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Nonlinear Optics

Hexagonal self-structuring due to optomechanical nonlinearities in cold atomic gases

G. Labeyrie, Enrico Tesio, P. M. Gomes, Gian‐Luca Oppo, W. J. Firth, Gordon R. M. Robb, Aidan S. Arnold, Robin Kaiser, T. Ackemann

Published Jan 1, 2013• 1 citation
Publisher

Abstract

We demonstrate an optomechanical instability in a sample of cold atoms driven by a single laser beam in presence of a feedback mirror. Hexagonal light filaments propagate in atom-depleted tubes forming a honeycomb lattice.
DOI
10.1364/nlo.2013.nw3b.4

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We discuss the formation of optomechanical structures from the interaction between linear dielectric scatterers and a light field via dipole forces without the need for optical nonlinearities. The experiment uses a high density sample of Rb atoms in a single mirror feedback geometry. We observe hexagonal structures in the light field and a complementary honeycomb pattern in the atomic density. Different theoretical approaches are discussed assuming either viscous damping of the atomic velocity or not. The interplay between electronic and optomechanical nonlinearities is analyzed. A prediction for dissipative light - matter density solitons is given. The investigations demonstrate novel prospects for the manipulation of matter in a pattern forming system in which quantum effects should be accessible.
We study the transverse self-structuring of cold atomic clouds with effective atomic interactions mediated by a coherent driving beam retroreflected by means of a single mirror. The resulting self-structuring due to optomechanical forces is much richer than that of an effective-Kerr medium, displaying hexagonal, stripe and honeycomb phases depending on the interaction strength parametrized by the linear susceptibility. Phase domains are described by Ginzburg-Landau amplitude equations with real coefficients. In the stripe phase the system recovers inversion symmetry. Moreover, the subcritical character of the honeycomb phase allows for light-density feedback solitons functioning as self-sustained dark atomic traps with motion controlled by phase gradients in the driving beam.
We theoretically, numerically and experimentally investigate spontaneous transverse instabilities in cold atomic gases, arising from the action of dispersive light forces. Previous research focused on pattern-forming instabilities in hot gases where optical nonlinearities arise from the internal structure of the atoms and spatio-temporal structures are encoded in the populations and coherences of the medium. Dipole forces acting on the center-of-mass of laser-cooled atoms, being dependent on gradients of the optical intensity, are also nonlinear in nature: previous studies focused, for instance, on beam filamentation. Here we investigate the situation where a positive feedback loop is present in the system leading to a pattern-forming instability. We stress that the resulting spatial structures are encoded also in the spatial density distribution, effectively leading to the self-assembly of an optical atomic lattice.
Self-structuring via symmetry breaking is a prominent collective phenomenon occurring in cold and ultracold atoms coupled to optical fields [1] . Experimental realizations by means of trapped dipolar gases and optical cavities have shed light onto supersolidity and crystallization in out-of-equilibrium atomic systems [2] , [3] . Recent work demonstrated the occurrence of structural phase transitions between hexagonally coordinated supersolid phases in dipolar condensates [4] . In this work, we address 2D structural transitions occurring in an ensemble of cold thermal atoms with effective optomechanical interactions mediated by a coherent beam retro-reflected by means of a feedback mirror. The feedback loop scheme is represented in Fig. 1(a) , where the dipole potential induces atomic density structures which, in turn, scatter photons into side-band modes enhancing the potential itself and leading to transverse light-atom self-structuring, sharing similarities with an effective-Kerr nonlinear medium [5] .
Summary form only given. Spontaneous optical pattern formation occurs in a variety of nonlinear systems [1], including hot atomic vapors [2]. On the other hand, the spatial self-organization of atomic ensembles due to opto-mechanical coupling has received a lot of interest in recent years [3].We report on the observation of transverse self-organization of a cold atomic cloud (issued from a magnetooptical trap) under the action of a single pump laser beam. Two symmetries (translation and rotation) in the plane orthogonal to the beam propagation direction are spontaneously broken. We use a simple optical feedback scheme [4], where the transmitted pump beam is retro-reflected to the atoms by a high-reflectivity mirror located at a distance d behind the cloud. This feedback loop transforms phase fluctuations of the transmitted wave into intensity fluctuations, which then react on the atomic medium. If the feedback is positive, a transverse instability can develop leading to the spontaneous apparition of patterns in the transmitted pump intensity profile, as shown in the figure below (left).Using a weak probe beam sent a few tens of μs after the e,tinction of the pump, we demonstrate that the instability also results in a transverse spatial ordering of the atomic medium as shown in the right image. The cold atoms thus e,perience strong spatial bunching due to the dipole force associated to the inhomogeneous intensity distribution. We identified two different instability regimes. For short pump durations (- 1 μs), high pump intensity and cloud optical density, the instability relies on the Kerr effect (electronic nonlinearity). For longer pump durations (- 100 μs), the instability is driven by the opto-mechanical effect, resulting in lower intensity and optical density thresholds than for the electronic nonlinearity. These observations are well reproduced by a theoretical model including the coupled dynamics of the light field and the atomic e,ternal degrees of freedom.
Optomechanical pattern forming instabilities in a cloud of cold atoms lead to self-organized spatial structures of light and atoms. Here, we consider the optomechanical self-structuring of a cold atomic cloud in the presence of a phase structured input field, carrying orbital angular momentum. For a planar ring cavity setup, a model of coupled cavity field and atomic density equations describes a wide range of drifting modulation instabilities in the transverse plane. This leads to the formation of rotating self-organized rings of light-atom lattices. Using linear stability analysis and numerical simulations of the coupled atomic and optical dynamics, we demonstrate the presence of macroscopic atomic transport corresponding to the pattern rotation, induced by the structured pump phase profile.