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arXiv:1603.06294 · New Journal of Physics

Spontaneous emergence of free-space optical and atomic patterns

Bonnie L. Schmittberger, Daniel J. Gauthier

Published Oct 14, 2016• 21 citations
arXivHTMLPDF

Abstract

The spontaneous formation of patterns in dynamical systems is a rich phenomenon that transcends scientific boundaries. Here, we report our observation of coupled optical–atomic pattern formation, which results in the creation of self-organized, multimode structures in free-space laser-driven cold atoms. We show that this process gives rise to spontaneous three-dimensional Sisyphus cooling even at very low light intensities and the emergence of self-organized structures on both sub- and super-wavelength scales.

DOI
10.1088/1367-2630/18/10/103021

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The spontaneous formation of patterns in dynamical systems is a rich phenomenon that transcends scientific boundaries. Here, we report our observation of coupled optical–atomic pattern formation, which results in the creation of self-organized, multimode structures in free-space laser-driven cold atoms. We show that this process gives rise to spontaneous three-dimensional Sisyphus cooling even at very low light intensities and the emergence of self-organized structures on both sub- and super-wavelength scales.
The nonlinear interaction between light and atoms is an extensive field of study with a broad range of applications in quantum information science and condensed matter physics. Nonlinear optical phenomena occurring in cold atoms are particularly interesting because such slowly moving atoms can spatially organize into density gratings, which allows for studies involving optical interactions with structured materials. In this thesis, I describe a novel nonlinear optical effect that arises when cold atoms spatially bunch in an optical lattice. I show that employing this spatial atomic bunching provides access to a unique physical regime with reduced thresholds for nonlinear optical processes and enhanced material properties. Using this method, I observe the nonlinear optical phenomenon of transverse optical pattern formation at record-low powers. These transverse optical patterns are generated by a wave- mixing process that is mediated by the cold atomic vapor. The optical patterns are highly multimode and induce rich non-equilibrium atomic dynamics. In particular, I find that there exists a synergistic interplay between the generated optical pat- terns and the atoms, wherein the scattered fields help the atoms to self-organize into new, multimode structures that are not externally imposed on the atomic sample. These self-organized structures in turn enhance the power in the optical patterns. I provide the first detailed investigation of the motional dynamics of atoms that have self-organized in a multimode geometry. I also show that the transverse optical patterns induce Sisyphus cooling in all three spatial dimensions, which is the first observation of spontaneous three-dimensional cooling. My experiment represents a unique means by which to study nonlinear optics and non-equilibrium dynamics at ultra-low required powers.
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 investigate how laser-driven, cooperative dipole-dipole interactions in weakly trapped atomic arrays give rise to self-organized configurations. Starting from an analytically tractable two-emitter system, we identify the possible steady-state spatial arrangements accessible to the atoms. We then extend this analysis to larger ensembles in both linear and ring geometries. In linear chains, we demonstrate the emergence of topologically nontrivial dimerized configurations across a range of initial interatomic spacings. In ring geometries, we find that the system undergoes self-organized contraction and expansion, enabling access to length scales below those set by the trapping lattice. Our results demonstrate that collective light-matter interactions in free space can spontaneously generate modified ordered geometries, even when the emitters are initially separated by distances larger than their transition wavelength.
Coherent scattering of light from ultracold atoms involves an exchange of energy and momentum introducing a wealth of nonlinear dynamical phenomena.As a prominent example, particles can spontaneously form stationary periodic configurations that simultaneously maximize the light scattering and minimize the atomic potential energy in the emerging optical lattice.Such self-ordering effects resulting in periodic lattices via bimodal symmetry breaking have been experimentally observed with cold gases and Bose-Einstein condensates (BECs) inside an optical resonator.Here, we study a new regime of periodic pattern formation for an atomic BEC in free space, driven by far off-resonant counterpropagating and noninterfering lasers of orthogonal polarization.In contrast to previous works, no spatial light modes are preselected by any boundary conditions and the transition from homogeneous to periodic order amounts to a crystallization of both light and ultracold atoms breaking a continuous translational symmetry.In the crystallized state the BEC acquires a phase similar to a supersolid with an emergent intrinsic length scale whereas the light field forms an optical lattice allowing phononic excitations via collective backscattering, which are gapped due to the infinte-range interactions.The system we study constitutes a novel configuration allowing the simulation of synthetic solid-state systems with ultracold atoms including long-range phonon dynamics.