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arXiv:2502.00588 · Physical Review Letters

Structural Dynamics and Strong Correlations in Dynamical Quantum Optical Lattices

Adrián U. Ramírez-Barajas, Santiago F. Caballero-Benítez

Published Aug 18, 2025• 0 citations

Abstract

When placing an ultracold atomic gas inside a cavity, the light-matter coupling is enhanced and nonlinear atomic dynamics is generated, offering a promising platform for quantum simulation of models with short- and long-range interactions. Recently, superradiant self-organized phases for ultracold atomic gases inside a cavity, pumped by a blue detuned optical lattice, have been observed. Here, we explore the formation of quantum many-body phases of bosonic atoms inside an optical cavity, subject to transverse blue detuned pumping. We investigate the strongly interacting regime, which can be reached by tuning the s-wave scattering length using external fields. We analyze the interplay between superradiant self-organization with superfluid and Mott insulator phases, without the need of including higher lying bands, as the Wannier functions are dynamically linked to the cavity light via backaction. We observe different kinds of structural phase transitions driven by the light inside the cavity and the interplay with atomic collisions. We observe the mode softening at the critical points in the quantum phase transitions which can be measured in future experiments. We obtain our results within a full self-consistent theoretical framework, the light-matter density matrix renormalization group (DMRG), which employs the computation of light dependent Wannier functions for the full quantum optical lattice in combination with DMRG for the atomic dynamics. The methods introduced here can be used to analyze the effects of strong quantum correlations in strongly interacting light-matter systems.

DOI: 10.1103/gvm2-b46t

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We investigate harmonically trapped, laser-pumped bosons with infinite-range interactions induced by a dissipative high-finesse red-detuned optical cavity with numerical and analytical methods. We obtain multiple cavity and atomic observables as well as the full phase diagram of the system using the multiconfigurational time-dependent Hartree method for indistinguishable particles (MCTDH-X) approach. Besides the transition from an unorganized normal phase to a superradiant phase where the atoms self-organize, we focus on an in-depth investigation of the self-organized superfluid to self-organized Mott-insulator phase transition in the superradiant phase as a function of the cavity-atom coupling. The numerical results are substantiated by an analytical study of an effective Bose-Hubbard model. We numerically analyze cavity fluctuations and emergent strong correlations between atoms in the many-body state across the Mott transition via the atomic density distributions and Glauber correlation functions. Unexpectedly, the weak harmonic trap leads to features like a lattice switching between the two symmetry-broken

{\mathbb{Z}}_{2}

configurations of the untrapped system and a reentrance of superfluidity in the Mott-insulating phase. Our analytical considerations quantitatively explain the numerically observed correlation features.

We investigate the nonlinear light-matter interaction of a Bose-Einstein condensate trapped in an external periodic potential inside an optical cavity which is weakly coupled to vacuum radiation modes and driven by a transverse pump field. Based on a generalized Bose-Hubbard model which incorporates a single cavity mode, we include the collective backaction of the atoms on the cavity light field and determine the nonequilibrium quantum phases within the nonperturbative bosonic dynamical mean-field theory. With the system parameters adapted to recent experiments, we find a quantum phase transition from a normal phase to a self-organized superfluid phase, which is related to the Hepp-Lieb-Dicke superradiance phase transition. For even stronger pumping, a self-organized Mott insulator phase arises.

We numerically simulate strongly correlated ultracold bosons coupled to a high-finesse cavity field, pumped by a laser beam in the transverse direction. Assuming a weak

\mathit{classical}

optical lattice added in the cavity direction, we model this system by a generalized Bose-Hubbard model, which is solved by means of bosonic dynamical mean-field theory. The complete phase diagram is established, which contains two novel self-organized quantum phases, lattice supersolid and checkerboard solid, in addition to conventional phases such as superfluid and Mott insulator. At finite but low temperature, thermal fluctuations are found to enhance the buildup of the self-organized phases. We demonstrate that cavity-mediated long-range interactions can give rise to stable lattice supersolid and checkerboard solid phases even in the regime of strong

s

-wave scattering. In the presence of a harmonic trap, we discuss coexistence of these self-organized phases, as relevant to experiments.

Ultracold bosonic atoms in optical lattices self-organize into a variety of structural and quantum phases when placed into a single-mode cavity and pumped by a laser. Cavity optomechanical effects induce an atom density modulation at the cavity-mode wavelength that competes with the optical lattice arrangement. Simultaneously short-range interactions via particle hopping promote superfluid order such that a variety of structural and quantum coherent phases can occur. We analyze the emerging phase diagram in two dimensions by means of an extended Bose-Hubbard model using a local mean-field approach combined with a superfluid cluster analysis. For commensurate ratios of the cavity and external lattice wavelengths, the Mott insulator-superfluid transition is modified by the appearance of charge density wave and supersolid phases, at which the atomic density supports the buildup of a cavity field. For incommensurate ratios, the optomechanical forces induce the formation of Bose-glass and superglass phases, namely, nonsuperfluid and superfluid phases, respectively, displaying quasiperiodic density modulations, which in addition can exhibit structural and superfluid stripe formation. The onset of such structures is constrained by the on-site interaction and is favorable at fractional densities. Experimental observables are identified and discussed.

We study a transversely pumped atomic Bose-Einstein condensate coupled to a single-mode optical cavity, where effective atom-atom interactions are mediated by pump and cavity photons. A number of experiments and theoretical works have shown the formation of a superradiant state in this setup, where interference of pump and cavity light leads to an optical lattice in which atoms self-consistently organize. This self-organization has been extensively studied using the approximate Dicke model (truncating to two momentum states), as well as through numerical Gross-Pitaevskii simulations in one and two dimensions. Here, we perform a full mean-field analysis of the system, including all relevant atomic momentum states and the cavity field. We map out the steady-state phase diagram vs pump strength and cavity detuning, and provide an in-depth understanding of the instabilities that are linked to the emergence of spatiotemporal patterns. We find and describe parameter regimes where the mean field predicts bistability, regimes where the dynamics form chaotic trajectories, instabilities caused by resonances between normal mode excitations, and states with atomic dynamics but vanishing cavity field.

The superfluid to Mott insulator transition and the superradiant transition are textbook examples of quantum phase transition and coherent quantum optics, respectively. Recent experiments in ETH and Hamburg have succeeded in loading degenerate bosonic atomic gases in optical lattices inside a cavity, which enables the first experimental study of the interplay between these two transitions. In this Rapid Communication we present the theoretical phase diagram for the ETH Zurich experimental setup, and determine the phase boundaries and the orders of the phase transitions between the normal superfluid phase, the superfluid with superradiant light, the normal Mott insulator, and the Mott insulator with superradiant light. We find that in contrast to the second-order superradiant transition in a weakly interacting Bose condensate, strong correlations in the superfluid nearby a Mott transition can render the superradiant transition to a first-order one. Our results will stimulate further experimental studies of interactions between cavity light and strongly interacting quantum matter.