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Register a new userStrongly interacting fermions in an optical lattice
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We analyze a system of two-component fermions which interact via a Feshbach resonance in the presence of a three-dimensional lattice potential. By expressing a two-channel model of the resonance in the basis of Bloch states appropriate for the lattice, we derive an eigenvalue equation for the two-particle bound states which is nonlinear in the energy eigenvalue. Compact expressions for the interchannel matrix elements, numerical methods for the solution of the nonlinear eigenvalue problem, and a renormalization procedure to remove ultraviolet divergences are presented. From the structure of the two-body solutions we identify the relevant degrees of freedom which describe the resonance behavior in the lowest Bloch band. These degrees of freedom, which we call dressed molecules, form an effective closed channel in a many-body model of the resonance, the Fermi resonance Hamiltonian (FRH). It is shown how the properties of the FRH can be determined numerically by solving a projected lattice two-channel model at the two-particle level. As opposed to single-channel lattice models such as the Hubbard model, the FRH is valid for general s-wave scattering length and resonance width. Hence, the FRH provides an accurate description of the BEC-BCS crossover for ultracold fermions on an optical lattice.
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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 $t-J$ model, and the effective superexchange term, $J$, 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 on-site 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 develop a theory of weakly interacting fermionic atoms in shaken optical lattices based on the orbital mixing in the presence of time-periodic modulations. Specifically, we focus on fermionic atoms in circularly shaken square lattice with near resonance frequencies, i.e., tuned close to the energy separation between $s$-band and the $p$-bands. First, we derive a time-independent four-band effective Hamiltonian in the non-interacting limit. Diagonalization of the effective Hamiltonian yields a quasi-energy spectrum consistent with the full numerical Floquet solution that includes all higher bands. In particular, we find that the hybridized $s$-band develops multiple minima and therefore non-trivial Fermi surfaces at different fillings. We then obtain the effective interactions for atoms in the hybridized $s$-band analytically and show that they acquire momentum dependence on the Fermi surface even though the bare interaction is contact-like. We apply the theory to find the phase diagram of fermions with weak attractive interactions and demonstrate that the pairing symmetry is $s+d$-wave. Our theory is valid for a range of shaking frequencies near resonance, and it can be generalized to other phases of interacting fermions in shaken lattices.
Mott insulators with both spin and orbital degeneracy are pertinent to a large number of transition metal oxides. The intertwined spin and orbital fluctuations can lead to rather exotic phases such as quantum spin-orbital liquids. Here we consider two-component (spin 1/2) fermionic atoms with strong repulsive interactions on the $p$-band of the optical square lattice. We derive the spin-orbital exchange for quarter filling of the $p$-band when the density fluctuations are suppressed, and show it frustrates the development of long range spin order. Exact diagonalization indicates a spin-disordered ground state with ferro-orbital order. The system dynamically decouples into individual Heisenberg spin chains, each realizing a Luttinger liquid accessible at higher temperatures compared to atoms confined to the $s$-band.
Correlations between particles can lead to subtle and sometimes counterintuitive phenomena. We analyze one such case, occurring during the sudden expansion of fermions in a lattice when the initial state has a strong admixture of double occupancies. We promote the notion of quantum distillation: during the expansion, and in the presence of strongly repulsive interactions, doublons group together, forming a nearly ideal band insulator, which is metastable with a low entropy. We propose that this effect could be used for cooling purposes in experiments with two-component Fermi gases.
Engineered spin-orbit coupling (SOC) in cold atom systems can aid in the study of novel synthetic materials and complex condensed matter phenomena. Despite great advances, alkali atom SOC systems are hindered by heating from spontaneous emission, which limits the observation of many-body effects, motivating research into potential alternatives. Here we demonstrate that SOC can be engineered to occur naturally in a one-dimensional fermionic 87Sr optical lattice clock (OLC). In contrast to previous SOC experiments, in this work the SOC is both generated and probed using a direct ultra-narrow optical clock transition between two electronic orbital states. We use clock spectroscopy to prepare lattice band populations, internal electronic states, and quasimomenta, as well as to produce SOC dynamics. The exceptionally long lifetime of the excited clock state (160 s) eliminates decoherence and atom loss from spontaneous emission at all relevant experimental timescales, allowing subsequent momentum- and spin-resolved in situ probing of the SOC band structure and eigenstates. We utilize these capabilities to study Bloch oscillations, spin-momentum locking, and Van Hove singularities in the transition density of states. Our results lay the groundwork for the use of OLCs to probe novel SOC phases of matter.
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