We study fermionic atoms of three different internal quantum states (colors) in an optical lattice, which are interacting through attractive on site interactions, U<0. Using a variational calculation for equal color densities and small couplings, |U|<|UC|, a color superfluid state emerges with a tendency to domain formation. For |U|>|UC|, triplets of atoms with different colors form singlet fermions (trions). These phases are the analogies of the color superconducting and baryonic phases in QCD. In ultracold fermions, this transition is found to be of second order. Our results demonstrate that quantum simulations with ultracold gases may shed light on outstanding problems in quantum field theory.

We show that a time-dependent magnetic field inducing a periodically modulated scattering length may lead to interesting novel scenarios for cold gases in optical lattices, characterized by a nonlinear hopping depending on the number difference at neighboring sites. We discuss the rich physics introduced by this hopping, including pair superfluidity, exactly defect-free Mott-insulator states for finite hopping, and pure holon and doublon superfluids. We also address experimental detection, showing that the introduced nonlinear hopping may lead in harmonically trapped gases to abrupt drops in the density profile marking the interface between different superfluid regions.PACS numbers: 37.10. Jk, 67.85.Hj, 73.43.Nq Ultracold atoms in optical lattices formed by laser beams provide an excellent environment for studying lattice models of general relevance in condensed-matter physics, and in particular, variations of the celebrated Hubbard model [1,2]. Cold lattice gases allow for an unprecedented degree of control of various experimental parameters, even in real time. In particular, interparticle interactions can be changed by means of Feshbach resonances [3]. Moreover, recent milestone achievements allow for site-resolved detection, permitting the study of in situ densities [4,5], and more involved measurements, as that of nonlocal parity order [6].The modulation of the lattice parameters in real time opens interesting possibilities of control and quantum engineering. In particular, a periodic lattice shaking translates by means of Floquet's theorem [7,8] into a modified hopping constant [9], which may even reverse its sign as shown in experiments [10,11]. This technique has been employed to drive the Mott-insulator (MI) to superfluid (SF) transition [12], and to simulate frustrated classical magnetism [13]. Recent experiments have explored as well the fascinating perspectives offered by periodically driven lattices in strongly correlated gases [14,15].The effective Hubbard-like models describing ultracold lattice gases are typically characterized by a hopping independent of the number of particles at the sites. This is, however, not necessarily the case. Multiband physics [16][17][18] and dipolar interactions for sufficiently large dipole moments [19] may lead to occupation-dependent hopping. A major consequence of nonlinear hopping is the possibility to observe pair superfluidity (PSF) [19,20], which resembles pairing in SF Fermi gases, although for bosons superfluidity exists as well without pairing.In this Letter, we consider a cold lattice gas in the presence of a periodically modulated magnetic field. In the vicinity of a Feshbach resonance, this field induces modulated interparticle interactions [21]. Interestingly, Ref.[22] has shown that periodic modulations of the interaction strength may lead to a many-body coherent destruction of tunneling in two-mode Bose-Einstein condensates. As shown below, the generalization of this effect to lattice gases leads under proper conditions to an effective Hubbard-like ...

As highly tunable interacting systems, cold atoms in optical lattices are ideal to realize and observe negative absolute temperatures, T<0. We show theoretically that, by reversing the confining potential, stable superfluid condensates at finite momentum and T<0 can be created with low entropy production for attractive bosons. They may serve as "smoking gun" signatures of equilibrated T<0. For fermions, we analyze the time scales needed to equilibrate to T<0. For moderate interactions, the equilibration time is proportional to the square of the radius of the cloud and grows with increasing interaction strengths as atoms and energy are transported by diffusive processes.

To investigate ultracold fermionic atoms of three internal states (colors) in an optical lattice, subject to strong attractive interaction, we study the attractive three-color Hubbard model in infinite dimensions by using a variational approach. We find a quantum phase transition between a weakcoupling superconducting phase and a strong-coupling trionic phase where groups of three atoms are bound to a composite fermion. We show how the Gutzwiller variational theory can be reformulated in terms of an effective field theory with three-body interactions and how this effective field theory can be solved exactly in infinite dimensions by using the methods of dynamical mean field theory.

We present a detailed study of the finite temperature dynamical properties of the quantum Potts model in one dimension. Quasiparticle excitations in this model have internal quantum numbers, and their scattering matrix deep in the gapped phases is shown to take a simple exchange form in the perturbative regimes. The finite temperature correlation functions in the quantum critical regime are determined using conformal invariance, while far from the quantum critical point we compute the decay functions analytically within a semiclassical approach of Sachdev and Damle [K. Damle and S. Sachdev, Phys. Rev. B 57, 8307 (1998)]. As a consequence, decay functions exhibit a diffusive character. We also provide robust arguments that our semiclassical analysis carries over to very low temperatures even in the vicinity of the quantum phase transition. Our results are also relevant for quantum rotor models, antiferromagnetic chains, and some spin ladder systems.

We consider a cloud of fermionic atoms in an optical lattice described by a Hubbard model with an additional linear potential. While homogeneous interacting systems mainly show damped Bloch oscillations and heating, a finite cloud behaves differently: It expands symmetrically such that gains of potential energy at the top are compensated by losses at the bottom. Interactions stabilize the necessary heat currents by inducing gradients of the inverse temperature 1/T , with T < 0 at the bottom of the cloud. An analytic solution of hydrodynamic equations shows that the width of the cloud increases with t 1/3 for long times consistent with results from our Boltzmann simulations. 05.60.Gg, 05.70.Ln Measuring the conductivity is probably the most fundamental experiment when investigating the properties of a metal. The influence of constant forces arising from electric or gravitational fields on quantum particles in periodic potentials is an old and well studied problem [1]. For free particles, Bragg scattering from the periodic potential induces Bloch oscillations [1][2][3] . While difficult to observe in solids due to disorder and interactions, such Bloch oscillations have been measured in semiconductor superlattices [4] and for ultracold bosonic atoms in optical lattices [2,3] created by standing waves of lasers, e.g., to determine the masses of atoms with high precision [5].Recent experimental developments make it also possible to load fermionic ultracold atoms in the lowest band of optical lattices. Using an equal population of two hyperfine levels and Feshbach resonances (e.g., of 40 K) it became possible to realize the Hubbard model (see below) with tunable interaction strength. While the temperatures in current experiments are still rather high, it was possible to see [6,7] signatures of the onset of a metal-insulator transition induced by strong interactions. Constant external forces can be realized using either gravitation or accelerated lattices [2] (after a careful elimination of other confining potentials as in Ref. [8]).The Hubbard model in an electric or gravitational field has attracted previously considerable attention [9][10][11][12][13][14][15][16], partially motivated by the question how large electric fields can lead to a breakdown of the Mott insulating state. When discussing the physics of such systems either for weak or strong interactions, it is important to take energy conservation into account. While real solids are usually probed in contact with some thermal bath, ultracold atoms provide almost ideal realizations of closed quantum systems implying severe restrictions on the dynamics. For a translationally invariant, infinite system one expects that even weak interactions lead to a damping of the Bloch oscillations (at least in the absence of superfluidity and in dimensions larger than 1). During this process, potential energy is converted into heat. As long as there is no coupling to an external bath which can transport the heat away, the system gets hotter and hotter. It finally reaches ...

We apply a semiclassical approach to express finite temperature dynamical correlation functions of gapped spin models analytically. We show that the approach of [Á. Rapp, G. Zaránd, Phys. Rev. B 74, 014433 (2006)] can also be used for the S = 1 antiferromagnetic Heisenberg chain, whose lineshape can be measured experimentally. We generalize our calculations to O(N ) quantum spin models and the sine-Gordon model in one dimension, and show that in all these models, the finite temperature decay of certain correlation functions is characterized by the same universal semiclassical relaxation function. PACS. 75.10.Pq Spin chain models -05.30.-d Quantum statistical mechanics -05.50.+q Lattice theory and statistics

We perform a variational Gutzwiller calculation to study the ground state of the repulsive SU(3) Hubbard model on the Bethe lattice with infinite coordination number. We construct a ground-state phase diagram focusing on phases with a two-sublattice structure and find five relevant phases: (1) a paramagnet, (2) a completely polarized ferromagnet, (3) a two-component antiferromagnet where the third component is depleted, (4) a two-component antiferromagnet with a metallic third component (an "orbital selective" Mott insulator), and (5) a density-wave state where two components occupy dominantly one sublattice and the last component the other one. First-order transitions between these phases lead to phase separation. A comparison of the SU(3) Hubbard model to the better-known SU(2) model shows that the effects of doping are completely different in the two cases.