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arXiv:2312.10502 · Physical Review Letters

Self-Organized Cavity Bosons beyond the Adiabatic Elimination Approximation

Giuliano Orso, Jakub Zakrzewski, Piotr Deuar

Published May 6, 2025• 7 citations
arXivHTMLPDF

Abstract

The longtime behavior of weakly interacting bosons moving in a two-dimensional optical lattice and coupled to a lossy cavity is investigated numerically via the truncated Wigner method, which allows us to take into full account the dynamics of the cavity mode, quantum fluctuations, cavity-boson correlations, and self-organization of individual runs. We first compare our results for small systems with quasi-exact calculations based on quantum trajectories, finding a remarkably good agreement for experimentally relevant boson fillings that improves further with system size. For large systems, we observe metastability at very long times and superfluid quasi-long range order, in sharp contrast with the true long range order found in the ground state of the approximate Bose-Hubbard model with extended interactions, obtained by adiabatically eliminating the cavity field. As the strength of the light-matter coupling increases, the system first becomes supersolid at the Dicke superradiant transition and then turns into a charge-density wave via the Berezinskii-Kosterlitz-Thouless mechanism. The two phase transitions are characterized via an accurate finite-size scaling analysis.

DOI
10.1103/physrevlett.134.183405

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The longtime behavior of weakly interacting bosons moving in a two-dimensional optical lattice and coupled to a lossy cavity is investigated numerically via the truncated Wigner method, which allows us to take into full account the dynamics of the cavity mode, quantum fluctuations, cavity-boson correlations, and self-organization of individual runs. We first compare our results for small systems with quasi-exact calculations based on quantum trajectories, finding a remarkably good agreement for experimentally relevant boson fillings that improves further with system size. For large systems, we observe metastability at very long times and superfluid quasi-long range order, in sharp contrast with the true long range order found in the ground state of the approximate Bose-Hubbard model with extended interactions, obtained by adiabatically eliminating the cavity field. As the strength of the light-matter coupling increases, the system first becomes supersolid at the Dicke superradiant transition and then turns into a charge-density wave via the Berezinskii-Kosterlitz-Thouless mechanism. The two phase transitions are characterized via an accurate finite-size scaling analysis.
We investigate the full quantum evolution of ultracold interacting bosonic atoms on a chain and coupled to an optical cavity. Extending the time-dependent matrix product state techniques to capture the global coupling to the cavity mode and the open nature of the cavity, we examine the long time behavior of the system beyond the mean-field elimination of the cavity field. We benchmark the newly developed method by computing the von Neumann entanglement entropy of the quantum trajectories. We investigate the many body steady states and the self-organization transition for a wide range of parameters. We show that in the self-organized phase the steady state consists in a mixture of the mean-field predicted density wave states and excited states with additional defects. For large dissipation strengths we develop a variant of the many-body adiabatic elimination technique and obtain a steady state with a fully mixed atomic sector. We observe numerically the crossover from the density wave state towards this mixed state.
We investigate the full quantum evolution of ultracold interacting bosonic atoms on a chain and coupled to an optical cavity. Extending the time-dependent matrix product state techniques and the many-body adiabatic elimination technique to capture the global coupling to the cavity mode and the open nature of the cavity, we examine the long time behavior of the system beyond the mean-field elimination of the cavity field. We investigate the many-body steady states and the self-organization transition for a wide range of parameters. We show that in the self-organized phase the steady state consists in a mixture of the mean-field predicted density wave states and excited states with additional defects. In particular, for large dissipation strengths a steady state with a fully mixed atomic sector is obtained crucially different from the predicted mean-field state.
The coupling of cold atoms to the radiation field within a high-finesse optical resonator, an optical cavity, induces long-range interactions which can compete with an underlying optical lattice. The interplay between short- and long-range interactions gives rise to new phases of matter including supersolidity (SS) and density waves (DW), and interesting quantum dynamics. Here it is shown that for hard-core bosons in one dimension the ground state phase diagram and the quantum relaxation after sudden quenches can be calculated exactly in the thermodynamic limit. Remanent DW order is observed for quenches from a DW ground state into the superfluid (SF) phase below a dynamical transition line. After sufficiently strong SF to DW quenches beyond a static metastability line DW order emerges on top of remanent SF order, giving rise to a dynamically generated SS state. Our method to handle infinite- and short-range interactions in the infinite system size limit opens a way to solve exactly other Hamiltonians with infinite- and short-range interactions as well.
We present two approaches capable of describing the dynamics of an interacting many-body system on a lattice coupled globally to a dissipative bosonic mode.Physical realizations are, for example, ultracold atom gases in optical lattice coupled to a photonic mode of an optical cavity or electronic gases in solids coupled to THz cavity fields.The first approach, applicable for large dissipation strengths and any system size, is a variant of the many-body adiabatic elimination method for investigating the long-time dynamics of the system.The second method extends the time-dependent matrix product techniques to capture the global coupling of the interacting particles to the bosonic mode and its open nature.It gives numerically exact results for small to intermediate system sizes.As a benchmark for our methods we perform the full quantum evolution of a Bose-Hubbard chain coupled to a cavity mode.We show that important deviations from the mean-field behavior occur when considering the full atoms cavity coupling [C.
We report on the first experimental realization of the Dicke quantum phase transition realized in the quantum motion of a Bose–Einstein condensate coupled to an optical cavity. Conceptually, the transition is driven by cavity-mediated long-range interactions, giving rise to the emergence of a self-organized supersolid phase. The Dicke phase transition, predicted in 1973, has not been demonstrated experimentally before this work, both due to fundamental and technological reasons. These challenges have been overcome in the present thesis by employing atomic momentum states of a Bose-Einstein condensate, which are coupled via two-photon Raman transitions involving a cavity photon and a free-space pump photon. This open-system implementation of the Dicke model allows to tune all relevant parameters and offers a unique detection scheme to monitor the manybody system in real time. We demonstrate that the phase transition is accompanied by a macroscopically occupied cavity field and a striking change in the atomic momentum distribution, due to spontaneous self-organization of the atomic density on a checkerboard lattice. The boundary of the transition is mapped out by scanning two parameters of the Dicke model, to reveal a phase diagram in close agreement with the model description. Two different ordered configurations are allowed in the superradiant phase, giving rise to the concept of spontaneous symmetry breaking at the phase transition. We experimentally distinguish the symmetry-broken states and study the origin of the symmetry-breaking process. The finite spatial extension of our system induces a small symmetry-breaking field which changes randomly on each experimental realization. The influence of this field is studied and shown to diminish upon dynamically crossing the transition point with increasing transition rates.
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.