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.

Supersolids are characterized by the counterintuitive coexistence of superfluid and crystalline order. Here we study a supersolid phase emerging in the steady state of a driven-dissipative system. We consider a transversely pumped Bose-Einstein condensate trapped along the axis of a ring cavity and coherently coupled to a pair of degenerate counterpropagating cavity modes. Above a threshold pump strength the interference of photons scattered into the two cavity modes results in an emergent superradiant lattice, which spontaneously breaks the continuous translational symmetry towards a periodic atomic pattern. The crystalline steady state inherits the superfluidity of the Bose-Einstein condensate, thus exhibiting genuine properties of a supersolid. A gapless collective Goldstone mode correspondingly appears in the superradiant phase, which can be nondestructively monitored via the relative phase of the two cavity modes on the cavity output. Despite cavity-photon losses the Goldstone mode remains undamped, indicating the robustness of the supersolid phase.

We investigate the dynamics of a Bose-Einstein condensate interacting with two non-interfering and counterpropagating modes of a ring resonator. Superfluid, supersolid and dynamic phases are identified experimentally and theoretically. The supersolid phase is obtained for sufficiently equal pump strengths for the two modes. In this regime we observe the emergence of a steady state with crystalline order, which spontaneously breaks the continuous translational symmetry of the system. The supersolidity of this state is demonstrated by the conservation of global phase coherence at the superfluid to supersolid phase transition. Above a critical pump asymmetry the system evolves into a dynamic run-away instability commonly known as collective atomic recoil lasing. We present a phase diagram and characterize the individual phases by comparing theoretical predictions with experimental observations.

Collective coherent scattering of laser light by an ensemble of polarizable point particles creates long-range interactions, whose properties can be tailored by the choice of injected laser powers, frequencies, and polarizations. We use a transfer matrix approach to study the forces induced by non-interfering fields of orthogonal polarization or different frequencies in a 1D geometry, and find long-range self-ordering of particles without a prescribed order. Adjusting the laser frequencies and powers allows one to tune the inter-particle distances and provides a wide range of possible dynamical couplings not accessible in usual standing wave geometries with prescribed order. In this work, we restrict the examples to two frequencies and polarizations, but the framework also allows one to treat multicolour light beams with random phases. These dynamical effects should be observable in existing experimental setups with effective 1D geometries, such as atoms or nanoparticles coupled to the field of an optical nanofibre or transversely trapped in counter-propagating Gaussian beams.

We explore the density and spin self-ordering of driven spin-1/2 collisionless fermionic atoms coupled to the electromagnetic fields of a ring resonator. The two spin states are two-photon Ramancoupled via a pair of degenerate counterpropagating cavity modes and two transverse pump fields. In this one-dimensional configuration the coupled atom-field system possesses a continuous U(1) translational symmetry and a discrete Z 2 spin inversion symmetry. At half filling for sufficiently strong pump strengths, the combined U(1)×Z 2 symmetry is spontaneously broken at the onset of a superradiant phase transition to a state with self-ordered density and spin structures. We predominately find an antiferromagnetic lattice order at the cavity wavelength. The self-ordered states exhibit unexpected positive momentum pair correlations between fermions with opposite spin. These strong cavity-mediated correlations vanish at higher pump strength.