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.
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.
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 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.
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 consider theoretically ultracold interacting bosonic atoms confined to quasi-one-dimensional ladder structures formed by optical lattices and coupled to the field of an optical cavity. The atoms can collect a spatial phase imprint during a cavity-assisted tunneling along a rung via Raman transitions employing a cavity mode and a transverse running wave pump beam. By adiabatic elimination of the cavity field we obtain an effective Hamiltonian for the bosonic atoms, with a self-consistency condition. Using the numerical density-matrix renormalization-group method, we obtain a rich steady-state diagram of self-organized steady states. Transitions between superfluid to Mott-insulating states occur, on top of which we can have Meissner, vortex liquid, and vortex lattice phases. Also a state that explicitly breaks the symmetry between the two legs of the ladder, namely, the biased-ladder phase, is dynamically stabilized. We investigate the influence that a trapping potential has on the stability of the self-organized phases.
We investigate fermionic atoms subjected to an optical lattice and coupled to a high finesse optical cavity with photon losses. A transverse pump beam introduces a coupling between the atoms and the cavity field. We explore the steady-state phase diagram taking fluctuations around the mean field of the atoms-cavity coupling into account. Our approach allows us to investigate both one- and higher-dimensional atomic systems. The fluctuations beyond mean field lead to an effective temperature that changes the nature of the self-organization transition. We find a strong dependence of the results on the atomic filling, in particular when contrasting the behavior at low filling and at half filling. At low filling, the transition to a self-organized phase takes place at a critical value of the pump strength. In the self-organized phase, the cavity field takes a finite expectation value and the atoms show a modulation in the density. Surprisingly, at even larger pump strengths a strongly nonmonotonous behavior of the temperature is found and hints toward effects of cavity cooling at many-body resonances. Additionally multiple self-organized stable solutions of the cavity field and the atoms occur, signaling the presence of a fluctuation-induced bistability, with the two solutions having different effective temperatures previously discussed by Tolle . []. In contrast, at half filling a bistable region arises at the self-organization transition already neglecting the fluctuations. The presence of the fluctuations induce an effective temperature, as at lower fillings, and change the behavior of the transition and the steady states drastically. We analyze the properties of the occurring steady states of the coupled atoms-cavity system.
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.