Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2502.07554 · Physical Review A

Optical pattern formation in self-focusing and self-defocusing diffractively thick media

G. Labeyrie, Ivor Krešić, Robin Kaiser, T. Ackemann

Published Jun 4, 2025• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.111.063506

Related papers

Transverse optical and atomic pattern formation

Bonnie L. Schmittberger, Daniel J. Gauthier

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.

arXiv:1603.06280•Journal of the Optical Society of America B•Jun 24, 2016•10 citations

Thick-medium model of transverse pattern formation in optically excited cold two-level atoms with a feedback mirror

W. J. Firth, Ivor Krešić, G. Labeyrie +2 more

We study a pattern-forming instability in a laser-driven optically thick cloud of cold two-level atoms with a planar feedback mirror. We develop a theoretical model, enabling a full analysis of transverse patterns in a medium with saturable nonlinearity, taking into account diffraction within the medium, and both the transmission and reflection gratings. The focus of the analysis is on the combined treatment of nonlinear propagation in a diffractively and optically thick medium and the boundary condition given by feedback. We demonstrate explicitly how diffraction within the medium breaks the degeneracy of Talbot modes inherent in thin-slice models. We predict the existence of envelope curves bounding all possible pattern-formation thresholds and illustrate their interaction with threshold curves by experimental observation of a sudden transition between length scales as mirror displacement is varied.

arXiv:1707.04090•Physical Review A•Nov 3, 2017•15 citations

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

G. Labeyrie, P. M. Gomes, Enrico Tesio +5 more

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.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•May 1, 2013•0 citations

Light self-trapping in a large cloud of cold atoms

G. Labeyrie, U. Bortolozzo

We show that, for a near-resonant propagating beam, a large cloud of cold 87Rb atoms acts as a saturable Kerr medium and produces self-trapping of light. By side fluorescence imaging we monitor the transverse size of the beam and, depending on the sign of the laser detuning with respect to the atomic transition, we observe self-focusing or -defocusing, with the waist remaining stationary for an appropriate choice of parameters. We analyze our observations by using numerical simulations based on a simple 2-level atom model.

•Jan 1, 2013•4 citations

Light self-trapping in a large cloud of cold atoms

G. Labeyrie, U. Bortolozzo

We show that, for a near-resonant propagating beam, a large cloud of cold Rb87 atoms acts as a saturable Kerr medium and produces self-trapping of light. By side fluorescence imaging, we monitor the transverse size of the beam and, depending on the sign of the laser detuning with respect to the atomic transition, we observe self-focusing or self-defocusing, with the waist remaining stationary for an appropriate choice of parameters. We analyze our observations by using numerical simulations based on a simple two-level atom model.

arXiv:1104.1916•Optics Letters•May 31, 2011•8 citations

Spatial Patterns in Nonlinear Optics: Nonlinear Effects and Patterns in a Cold Atomic Cloud

G. Labeyrie, T. Ackemann, Bruce G. Klappauf +3 more

The nonlinear interaction between an optical medium and an electro-magnetic field can induce gradients in the index of refraction distribution, leading to patterns or filamentation in the most diverse nonlinear materials: solids, anisotropic soft matter (liquid crystals), cells containing thermal vapors, etc. One common difficulty in interpreting the results of these experiments and in comparing them to models is that the details of the interaction in these media are very complex. Cold atomic systems have well known linear and nonlinear optical properties, as illustrated in experiments on four wave mixing, electro-magnetic induced transparency or slow light propagation. Such samples are thus an excellent candidate for improving the comparison between theory and experiments, but so far to our knowledge no investigations on patterns have been performed in such systems.

Optics and Photonics News•Dec 1, 2003•0 citations
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.
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.
We study a pattern-forming instability in a laser-driven optically thick cloud of cold two-level atoms with a planar feedback mirror. We develop a theoretical model, enabling a full analysis of transverse patterns in a medium with saturable nonlinearity, taking into account diffraction within the medium, and both the transmission and reflection gratings. The focus of the analysis is on the combined treatment of nonlinear propagation in a diffractively and optically thick medium and the boundary condition given by feedback. We demonstrate explicitly how diffraction within the medium breaks the degeneracy of Talbot modes inherent in thin-slice models. We predict the existence of envelope curves bounding all possible pattern-formation thresholds and illustrate their interaction with threshold curves by experimental observation of a sudden transition between length scales as mirror displacement is varied.
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 show that, for a near-resonant propagating beam, a large cloud of cold 87Rb atoms acts as a saturable Kerr medium and produces self-trapping of light. By side fluorescence imaging we monitor the transverse size of the beam and, depending on the sign of the laser detuning with respect to the atomic transition, we observe self-focusing or -defocusing, with the waist remaining stationary for an appropriate choice of parameters. We analyze our observations by using numerical simulations based on a simple 2-level atom model.
We show that, for a near-resonant propagating beam, a large cloud of cold Rb87 atoms acts as a saturable Kerr medium and produces self-trapping of light. By side fluorescence imaging, we monitor the transverse size of the beam and, depending on the sign of the laser detuning with respect to the atomic transition, we observe self-focusing or self-defocusing, with the waist remaining stationary for an appropriate choice of parameters. We analyze our observations by using numerical simulations based on a simple two-level atom model.
The nonlinear interaction between an optical medium and an electro-magnetic field can induce gradients in the index of refraction distribution, leading to patterns or filamentation in the most diverse nonlinear materials: solids, anisotropic soft matter (liquid crystals), cells containing thermal vapors, etc. One common difficulty in interpreting the results of these experiments and in comparing them to models is that the details of the interaction in these media are very complex. Cold atomic systems have well known linear and nonlinear optical properties, as illustrated in experiments on four wave mixing, electro-magnetic induced transparency or slow light propagation. Such samples are thus an excellent candidate for improving the comparison between theory and experiments, but so far to our knowledge no investigations on patterns have been performed in such systems.