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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Transverse self-organization in cold atoms due to opto-mechanical coupling

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

Published May 1, 2013• 0 citations
Publisher

Abstract

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.

DOI
10.1109/cleoe-iqec.2013.6801786

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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.
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.
The rapidly developing field of optomechanics aims at the combined control of optical and mechanical (solid-state or atomic) modes. In particular, laser cooled atoms have been used to exploit optomechanical coupling for self-organization in a variety of schemes where the accessible length scales are constrained by a combination of pump modes and those associated to a second imposed axis, typically a cavity axis. Here, we consider a system with many spatial degrees of freedom around a single distinguished axis, in which two symmetries - rotations and translations in the plane orthogonal to the pump axis - are spontaneously broken. We observe the simultaneous spatial structuring of the density of a cold atomic cloud and an optical pump beam. The resulting patterns have hexagonal symmetry. The experiment demonstrates the manipulation of matter by opto-mechanical self-assembly with adjustable length scales and can be potentially extended to quantum degenerate gases.
This article discusses self-organization in cold atoms via light-mediated interactions induced by feedback from a single retro-reflecting mirror. Diffractive dephasing between the pump beam and the spontaneous sidebands selects the lattice period. Spontaneous breaking of the rotational and translational symmetry occur in the 2D plane transverse to the pump. We elucidate how diffractive ripples couple sites on the self-induced atomic lattice. The nonlinear phase shift of the atomic cloud imprinted onto the optical beam is the parameter determining coupling strength. The interaction can be tailored to operate either on external degrees of freedom leading to atomic crystallization for thermal atoms and supersolids for a quantum degenerate gas, or on internal degrees of freedom like populations of the excited state or Zeeman sublevels. Using the light polarization degrees of freedom on the Poincaré sphere (helicity and polarization direction), specific irreducible tensor components of the atomic Zeeman states can be coupled leading to spontaneous magnetic ordering of states of dipolar and quadrupolar nature. The requirements for critical interaction strength are compared for the different situations. Connections and extensions to longitudinally pumped cavities, counterpropagating beam schemes and the CARL instability are discussed.
We report a new nonlinear optical process that occurs in a cloud of cold atoms at low-light-levels when the incident optical fields simultaneously polarize, cool, and spatially-organize the atoms. We observe an extremely large effective fifth-order nonlinear susceptibility of χ(⁵) = 7.6 × 10⁻¹⁵ (m/V)⁴, which results in efficient Bragg scattering via six-wave mixing, slow group velocities (∼ c/10⁵), and enhanced atomic coherence times (> 100 μs). In addition, this process is particularly sensitive to the atomic temperatures, and provides a new tool for in-situ monitoring of the atomic momentum distribution in an optical lattice. For sufficiently large light-matter couplings, we observe an optical instability for intensities as low as ∼ 1 mW/cm² in which new, intense beams of light are generated and result in the formation of controllable transverse optical patterns.
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.
The study of transverse optical pattern formation has been studied extensively in nonlinear optics, with a recent experimental interest in studying the phenomenon using cold atoms, which can undergo real-space self-organization. Here, we describe our experimental observation of pattern formation in cold atoms, which occurs using less than 1 μW of applied power. We show that the optical patterns and the self-organized atomic structures undergo continuous symmetry breaking, which is characteristic of nonequilibrium phenomena in a multimode system. To theoretically describe pattern formation in cold atoms, we present a self-consistent model that allows for tight atomic bunching in the applied optical lattice. We derive the nonlinear refractive index of a gas of multilevel atoms in an optical lattice, and we derive the threshold conditions under which pattern formation occurs. We show that by using small detunings and sub-Doppler temperatures, one achieves intensity thresholds for pattern formation that are reduced by two orders of magnitude compared to warm atoms.