The successful emulation of the Hubbard model [1] in optical lattices [2,3] has stimulated world wide efforts to extend their scope to also capture more complex, incompletely understood scenarios of many-body physics [4,5]. Unfortunately, for bosons, Feynmans fundamental "nonode" theorem [6] under very general circumstances predicts a positive definite ground state wave function with limited relevance for manybody systems of interest.A promising way around Feynmans statement is to consider higher bands in optical lattices with more than one dimension [7], where the orbital degree of freedom with its intrinsic anisotropy due to multiple orbital orientations gives rise to a structural diversity, highly relevant, for example, in the area of strongly correlated electronic matter. In homogeneous two-dimensional optical lattices, lifetimes of excited bands on the order of a hundred milliseconds are possible [8,9] but the tunneling dynamics appears not to support cross-dimensional coherence [8,10]. Here we report the first observation of a superfluid in the P -band of a bipartite optical square lattice with S-orbits and P -orbits arranged in a chequerboard pattern. This permits us to establish full cross-dimensional coherence with a life-time of several ten milliseconds. Depending on a small adjustable anisotropy of the lattice, we can realize real-valued striped superfluid order parameters with different orientations P x ± P y or a complex-valued P x ± iP y order parameter, which breaks time reversal symmetry and resembles the π-flux model proposed in the context of high temperature superconductors [11]. Our experiment opens up the realms of orbital superfluids to investigations with optical lattice models.Orbital optical lattices permit to prepare exciting new many-body scenarios with relevant counterparts in the area of strongly correlated electronic matter, where the orbital degree of freedom with its rich structure of possible orientations gives rise to a wealth of interesting phenomena. For example, in the transition-metal oxides orbital physics is believed to be a key element for understanding their metal-insulator transitions, superconductivity, or colossal magnetoresistance. Recent theoretical proposals have considered, for example, the formation of multiflavor and multiorbital systems [8,9,12,13], supersolid quantum phases in cubic lattices [14,15], quantum stripe ordering in triangular lattices [16], or Wigner crystallization in honeycomb lattices [17]. The recent prediction, that the life time of atoms in higher Bloch bands can be unexpectedly long, has further strengthened the potential significance of orbital physics in optical lattices [8,9]. Previous experiments have demonstrated that the excitation of higher Bloch bands is in fact possible [18,19]. In a recent experiment, investigating a homogeneous quasi one-dimensional (1D) lattice of bosons, transient partial coherence in the P -band has been observed [10]. In an extension to a two-dimensional square lattice, however, no cross-coherence could be est...

The Dicke model with a weak dissipation channel is realized by coupling a Bose-Einstein condensate to an optical cavity with ultranarrow bandwidth. We explore the dynamical critical properties of the Hepp-Lieb-Dicke phase transition by performing quenches across the phase boundary. We observe hysteresis in the transition between a homogeneous phase and a self-organized collective phase with an enclosed loop area showing power-law scaling with respect to the quench time, which suggests an interpretation within a general framework introduced by Kibble and Zurek. The observed hysteretic dynamics is well reproduced by numerically solving the mean-field equation derived from a generalized Dicke Hamiltonian. Our work promotes the understanding of nonequilibrium physics in open many-body systems with infinite range interactions.dynamical phase transition | critical behavior | Dicke model | quantum gas | cavity QED A lthough equilibrium phases in quantum many-body systems have been explored for a long time with great success, nonequilibrium phenomena in such systems are far less well understood (1). A paradigm for exploring nonequilibrium dynamics is the quench scenario, where a system parameter is subjected to a sudden change between two values associated with different equilibrium phases. Quantum degenerate atomic gases with their unique degree of control are particularly adapted for experimental quench studies (2, 3). For isolated quantum manybody systems a wealth of theoretical and experimental investigations of quench dynamics has appeared recently (4-11). A natural extension of such studies is to consider driven open systems, where dynamical equilibrium states can arise via a competition between dissipation and driving, and nonequilibrium transitions between such phases can occur as a function of some external control parameter (12-15). A nearly ideal experimental platform for this endeavor are quantum degenerate atomic gases subjected to optical high-finesse cavities, where the usual extensive control in cold gas systems can be combined with a precisely engineered coupling to the external bath of vacuum radiation modes (16).Here, we study a dynamical phase transition in the open Dicke model emulated in an atom-cavity system prepared near zero temperature. The Dicke model is a paradigmatic scenario of quantum many-body physics, still subject to intensive research despite a history more than half a century long (17-28). It describes the interaction of N two-level atoms with a common mode of the electromagnetic radiation field. Hepp and Lieb already pointed out in the 1970s that upon varying the coupling strength, this model possesses a second-order equilibrium quantum phase transition between a homogeneous 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 (19,22). It has been early suspected that the critical properties of the externally pumped open Dicke model should give rise to nonlinear hysteretic ...

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...

Optical lattices play a versatile role in advancing our understanding of correlated quantum matter. The recent implementation of orbital degrees of freedom in chequerboard and hexagonal optical lattices opens up a new thrust towards discovering novel quantum states of matter, which have no prior analogs in solid state electronic materials. Here, we demonstrate that an exotic topological semimetal emerges as a parity-protected gapless state in the orbital bands of a two-dimensional fermionic optical lattice. The new quantum state is characterized by a parabolic band-degeneracy point with Berry flux $2\pi$, in sharp contrast to the $\pi$ flux of Dirac points as in graphene. We prove that the appearance of this topological liquid is universal for all lattices with D$_4$ point group symmetry as long as orbitals with opposite parities hybridize strongly with each other and the band degeneracy is protected by odd parity. Turning on inter-particle repulsive interactions, the system undergoes a phase transition to a topological insulator whose experimental signature includes chiral gapless domain-wall modes, reminiscent of quantum Hall edge states.Comment: 6 pages, 3 figures and Supplementary Informatio