Ultracold bosonic gases coupled to an optical cavity mode
Ultracold atoms coupled to a photonic mode of an optical cavity show fascinating phenomena such as the Dicke phase transition. This is a self-organized phase transition in which the atoms spontaneously order into a checkerboard density pattern and the photonic mode becomes occupied due to the feedback mechanism between the atoms and the photonic mode. In this project we will investigate bosonic atoms which are coupled to photonic modes and are additionally confined to optical lattice structures. We will mainly focus on a novel coupling dominantly to the tunneling process of the atoms with or without spatially dependent phase imprint which has been proposed by the PI. We expect interesting phases to occur such as the self-organization of complex Mott-insulating and superfluid phases or in the presence of a phase imprint, Meissner and vortex phases.
The full solution of the dynamics of the combined atom-cavity system is very demanding mainly due to three reasons: (i) the strongly correlated nature of the interacting bosonic atoms in optical lattices, (ii) the coupling of the spatially extended cavity mode to the atoms, which can induce effective, long-range interactions between the atoms, and (iii) the dissipative nature of the cavity mode by the leaking of the photons out of the cavity due to imperfect mirrors. We describe the combined and dissipative system by a Markovian master equation with a Lindblad dissipator. In order to determine the resulting dynamics we will employ different approaches. In a first approach, we will reduce the model by adiabatically eliminating the cavity mode to an effective interacting bosonic model – with long-range processes – subjected to a self-consistency condition. For the solution of this self-consistent model we will develop a self-consistent implementation of the matrix product state (MPS) algorithm and the quantum Monte-Carlo method in collaboration with project P6. The second approach aims at a full numerical simulation in quasi-one-dimensional systems. The implementation of a time-dependent MPS taking into account the dissipative and extended cavity mode with a large local Hilbert space is one of the main challenges of the project.