Abstract
Coherent scattering of light from ultracold atoms involves an exchange of energy and momentum introducing a wealth of non-linear dynamical phenomena. As a prominent example particles can spontaneously form stationary periodic configurations which 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 non-interfering 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 back scattering, which are gapped due to the infinte-range interactions. The studied system constitutes a novel configuration allowing the simulation of synthetic solid state systems with ultracold atoms including long-range phonon dynamics.
Highlights
For a gas of pointlike particles off-resonantly illuminated by coherent light, the individual dipoles oscillate in phase, each emitting radiation in a characteristic pattern
If the motional degree of freedom is relevant on the considered time scales, any high-field-seeking particle will be drawn towards the corresponding local light field maxima, where in turn light scattering is enhanced
If we perform the standard thermodynamic limit N=L 1⁄4 const, the energy of the system diverges and the crystallization threshold vanishes. This divergence is an artifact of our model in which the light-mediated atom-atom interaction is of infinite range since the EM field is adiabatically adapting to the Bose-Einstein condensates (BECs) configuration
Summary
For a gas of pointlike particles off-resonantly illuminated by coherent light, the individual dipoles oscillate in phase, each emitting radiation in a characteristic pattern. In order to include such features, one necessarily needs to couple the particles to several electromagnetic modes, ideally a continuum This is the case in one-dimensional tapered optical nanofibers [34,35] or confocal cavities [36], where transversally driven atoms are predicted to spontaneously break the continuous symmetry into a crystal phase. The total optical potential for the BEC has two contributions: VðxÞ 1⁄4 VtrapðxÞ þ VoptðxÞ; ð2Þ representing the static trapping potential Vtrap and the longitudinal (along x) optical potential Vopt determined by the dynamical part of the injected and scattered EM field [see Eq (5)] This is due to the fact that no specific modes are selected and the fields can counterpropagate independently
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