A continuous time cluster algorithm for two-level systems coupled to a dissipative bosonic bath is presented and applied to the sub-Ohmic spin-boson model. When the power s of the spectral function Jomega proportional, variant omegas is smaller than 1/2, the critical exponents are found to be classical, mean-field like. Potential sources for the discrepancy with recent renormalization group predictions are traced back to the effect of a dangerously irrelevant variable.

We determine the quantum ground-state properties of ultracold bosonic atoms interacting with the mode of a high-finesse resonator. The atoms are confined by an external optical lattice, whose period is incommensurate with the cavity mode wave length, and are driven by a transverse laser, which is resonant with the cavity mode. While for pointlike atoms photon scattering into the cavity is suppressed, for sufficiently strong lasers quantum fluctuations can support the build-up of an intracavity field, which in turn amplifies quantum fluctuations. The dynamics is described by a Bose-Hubbard model where the coefficients due to the cavity field depend on the atomic density at all lattice sites. Quantum Monte Carlo simulations and mean-field calculations show that for large parameter regions cavity backaction forces the atoms into clusters with a checkerboard density distribution. Here, the ground state lacks superfluidity and possesses finite compressibility, typical of a Bose-glass. This system constitutes a novel setting where quantum fluctuations give rise to effects usually associated with disorder.PACS numbers: 03.75. Hh, 05.30.Jp, 32.80.Qk, 42.50.Lc Bragg diffraction is a manifestation of the waveproperties of light and a powerful probe of the microscopic structure of a medium: Bragg peaks are intrinsically related to the existence of spatial order of the scatterers composing a medium and provide a criterion for the existence of long-range order [1]. Bragg diffraction of light by atoms in optical lattices has been measured for various geometries and settings, from gratings of laser-cooled atoms [2-5] to ultracold bosons in the Mott-Insulator (MI) phase [6]. In most of these setups the backaction of light on the atomic medium, due to the mechanical effects of atom-photon interactions, is usually negligible, while photon recoil can give rise to visible effects in the spectrum of the diffracted light [7].Recent work proposed to use high-finesse optical resonators to enhance light scattering into one spatial direction, increasing the collection efficiency and thereby suppressing diffusion related to photon scattering [8]. For appropriate geometries, properties of the medium's quantum state can be revealed by measuring the light at the cavity output [7,8]. These proposals assume that backaction of the cavity field on the atoms can be discarded. Such an assumption is, however, not valid in the regime considered in Refs. [9][10][11][12][13][14]: Here, the strong coupling between cavity and atoms can induce the formation of stable Bragg gratings in cold [9,10] and ultracold atomic gases [11][12][13][14] that coherently scatter light from a transverse laser into the cavity mode. This phenomenon occurs when the intensity of the pump exceeds a certain threshold [10,11,13,15]. At ultralow temperatures the self-organized medium is a supersolid [13], while for larger pump intensities incompressible phases are expected [16].Let us now assume that the atoms are inside a highfinesse standing-wave cavity and form a periodic ...

We consider multiple non-interacting quantum mechanical two-level systems coupled to a common bosonic bath and study its quantum phase transition with Monte Carlo simulations using a continuous imaginary time cluster algorithm. The common bath induces an effective ferromagnetic interaction between the otherwise independent two-level systems, which can be quantified by an effective interaction strength. For degenerate energy levels above a critical value of the bath coupling strength α all two-level systems freeze into the same state and the critical value α c decreases asymptotically as 1/N with increasing N. For a finite number, N, of two-level systems the quantum phase transition (at zero temperature) is in the same universality class as the single spin-boson model, in the limit N → ∞ the system shows mean-field critical behavior independent of the power of the spectral function of the bosonic bath. We also study the influence of a spatial separation of the spins in a bath of bosonic modes with linear dispersion relation on the location and characteristics of the phase transition as well as on correlations between the two-level systems.

Ultracold bosonic atoms are confined by an optical lattice inside an optical resonator and interact with a cavity mode, whose wave length is incommensurate with the spatial periodicity of the confining potential. We predict that the intracavity photon number can be significantly different from zero when the atoms are driven by a transverse laser whose intensity exceeds a threshold value and whose frequency is suitably detuned from the cavity and the atomic transition frequency. In this parameter regime the atoms form clusters in which they emit in phase into the cavity. The clusters are phase locked, thereby maximizing the intracavity photon number. These predictions are based on a Bose-Hubbard model, whose derivation is here reported in detail. The BoseHubbard Hamiltonian has coefficients which are due to the cavity field and depend on the atomic density at all lattice sites. The corresponding phase diagram is evaluated using Quantum Monte Carlo simulations in onedimension and mean-field calculations in two dimensions. Where the intracavity photon number is large, the ground state of the atomic gas lacks superfluidity and possesses finite compressibility, typical of a Bose-glass.

We investigate the response of two-dimensional pattern-forming systems with a broken up-down symmetry, such as chemical reactions, to spatially resonant forcing and propose related experiments. The nonlinear behavior immediately above threshold is analyzed in terms of amplitude equations suggested for a 1:2 and 1:1 ratio between the wavelength of the spatial periodic forcing and the wavelength of the pattern of the respective system. Both sets of coupled amplitude equations are derived by a perturbative method from the Lengyel-Epstein model describing a chemical reaction showing Turing patterns, which gives us the opportunity to relate the generic response scenarios to a specific pattern-forming system. The nonlinear competition between stripe patterns and distorted hexagons is explored and their range of existence, stability, and coexistence is determined. Whereas without modulations hexagonal patterns are always preferred near onset of pattern formation, single-mode solutions (stripes) are favored close to threshold for modulation amplitudes beyond some critical value. Hence distorted hexagons only occur in a finite range of the control parameter and their interval of existence shrinks to zero with increasing values of the modulation amplitude. Furthermore, depending on the modulation amplitude, the transition between stripes and distorted hexagons is either subcritical or supercritical.