Optical cavity QED provides a platform with which to explore quantum many-body physics in drivendissipative systems. Single-mode cavities provide strong, infinite-range photon-mediated interactions among intracavity atoms. However, these global all-to-all couplings are limiting from the perspective of exploring quantum many-body physics beyond the mean-field approximation. The present work demonstrates that local couplings can be created using multimode cavity QED. This is established through measurements of the threshold of a superradiant, self-organization phase transition versus atomic position. Specifically, we experimentally show that the interference of near-degenerate cavity modes leads to both a strong and tunable-range interaction between Bose-Einstein condensates (BECs) trapped within the cavity. We exploit the symmetry of a confocal cavity to measure the interaction between real BECs and their virtual images without unwanted contributions arising from the merger of real BECs. Atom-atom coupling may be tuned from short range to long range. This capability paves the way toward future explorations of exotic, strongly correlated systems such as quantum liquid crystals and driven-dissipative spin glasses.

We observe the joint spin-spatial (spinor) self-organization of a two-component BEC strongly coupled to an optical cavity. This unusual nonequilibrium Hepp-Lieb-Dicke phase transition is driven by an off-resonant two-photon Raman transition formed from a classical pump field and the emergent quantum dynamical cavity field. This mediates a spinor-spinor interaction that, above a critical strength, simultaneously organizes opposite spinor states of the BEC on opposite checkerboard configurations of an emergent 2D lattice. The resulting spinor density-wave polariton condensate is observed by directly detecting the atomic spin and momentum state and by holographically reconstructing the phase of the emitted cavity field. The latter provides a direct measure of the spin state, and a spin-spatial domain wall is observed. The photon-mediated spin interactions demonstrated here may be engineered to create dynamical gauge fields and quantum spin glasses. arXiv:1807.04915v1 [cond-mat.quant-gas]

Phase transitions, where observable properties of a many-body system change discontinuously, can occur in both open and closed systems. By placing cold atoms in optical cavities and inducing strong coupling between light and excitations of the atoms, one can experimentally study phase transitions of open quantum systems. Here we observe and study a non-equilibrium phase transition, the condensation of supermode-density-wave polaritons. These polaritons are formed from a superposition of cavity photon eigenmodes (a supermode), coupled to atomic density waves of a quantum gas. As the cavity supports multiple photon spatial modes and because the light–matter coupling can be comparable to the energy splitting of these modes, the composition of the supermode polariton is changed by the light–matter coupling on condensation. By demonstrating the ability to observe and understand density-wave-polariton condensation in the few-mode-degenerate cavity regime, our results show the potential to study similar questions in fully multimode cavities.

Sign-changing interactions constitute a crucial ingredient in the creation of frustrated many-body systems such as spin glasses. We present here the demonstration of a photon-mediated sign-changing interaction between Bose-Einstein condensed (BEC) atoms in a confocal cavity. The interaction between two atoms is of an unusual, nonlocal form proportional to the cosine of the inner product of the atoms' position vectors. This interaction arises from the differing Gouy phase shifts of the cavity's degenerate modes. Moreover, these Gouy phase anomalies induce an extra pattern of Z2-symmetry-breaking in the atomic density-wave self-ordering that arises from a nonequilibrium Dicke-type phase transition in the system. This state is detected via the holographic imaging of the cavity's superradiant emission. Together with Ref.[1], we explore this interaction's influence on superradiant phase transitions in multimode cavities. Employing this interaction in cavity QED spin systems may enable the creation of artificial spin glasses and quantum neural networks. arXiv:1810.11086v1 [cond-mat.quant-gas]

Optical cavities can induce photon-mediated interactions among intracavity-trapped atoms. Multimode cavities provide the ability to tune the form of these interactions, e.g., by inducing a nonlocal, sign-changing term to the interaction. By accounting for the Gouy phase shifts of the modes in a nearly degenerate, confocal, Fabry-Pérot cavity, we provide a theoretical description of this interaction, along with additional experimental confirmation to complement that presented in the companion paper, Ref. [1]. Furthermore, we show that this interaction should be written in terms of a complex order parameter, allowing for a U(1)-symmetry to emerge. This symmetry corresponds to the phase of the atomic density wave arising from self-organization when the cavity is transversely pumped above a critical threshold power. We theoretically and experimentally show how this phase depends on the position of the Bose-Einstein condensate (BEC) within the cavity and discuss mechanisms that break the U(1)-symmetry and lock this phase. We then consider alternative Fabry-Pérot multimode cavity geometries (i.e., beyond the confocal) and schemes with more than one pump laser and show that these provide additional capabilities for tuning the cavity-meditated interaction among atoms, including the ability to restore the U(1)-symmetry despite the presence of symmetry-breaking effects. These photon-mediated interactions may be exploited for realizing quantum liquid crystalline states and spin glasses using multimode optical cavities.