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Physical Review A

Optical pattern formation with a two-level nonlinearity

A. Camara, Robin Kaiser, G. Labeyrie, W. J. Firth, Gian‐Luca Oppo, Gordon R. M. Robb, Aidan S. Arnold, T. Ackemann

Published Jul 13, 2015• 22 citations
Publisher

Abstract

We present an experimental and theoretical investigation of spontaneous pattern formation in the transverse section of a single retroreflected laser beam passing through a cloud of cold rubidium atoms. In contrast to previously investigated systems, the nonlinearity at work here is that of a two-level atom, which realizes the paradigmatic situation considered in many theoretical studies of optical pattern formation. In particular, we are able to observe the disappearance of the patterns at high intensity due to the intrinsic saturable character of two-level atomic transitions.

DOI
10.1103/physreva.92.013820

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We present an experimental and theoretical investigation of spontaneous pattern formation in the transverse section of a single retroreflected laser beam passing through a cloud of cold rubidium atoms. In contrast to previously investigated systems, the nonlinearity at work here is that of a two-level atom, which realizes the paradigmatic situation considered in many theoretical studies of optical pattern formation. In particular, we are able to observe the disappearance of the patterns at high intensity due to the intrinsic saturable character of two-level atomic transitions.
We present an experimental and theoretical investigation of spontaneous pattern formation in the transverse section of a single retro-reflected laser beam passing through a cloud of cold Rubidium atoms. In contrast to previously investigated systems, the nonlinearity at work here is that of a 2-level atom, which realizes the paradigmatic situation considered in many theoretical studies of optical pattern formation. In particular, we are able to observe the disappearance of the patterns at high intensity due to the intrinsic saturable character of 2-level atomic transitions.
Cold atomic clouds constitute highly resonant nonlinear optical media, whose refractive index can easily be tuned via the light frequency. When subjected to a retroreflected laser beam and under appropriate conditions, the cloud undergoes spontaneous symmetry breaking, and spatial patterns develop in the transverse cross section of the beam. We investigate the impact of the sign of the light detuning from the atomic resonance on these patterns, thus directly comparing pattern formation for self-focusing and self-defocusing nonlinearities. Our observations emphasize the need for a ``diffractively thick'' medium description of the light-cloud interaction in which diffraction and nonlinear propagation inside the sample are taken into account.
Pattern formation in nonlinear systems is a very active subject in many areas of physics. For example, in hydrodynamics the arrangement of the convective cells of the Rayleigh-Bernard instability [1] constitutes a model problem for pattern formation. In optics, important advances have been recently obtained in the case of lasers [2]. In contrast, transverse pattern formation in mirrorless optical passive systems [3] is no so wellknown because of the intrinsic complexity of a system without cavity and of the fact that the first experiments were done with pulsed lasers [4]. We present here results obtained with c.w. lasers and rubidium atoms. In particular, the relationship with hydrodynamics observations, suggests the possible existence of some general rule for pattern formation.
Pattern formation in nonlinear systems is a very active subject in many areas of physics. For example, in hydrodynamics the arrangement of the convective cells of the Rayleigh-Bernard instability [1] constitutes a model problem for pattern formation. In optics, important advances have been recently obtained in the case of lasers [2]. In contrast, transverse pattern formation in mirrorless optical passive systems [3] is no so wellknown because of the intrinsic complexity of a system without cavity and of the fact that the first experiments were done with pulsed lasers [4], We present here results obtained with c.w. lasers and rubidium atoms. In particular, we show some interesting relationship with the hydrodynamics observations.
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.
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.