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arXiv:0705.3754 · Journal of Physics B Atomic Molecular and Optical Physics

Resonant Feshbach scattering of fermions in one-dimensional optical lattices

M Grupp, R. Walser, Wolfgang P. Schleich, A. Muramatsu, Martin Weitz

Published Jun 20, 2007• 17 citations
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Abstract

We consider Feshbach scattering of fermions in a one-dimensional optical lattice. By formulating the scattering theory in the crystal momentum basis, one can exploit the lattice symmetry and factorize the scattering problem in terms of centre-of-mass and relative momentum in the reduced Brillouin zone scheme. Within a single-band approximation, we can tune the position of a Feshbach resonance with the centre-of-mass momentum due to the non-parabolic form of the energy band.

DOI
10.1088/0953-4075/40/13/014

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We consider Feshbach scattering of fermions in a one-dimensional optical lattice. By formulating the scattering theory in the crystal momentum basis, one can exploit the lattice symmetry and factorize the scattering problem in terms of centre-of-mass and relative momentum in the reduced Brillouin zone scheme. Within a single-band approximation, we can tune the position of a Feshbach resonance with the centre-of-mass momentum due to the non-parabolic form of the energy band.
To test effective Hamiltonians for strongly interacting fermions in an optical lattice, we numerically find the energy spectrum for two fermions interacting across a Feshbach resonance in a double-well potential. From the spectrum, we determine the range of detunings for which the system can be described by an effective lattice model, and how the model parameters are related to the experimental parameters. We find that for a range of strong interactions the system is well described by an effective ttt-JJJ model, and the effective superexchange term, JJJ, can be smoothly tuned through zero on either side of unitarity. Right at and around unitarity, an effective one-band general Hubbard model is appropriate, with a finite and small onsite energy, due to a lattice-induced anharmonic coupling between atoms at the scattering threshold and a weakly bound Feshbach molecule in an excited center-of-mass state.
We numerically study the problem of two fermions in a three-dimensional optical lattice interacting via a zero-range Feshbach resonance and display the dispersions of the bound states as a two-particle band structure with unique features compared to typical single-particle band structures. We show that the exact two-particle solutions of a projected Hamiltonian may be used to define an effective two-channel, few-band model for the low-energy, low-density physics of many fermions at arbitrary s-wave scattering length. Our method applies to resonances of any width and can be adapted to multichannel situations or higher-ℓ pairing. In strong contrast to usual Hubbard physics, we find that pair hopping is significantly altered by strong interactions and the presence of the lattice, and the lattice induces multiple molecular bound states.
We study a spin-polarized degenerate Fermi gas interacting via a p-wave Feshbach resonance in an optical lattice. The strong confinement available in this system allows us to realize one- and two-dimensional gases and, therefore, to restrict the asymptotic scattering states of atomic collisions. When aligning the atomic spins along (or perpendicular to) the axis of motion in a one-dimensional gas, scattering into channels with the projection of the angular momentum of /m/ = 1 (or m = 0) can be inhibited. In two and three dimensions, we observe the doublet structure of the p-wave Feshbach resonance. For both the one-dimensional and the two-dimensional gases, we find a shift of the position of the resonance with increasing confinement due to the change in collisional energy. In a three-dimensional optical lattice, the losses on the Feshbach resonance are completely suppressed.
We calculate the spectrum for three atoms in a one-dimensional harmonic well near an sss-wave Feshbach resonance using a two-channel model to describe the Feshbach physics. This is relevant to the study of cold 40K^{40}\text{K}40K atoms trapped in a one-dimensional optical lattice. Our results indicate that, for this one-dimensional system, one- and two-channel models will differ close to the Feshbach resonance, although the two theories would converge in the limit of strong Feshbach coupling. We also find level crossings in the low-energy spectrum of a single well with three atoms that may lead to quantum phase transition for an optical lattice of many wells. We discuss the stability of the system to a phase with nonuniform density.
In this paper, we study the orbital Feshbach resonance of ultracold two-electron 173 Yb Fermi gas in a one-dimensional optical lattice. We consider a two-band model under the assumptions of a local-density approximation for the optical lattice potential and a mean-field approximation for the intraband Cooper pairings. We get three crucially important properties for the system, the superfluid-Landau–Fermi-liquid (LFL) crossover corresponding to the tunneling energy, the particle condensation in the momentum space, and the superfluid-LFL phase transition corresponding to the temperature. We explain how to realize and manipulate these properties.
We propose a scheme to realize the itinerant ferromagnetism of two-component cold fermionic atoms in the ppp-orbital bands in optical lattices. The band flatness in the two-dimensional honeycomb lattice dramatically amplifies the interaction effect, driving the ferromagnetic transition even with a relatively weak repulsive interaction. This scheme has the advantage that the stability of the system can be maintained without causing decay to the molecular state as one approaches the Feshbach resonance from the side with the positive scattering length. Experimental signatures and detections are also discussed.