Self-trapping of bosons and fermions in optical lattices

We theoretically investigate the enhanced localization of bosonic atoms by fermionic atoms in three-dimensional optical lattices and find a self-trapping of the bosons for attractive boson-fermion interaction. Because of this mutual interaction, the fermion orbitals are substantially squeezed, which results in a strong deformation of the effective potential for bosons. This effect is enhanced by an increasing bosonic filling factor leading to a large shift of the transition between the superfluid and the Mott-insulator phase. We find a nonlinear dependency of the critical potential depth on the boson-fermion interaction strength. The results, in general, demonstrate the important role of higher Bloch bands for the physics of attractively interacting quantum gas mixtures in optical lattices and are of direct relevance to recent experiments with 87Rb-40K mixtures, where a large shift of the critical point has been found.     

Wave propagation in axion electrodynamics

In this paper, the axion contribution to the electromagnetic wave propagation is studied. First we show how the axion electrodynamics model can be embedded into a premetric formalism of Maxwell electrodynamics. In this formalism, the axion field is not an arbitrary added Chern–Simon term of the Lagrangian, but emerges in a natural way as an irreducible part of a general constitutive tensor. We show that in order to represent the axion contribution to the wave propagation it is necessary to go beyond the geometric approximation, which is usually used in the premetric formalism. We derive a covariant dispersion relation for the axion modified electrodynamics. The wave propagation in this model is studied for an axion field with timelike, spacelike and null derivative covectors. The birefringence effect emerges in all these classes as a signal of Lorentz violation. This effect is however completely different from the ordinary birefringence appearing in classical optics and in premetric electrodynamics. The axion field does not simple double the ordinary light cone structure. In fact, it modifies the global topological structure of light cones surfaces. In CFJ-electrodynamics, such a modification results in violation of causality. In addition, the optical metrics in axion electrodynamics are not pseudo-Riemannian. In fact, for all types of the axion field, they are even non-Finslerian.     

Local quantum criticality in confined fermions on optical lattices

Using quantum Monte Carlo simulations, we show that the one-dimensional fermionic Hubbard model in a harmonic potential displays quantum critical behavior at the boundaries of a Mott-insulating region. A local compressibility defined to characterize the Mott-insulating phase has a nontrivial critical exponent. Both the local compressibility and the variance of the local density show universality with respect to the confining potential. We determine a generic phase diagram, which allows the prediction of the phases to be observed in experiments with ultracold fermionic atoms trapped on optical lattices.     

Stability of superflow for ultracold fermions in optical lattices

We investigate the stability of superflow of paired fermions in an optical lattice. We show that there are two distinct dynamical instabilities which limit the superflow in this system. One dynamical instability occurs when the superfluid stiffness becomes negative; this evolves, with increasing pairing interaction, from the fermion pair breaking instability to the well-known dynamical instability of lattice bosons. The second, more interesting, dynamical instability is marked by the emergence of a transient atom density wave. Both dynamical instabilities can be experimentally accessed by tuning the pairing interaction and the fermion density.     

Phase diagram of two-component dipolar fermions in one-dimensional optical lattices

We theoretically map out the ground state phase diagram of interacting dipolar fermions in one-dimensional lattice. Using a bosonization theory in the weak coupling limit at half filing, we show that one can construct a rich phase diagram by changing the angle between the lattice orientation and the polarization direction of the dipoles. In the strong coupling limit, at a general filing factor, we employ a variational approach and find that the emergence of a Wigner crystal phases. The structure factor provides clear signatures of the particle ordering in the Wigner crystal phases.     

Interaction-induced adiabatic cooling and antiferromagnetism of cold fermions in optical lattices

We propose an interaction-induced cooling mechanism for two-component cold fermions in an optical lattice. It is based on an increase of the spin entropy upon localization, an analogue of the Pomeranchuk effect in liquid helium 3. We discuss its application to the experimental realization of the antiferromagnetic phase. We illustrate our arguments with dynamical mean-field theory calculations.     

Simulating Dirac fermions with Abelian and non-Abelian gauge fields in optical lattices

In this work we present an optical lattice setup to realize a full Dirac Hamiltonian in 2+1 dimensions. We show how all possible external potentials coupled to the Dirac field can arise from perturbations of the existing couplings of the honeycomb lattice pattern. This greatly simplifies the proposed implementations, requiring only spatial modulations of the intensity of the laser beams to induce complex non-Abelian potentials. We finally suggest several experiments to observe the properties of the quantum field theory in the setup.     

Quantum simulation of the Hubbard model with ultracold fermions in optical lattices

Ultracold atomic gases provide a fantastic platform to implement quantum simulators and investigate a variety of models initially introduced in condensed matter physics or other areas. One of the most promising applications of quantum simulation is the study of strongly correlated Fermi gases, for which exact theoretical results are not always possible with state-of-the-art approaches. Here, we review recent progress of the quantum simulation of the emblematic Fermi–Hubbard model with ultracold atoms. After introducing the Fermi–Hubbard model in the context of condensed matter, its implementation in ultracold atom systems, and its phase diagram, we review landmark experimental achievements, from the early observation of the onset of quantum degeneracy and superfluidity to the demonstration of the Mott insulator regime and the emergence of long-range anti-ferromagnetic order. We conclude by discussing future challenges, including the possible observation of high-$T_{\mathrm{c}}$ superconductivity, transport properties, and the interplay of strong correlations and disorder or topology.     

Wilson and Kadowaki-Woods ratios in heavy fermions

Recently we have shown that a one-parameter scaling, , describes the physical behavior of several heavy fermions in a region of their phase diagram. In this paper we fully characterize this region, obtaining the uniform susceptibility, the resistivity and the specific heat in terms of the coherence temperature . This allows for an explicit evaluation of the Wilson and the Kadowaki-Woods ratios in this regime. These quantities turn out to be independent of the distance to the quantum critical point (QCP). The theory of the one-parameter scaling corresponds to a local interacting model. Although spatial correlations are irrelevant in this case, time fluctuations are critically correlated as a consequence of the quantum character of the transition. Received 23 December 1998 and Received in final form 10 June 1999     

Wilson fermions in a two-dimensional model

Wilson's action for fermions on a lattice is compared to the continuum action in a model obtained from the chiral Gross-Neveu model by performing a chiral transformation. The local definition of the axial current leads to two anomalies unrelated by the constraint of Lorentz invariance. In the large-N limit, the mass counterterm of the action is determined; this term is unnecessary in the Osterwalder-Seiler regularization. An expansion in the fermion propagator and in the axial current coupling may be formulated and summed to all orders for large N.     

Spins and fermions on arbitrary lattices

It is proved that the system of free fermions on arbitrary lattices is equivalent to the set of locally interacting constrained spins. The fermionic counterpart of the unconstrained spin system is also derived. The generalization to the interacting theories is possible.     

The sigma-model with Wilson lattice fermions

The σ-model with Wilson fermions is considered in one-loop lattice perturbation theory and in the hopping-parameter expansion at large bare couplings. Chiral-symmetry restoration in the large cut-off limit of perturbation theory is only possible if asymmetric counterterms are added to the lattice action. In the hopping-parameter expansion at infinitely large bare Yukawa coupling, dynamical parity doubling of the fermion occurs.     

Improved lattice action for Wilson fermions

An improved lattice action for gauge theories with Wilson fermions is presented.