It is well known that the bosonic Hubbard model possesses a Mott insulator phase. Likewise, it is known that the Dicke model exhibits a self-organized superradiant phase. By implementing an optical lattice inside of a high finesse optical cavity both models are merged such that an extended Hubbard model with cavity-mediated infinite range interactions arises. In addition to a normal superfluid phase, two superradiant phases are found, one of them coherent and hence superfluid and one incoherent Mott insulating.PACS numbers: 42.50.Gy, 42.60.Lh, The Dicke model, describing the interaction of N twolevel atoms with a common mode of the electromagnetic radiation field, is a fundamental paradigm of quantum many-body physics, which despite its long history is still the subject of intensive theoretical research [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. As one of its prominent features it exhibits a second order quantum phase transition between a normal phase, in which each atom interacts separately with the radiation mode, and a collective phase in which all atomic dipoles align to form a macroscopic dipole moment [3,6]. Only recently, a weekly dissipative variant of this model has been experimentally realized close to zero temperature [17,18] by implementing Bose-Einstein condensates inside high finesse optical cavities, which has triggered wide-spread renewed interest [19].A similarly elementary model of quantum many-body physics is the Hubbard model, which gives an approximate description of the dynamics of particles on a lattice in terms of the competition of hopping between nearest neighbor sites and on-site collisions [20,21]. The Bose- Hubbard model -its bosonic variant -has been originally motivated in the context of superfluid Helium but has received renewed interest after its realization in optical lattices [22,23]. At zero temperature, this model is known to possess a quantum phase transition from a superfluid to a Mott insulating ground state [24] which was confirmed experimentally [23].In the present work we consider an extended scenario, subsequently referred to as the open Dicke-Hubbard model, which encompasses the physics of both the open Dicke model and the bosonic Hubbard model. Related extensions of Hubbard models have raised wide-spread interest recently due to predictions of highly unconventional phenomena, as for example overlapping, competing Mott-insulator states and strong atom field entanglement [25][26][27][28]. We study a Bose-Einstein condensate subject to an external lattice potential and interacting with a single light mode of a high finesse optical cavity. In accordance with previous theoretical predictions [29,30] evidence is found for the existence of three distinct quantum states in the ground state phase diagram: a homogeneous superfluid (HSF) phase, a self-organized superfluid (SSF) phase associated with a spontaneously emerging density grating and a self-organized Mott-insulating (SMI) phase. The phase boundary between the SSF and the SMI phase is observed via a sudd...

[1] The Thunderstorm Energetic Radiation Array (TERA) is located at the University of Florida, Florida Tech International Center for Lightning Research and Testing (ICLRT) at Camp Blanding, Florida. The array includes forty-five 7.6-cm-diameter NaI/photomultiplier tube detectors enclosed in 24 separate aluminum boxes that shield the detectors from light, moisture, and RF noise. The array covers the $1 km 2 ICLRT facility, centered on the rocket launch tower, used to trigger lightning. From 2005 to 2007, TERA recorded seven rocket-triggered lightning flashes. In this paper we present an analysis of the X-ray emission of three of these flashes. The X-ray emission is observed to occur during the dart leader phase of each stroke, just prior to the time of the return stroke. Significant X-rays are observed on all the detectors to a distance of 500 m from the lightning channel for times up to 200 ms prior to the start of the return stroke. Using Monte Carlo simulations to model the X-ray propagation, we find that the energetic electrons that emit the X-rays have a characteristic energy of about 1 MeV for one particular dart-stepped leader event. The X-ray emission for all three events has a radial fall off proportional to [exp (Àr/120)]/r and is most consistent with the energetic source electrons being emitted isotropically from the leader. It is also found that the X-ray and energetic electron luminosities of the leader channel decreases with increasing height above the ground. These results help shed light onto the mechanism for producing energetic radiation from lightning. For instance, a characteristic energy of 1 MeV is not consistent with the relativistic runaway electron avalanche mechanism, suggesting that so-called cold runaway electrons, produced by very strong electric fields, dominate the production of the X-rays.

Spin-polarized attractive Fermi gases in one-dimensional (1D) optical lattices are expected to be remarkably good candidates for the observation of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We model these systems with an attractive Hubbard model with population imbalance. By means of the density-matrix renormalization-group method, we compute the pairing correlations as well as the static spin and charge structure factors in the whole range from weak to strong coupling. We demonstrate that pairing correlations exhibit quasi-long-range order and oscillations at the wave number expected from the FFLO theory. However, we also show by numerically computing the mixed spin-charge static structure factor that charge and spin degrees of freedom appear to be coupled already for a small imbalance. We discuss the consequences of this coupling for the observation of the FFLO phase, as well as for the stabilization of the quasi-long-range order into long-range order by coupling many identical 1D systems, such as in quasi-1D optical lattices

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 the 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 back action of the atoms on the cavity light field and determine the nonequilibrium quantum phases within the non-perturbative 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.

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