden quench along path B, can be very slow and thus inefficient (see also Ref. [34]). Our analysis sets the stage for the development of a kinetic equation that is valid in the full quantum regime [47][48][49][50][51].…”

Section: Arxiv:151205243v2 [Quant-ph] 20 Jul 2016mentioning

confidence: 99%

Dissipation-Assisted Prethermalization in Long-Range Interacting Atomic Ensembles

2016

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We theoretically characterize the semiclassical dynamics of an ensemble of atoms after a sudden quench across a driven-dissipative second-order phase transition. The atoms are driven by a laser and interact via conservative and dissipative long-range forces mediated by the photons of a singlemode cavity. These forces can cool the motion and, above a threshold value of the laser intensity, induce spatial ordering. We show that the relaxation dynamics following the quench exhibits a long prethermalizing behaviour which is first dominated by coherent long-range forces, and then by their interplay with dissipation. Remarkably, dissipation-assisted prethermalization is orders of magnitude longer than prethermalization due to the coherent dynamics. We show that it is associated with the creation of momentum-position correlations, which remain nonzero for even longer times than mean-field predicts. This implies that cavity cooling of an atomic ensemble into the selforganized phase can require longer time scales than the typical experimental duration. In general, these results demonstrate that noise and dissipation can substantially slow down the onset of thermalization in long-range interacting many-body systems. The quest for a systematic understanding of nonequilibrium phenomena is an open problem in theoretical physics for its importance in the description of dynamics from the microscopic up to astrophysical scales [1-3]. Aspects of these dynamics are studied in the relaxation of systems undergoing temporal changes (quenches) of the control field across a critical point [4][5][6]. Quenches across a non-equilibrium phase transition provide further insight into the interplay between noise and external drives on criticality and thermalization [7,8]. In this context photonic systems play a prominent role, thanks to their versatility [9][10][11][12][13][14][15].Polarizable particles in a high-finesse cavity, like in the setup illustrated in Fig. 1(a), offer a unique system to study relaxation in long-range interacting systems. Here, multiple photon scattering mediates particleparticle interactions whose range scales with the system size in a single-mode cavity [15][16][17][18]. In this limit, atomic ensembles in cavities are expected to share several features with other long-range interacting systems such as gravitational clusters and non-neutral plasmas in two or more dimensions [3,16,19]. The equilibrium thermodynamics of these systems can exhibit ensemble inequivalence [3,20], while quasi-stationary states (QSS) typically characterise the out-of-equilibrium dynamics [3,[21][22][23]. QSS are metastable states in which the system is expected to remain trapped in the thermodynamic limit, they are Vlasov-stable solutions and thus depend on the initial state. So far, however, evidence of QSS has been elusive. It has been conjectured that noise and dissipation can set a time scale that limits the QSS lifetime [24][25][26][27], and possibly gives rise to dynamical phase transitions [25]. In Ref. [28] it was shown that, in pr...

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Section: Arxiv:151205243v2 [Quant-ph] 20 Jul 2016mentioning

confidence: 99%

Dissipation-Assisted Prethermalization in Long-Range Interacting Atomic Ensembles

2016

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“…Such a treatment misses, however, correlations in the density and field fluctuations which lead to cooling and heating on longer time scales [20].…”

Section: Modelmentioning

confidence: 99%

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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“…We then compare the predictions of our model on the atomic distribution with the predictions extracted with the model in Refs. [19,25]. This article is organized as follows.…”

Section: Arxiv:13072883v2 [Quant-ph] 25 Sep 2013mentioning

confidence: 99%

“…Such approximation becomes invalid for small photon numbers, and thus for instance below and close to the selforganization threshold. Nevertheless, this equation is used in the literature for studying the dynamics of the system below threshold [17,25].…”

Section: A Semiclassical Model Below the Selforganization Thresholdmentioning

confidence: 99%

Cooling of atomic ensembles in optical cavities: Semiclassical limit

2013

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The semiclassical dynamics of atoms are theoretically studied, when the atoms are confined inside a standing-wave high-finesse resonator. The atoms are cooled by scattering processes in which the photons of a transverse laser are coherently scattered into the cavity mode. We derive a FokkerPlanck equation for the atomic center-of-mass variables which allows us to determine the equations of motion in the semiclassical limit for any value of the intensity of the laser field. We extract its prediction for the dynamics when the resonator is essentially in the vacuum state and the atoms are cooled by scattering photons into the cavity mode, which then decays. Its predictions for the stationary atomic distribution are compared with the ones of the Fokker-Planck equation in [P. Domokos, P. Horak, and H. Ritsch, J. Phys. B 34, 187 (2001)], which has been derived under different assumptions. We find full agreement in the considered parameter regime.

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Kinetic theory of cavity cooling and self-organisation of a cold gas

Cited by 35 publications

References 24 publications

Dissipation-Assisted Prethermalization in Long-Range Interacting Atomic Ensembles

Dissipation-Assisted Prethermalization in Long-Range Interacting Atomic Ensembles

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

Cooling of atomic ensembles in optical cavities: Semiclassical limit

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