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Register a new userLoss of superfluidity by fermions in the boson Hubbard model on an optical lattice
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The experimentally observed loss of superfluidity by introducing fermions to the boson Hubbard system on an optical lattice is explained. We show that the virtual transitions of the bosons to the higher Bloch bands, coupled with the contact boson-fermion interactions of either sign, result in an effective increase of the boson on-site repulsion. If this renormalization of the on-site potential is dominant over the fermion screening of the boson interactions, the Mott insulating lobes of the Bose-Hubbard phase diagram will be enhanced for either sign of the boson-fermion interactions. We discuss implications for cold atom experiments where the expansion of the Mott lobes by fermions has been conclusively established.
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The study of superfluid fermion pairs in a periodic potential has important ramifications for understanding superconductivity in crystalline materials. Using cold atomic gases, various condensed matter models can be studied in a highly controllable environment. Weakly repulsive fermions in an optical lattice could undergo d-wave pairing at low temperatures, a possible mechanism for high temperature superconductivity in the cuprates. The lattice potential could also strongly increase the critical temperature for s-wave superfluidity. Recent experimental advances in the bulk include the observation of fermion pair condensates and high-temperature superfluidity. Experiments with fermions and bosonic bound pairs in optical lattices have been reported, but have not yet addressed superfluid behavior. Here we show that when a condensate of fermionic atom pairs was released from an optical lattice, distinct interference peaks appear, implying long range order, a property of a superfluid. Conceptually, this implies that strong s-wave pairing and superfluidity have now been established in a lattice potential, where the transport of atoms occurs by quantum mechanical tunneling and not by simple propagation. These observations were made for unitarity limited interactions on both sides of a Feshbach resonance. For larger lattice depths, the coherence was lost in a reversible manner, possibly due to a superfluid to insulator transition. Such strongly interacting fermions in an optical lattice can be used to study a new class of Hamiltonians with interband and atom-molecule couplings.
High order ring-exchange interactions are crucial for the study of quantum fluctuations on highly frustrated systems. We present the first exact quantum Monte Carlo study of a model of hard-core bosons with sixth order ring-exchange interactions on a two-dimensional kagome lattice. By using the Stochastic Green Function algorithm, we show that the system becomes unstable in the limit of large ring-exchange interactions. It undergoes a phase separation at all fillings, except at 1/3 and 2/3 fillings for which the superfluid density vanishes and an unusual mixed valence bond and charge density ordered solid is formed.
Motivated by the recent discovery of a spin liquid phase for the Hubbard model on the honeycomb lattice at half-filling, we apply both perturbative and non-perturbative techniques to derive effective spin Hamiltonians describing the low-energy physics of the Mott-insulating phase of the system. Exact diagonalizations of the so-derived models on small clusters are performed, in order to assess the quality of the effective low-energy theory in the spin-liquid regime. We show that six-spin interactions on the elementary loop of the honeycomb lattice are the dominant sub-leading effective couplings. A minimal spin model is shown to reproduce most of the energetic properties of the Hubbard model on the honeycomb lattice in its spin-liquid phase. Surprisingly, a more elaborate effective low-energy spin model obtained by a systematic graph expansion rather disagrees beyond a certain point with the numerical results for the Hubbard model at intermediate couplings.
In this work, we discuss the emergence of $p$-wave superfluids of identical fermions in 2D lattices. The optical lattice potential manifests itself in an interplay between an increase in the density of states on the Fermi surface and the modification of the fermion-fermion interaction (scattering) amplitude. The density of states is enhanced due to an increase of the effective mass of atoms. In deep lattices, for short-range interacting atoms, the scattering amplitude is strongly reduced compared to free space due to a small overlap of wavefunctions of fermions sitting in the neighboring lattice sites, which suppresses the $p$-wave superfluidity. However, we show that for a moderate lattice depth there is still a possibility to create atomic $p$-wave superfluids with sizable transition temperatures. The situation is drastically different for fermionic polar molecules. Being dressed with a microwave field, they acquire a dipole-dipole attractive tail in the interaction potential. Then, due to a long-range character of the dipole-dipole interaction, the effect of the suppression of the scattering amplitude in 2D lattices is absent. This leads to the emergence of a stable topological $p_x+ip_y$ superfluid of identical microwave-dressed polar molecules.
We study bosons in the first excited Bloch band of a double-well optical lattice, recently realized at NIST. By calculating the relevant parameters from a realistic nonseparable lattice potential, we find that in the most favorable cases the boson lifetime in the first excited band can be several orders of magnitude longer than the typical nearest-neighbor tunnelling timescales, in contrast to that of a simple single-well lattice. In addition, for sufficiently small lattice depths the excited band has minima at nonzero momenta incommensurate with the lattice period, which opens a possibility to realize an exotic superfluid state that spontaneously breaks the time-reversal, rotational, and translational symmetries. We discuss possible experimental signatures of this novel state.
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