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Register a new userSuperfluidity of fermions with repulsive on-site interaction in an anisotropic optical lattice near a Feshbach resonance
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We present a numerical study on ground state properties of a one-dimensional (1D) general Hubbard model (GHM) with particle-assisted tunnelling rates and repulsive on-site interaction (positive-U), which describes fermionic atoms in an anisotropic optical lattice near a wide Feshbach resonance. For our calculation, we utilize the time evolving block decimation (TEBD) algorithm, which is an extension of the density matrix renormalization group and provides a well-controlled method for 1D systems. We show that the positive-U GHM, when hole-doped from half-filling, exhibits a phase with coexistence of quasi-long-range superfluid and charge-density-wave orders. This feature is different from the property of the conventional Hubbard model with positive-U, indicating the particle-assisted tunnelling mechanism in GHM brings in qualitatively new physics.
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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.
Quantum lattice solitons in a system of two ultracold bosons near Feshbach resonance are investigated. It is shown that their binding energy, effective mass, and spatial width, can be manipulated varying the detuning from the Feshbach resonance. In the case of attractive atomic interactions, the molecule creation stabilizes the solitons. In the case of repulsive interactions, the molecule creation leads to the possibility of existence of bright solitons in some interval of detunings. Due to quantum fluctuations the soliton width is a random quantity. Its standard deviation is larger than the mean value for such a small number of particles.
Interacting Fermi gas provides an ideal model system to understand unconventional pairing and intertwined orders relevant to a large class of quantum materials. Rydberg-dressed Fermi gas is a recent experimental system where the sign, strength, and range of the interaction can be controlled. The interaction in momentum space has a negative minimum at $q_c$ inversely proportional to the characteristic length-scale in real space, the soft-core radius $r_c$. We show theoretically that single-component (spinless) Rydberg-dressed Fermi gas in two dimensions has a rich phase diagram with novel superfluid and density wave orders due to the interplay of the Fermi momentum $p_F$, interaction range $r_c$, and interaction strength $u_0$. For repulsive bare interactions $u_0>0$, the dominant instability is $f$-wave superfluid for $p_Fr_clesssim 2$, and density wave for $p_Fr_cgtrsim 4$. The $f$-wave pairing in this repulsive Fermi gas is reminiscent of the conventional Kohn-Luttinger mechanism, but has a much higher $T_c$. For attractive bare interactions $u_0<0$, the leading instability is $p$-wave pairing. The phase diagram is obtained from functional renormalization group that treats all competing many-body instabilities in the particle-particle and particle-hole channels on equal footing.
We present a model space particle-hole Greens function calculation for the quadrupole excitations of cold Fermi gas near Feshbach resonance using a simple model where atoms are confined in a harmonic oscillator potential. Both the Tamm-Dancoff and random phase approximations are employed. By summing up exactly the ladder diagrams between a pair of interacting atoms to all orders, we obtain a renormalized atomic interaction which has well defined and identical limits as the scattering length tends to $pm infty$. The experimentally observed abrupt rise in the excitation spectrum and its associated large decay width are satisfactorily reproduced by our calculation.
We explore theoretically the novel superfluidity of harmonically-trapped polarized ultracold fermionic atoms in a two-dimensional (2D) optical lattice by solving the Bogoliubov-de Gennes equations. The pairing amplitude is found to oscillate along the radial direction at low particle density and along the angular direction at high density. The former is consistent with the existing experiments and the latter is a newly predicted Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, which can be tested in experiments.
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