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Register a new userEmergent and broken symmetries of atomic self-organization arising from Gouy phase shifts in multimode cavity QED
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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-Perot 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-Perot 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.
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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 cavitys degenerate modes. Moreover, these Gouy phase anomalies induce an extra pattern of Z_2-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 cavitys superradiant emission. Together with Ref. [1], we explore this interactions 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.
Optical cavity QED provides a platform with which to explore quantum many-body physics in driven-dissipative 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 present a novel cavity QED system in which a Bose-Einstein condensate (BEC) is trapped within a high-finesse optical cavity whose length may be adjusted to access both single-mode and multimode configurations. We demonstrate the coupling of an atomic ensemble to the cavity in both configurations. The atoms are confined either within an intracavity far-off-resonance optical dipole trap (FORT) or a crossed optical dipole trap via transversely oriented lasers. Multimode cavity QED provides fully emergent and dynamical optical lattices for intracavity BECs. Such systems will enable explorations of quantum soft matter, including superfluid smectics, superfluid glasses, and spin glasses as well as neuromorphic associative memory.
We investigate the mean-field phase diagram of the Bose-Hubbard model with infinite-range interactions in two dimensions. This model describes ultracold bosonic atoms confined by a two-dimensional optical lattice and dispersively coupled to a cavity mode with the same wavelength as the lattice. We determine the ground-state phase diagram for a grand-canonical ensemble by means of analytical and numerical methods. Our results mostly agree with the ones reported in Dogra et al. [PRA 94, 023632 (2016)], and have a remarkable qualitative agreement with the quantum Monte Carlo phase diagrams of Flottat et al. [PRB 95, 144501 (2017)]. The salient differences concern the stability of the supersolid phases, which we discuss in detail. Finally, we discuss differences and analogies between the ground state properties of strong long-range interacting bosons with the ones predicted for repulsively interacting dipolar bosons in two dimensions.
We study information scrambling, as diagnosed by the out-of-time order correlations (OTOCs), in a system of large spins collectively interacting via spatially inhomogeneous and incommensurate exchange couplings. The model is realisable in a cavity QED system in the dispersive regime. Fast scrambling, signalled by an exponential growth of the OTOCs, is observed when the couplings do not factorise into the product of a pair of local interaction terms, and at the same time the state of the spins points initially coplanar to the equator of the Bloch sphere. When one of these conditions is not realised, OTOCs grow algebraically with an exponent sensitive to the orientation of the spins in the initial state. The impact of initial conditions on the scrambling dynamics is attributed to the presence of a global conserved quantity, which critically slows down the evolution for initial states close to the poles of the Bloch sphere.
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