We study a model describing $N$ identical bosonic atoms trapped in a double-well potential together with a single impurity atom, comparing and contrasting it throughout with the Dicke model. As the boson-impurity coupling strength is varied, there is
a symmetry-breaking pitchfork bifurcation which is analogous to the quantum phase transition occurring in the Dicke model. Through stability analysis around the bifurcation point, we show that the critical value of the coupling strength has the same dependence on the parameters as the critical coupling value in the Dicke model. We also show that, like the Dicke model, the mean-field dynamics go from being regular to chaotic above the bifurcation and macroscopic excitations of the bosons are observed. Overall, the boson-impurity system behaves like a poor mans version of the Dicke model.
Cold atoms, driven by a laser and simultaneously coupled to the quantum field of an optical resonator, can self-organize in periodic structures. These structures are supported by the optical lattice, which emerges from the laser light they scatter in
to the cavity mode, and form when the laser intensity exceeds a threshold value. We study theoretically the quantum ground state of these structures above the pump threshold of self-organization, by mapping the atomic dynamics of the self-organized crystal to a Bose-Hubbard model. We find that the quantum ground state of the self-organized structure can be the one of a Mott-insulator or a superfluid, depending on the pump strength of the driving laser. For very large pump strengths, where the intracavity intensity is maximum and one would expect a Mott-insulator state, we find intervals of parameters where the system is superfluid. These states could be realized in existing experimental setups.
We study systems of fully polarized ultracold atomic gases obeying Fermi statistics. The atomic transition interacts dispersively with a mode of a standing-wave cavity, which is coherently pumped by a laser. In this setup, the intensity of the intrac
avity field is determined by the refractive index of the atomic medium, and thus by the atomic density distribution. Vice versa, the density distribution of the atom is determined by the cavity field potential, whose depth is proportional to the intracavity field amplitude. In this work we show that this nonlinearity leads to an instability in the intracavity intensity that differs substantially from dispersive optical bistability, as this effect is already present in the regime, where the atomic dipole is proportional to the cavity field. Such instability is driven by the matter waves fluctuations and exhibits a peculiar dependence on the fluctuations in the atomic density distribution.
We investigate a paradigm example of cavity quantum electrodynamics with many body systems: an ultracold atomic gas inside a pumped optical resonator. In particular, we study the stability of atomic insulator-like states, confined by the mechanical p
otential emerging from the cavity field spatial mode structure. As in open space, when the optical potential is sufficiently deep, the atomic gas is in the Mott-like state. Inside the cavity, however, the potential depends on the atomic distribution, which determines the refractive index of the medium, thus altering the intracavity field amplitude. We derive the effective Bose-Hubbard model describing the physics of the system in one dimension and study the crossover between the superfluid -- Mott insulator quantum states. We determine the regions of parameters where the atomic insulator states are stable, and predict the existence of overlapping stability regions corresponding to competing insulator-like states. Bistable behavior, controlled by the pump intensity, is encountered in the vicinity of the shifted cavity resonance.
