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arXiv:cond-mat/0306497 · Physical Review A

Fermionic atoms in optical superlattices

B. Paredes, C. Tejedor, J. I. Cirac

Published Jun 1, 2005• 37 citations
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Abstract

Fermionic atoms in an optical superlattice can realize a very peculiar Anderson lattice model in which impurities interact with each other through a discretized set of delocalized levels. We show that under these finite-size features strongly correlated phases appear. By tuning the parameters of the superlattice two different phases could be observed: a Kondo-singlet phase in which each impurity forms a singlet with the Fermi level of its neighboring conducting islands, and a magnetic phase in which long range magnetic order is established between the impurities mediated by the intermediate islands. The interplay between these two phenomena depends on the parity of the number of particles per discretized set. We show how Kondo-induced resonances of measurable size can be observed through the atomic interference pattern.

DOI
10.1103/physreva.71.063608

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Fermionic atoms in an optical superlattice can realize a very peculiar Anderson lattice model in which impurities interact with each other through a discretized set of delocalized levels. We show that under these finite-size features strongly correlated phases appear. By tuning the parameters of the superlattice two different phases could be observed: a Kondo-singlet phase in which each impurity forms a singlet with the Fermi level of its neighboring conducting islands, and a magnetic phase in which long range magnetic order is established between the impurities mediated by the intermediate islands. The interplay between these two phenomena depends on the parity of the number of particles per discretized set. We show how Kondo-induced resonances of measurable size can be observed through the atomic interference pattern.
Ultracold atoms in optical lattices provide a versatile platform for studying many-body physics in a defect-free system with tunable parameters. For the analog quantum simulation of the Fermi-Hubbard model, fermionic atoms take on the role of the valence electrons and optical lattices provide the periodic potential in place of the solid-state crystal. The dynamics in the system are described by the tunneling amplitude t between neighboring lattice sites and the interaction energy U of two particles occupying the same lattice site. With the depth of the optical lattices and an external magnetic field, both parameters can be tuned to access a wide range of regimes. Two superimposed lattices with different lattice periods form an optical superlattice, where the most common configuration is a bichromatic superlattice with lattice periods different by a factor of two. Depending on the lattice depths and the relative phase of the lattices, the bichromatic superlattice potential ranges from an array of weakly-coupled double wells to a continuous lattice potential with a staggered energy offset. We developed a calibration technique for measuring the depth of an optical lattice with local resolution. The band structure of the optical lattice is probed by modulating the lattice depth and exciting the atoms to higher bands. However, compared to resolving the band occupations in a time-of-flight measurement, we further excite the atoms to an untrapped band to deplete the optical lattice along equipotential lines where the modulation frequency is resonant with the local band transitions. From the profile of the lattice depth, we obtain the calibration factor for the power regulation, the waist of the underlying lattice beams and the position of the lattice axis. This technique combines several calibration measurements, thereby reducing the measurement time and enabling an automation of the lattice alignment. For the bichromatic superlattice we realized an active stabilization of the superlattice phase that enables long-term measurements with a precise control over the superlattice phase. The instability of the superlattice phase is a result of the different refractive indices for the two lattices in air and the optical elements along the optical path. Using environmental sensors, we monitor the temperature, the pressure, and the relative humidity to apply the expected correction to the superlattice phase. The stabilized superlattice phase enabled the investigation of Floquet-driven double wells by modulating the energy offset through the superlattice phase. We used a near-resonant driving frequency with respect to the interaction energy to enhance the pair-tunneling amplitude in doubly-occupied double wells compared to static double wells and compared to the tunneling amplitude in singly-occupied double wells.
This dissertation summarizes my recent work regarding systems of strongly interacting fermionic atoms in optical lattices. This work addresses the combination of two experimental techniques that have been the subject of much recent research in ultracold atom physics. One is the use of optical lattices, which provide a means to realize diverse interaction configurations within a clean, controllable system. The other is the use of magnetically tunable Feshbach resonances to control the strength of the interatomic interaction. Together, these techniques offer the possibility of an experimental realization of many important model Hamiltonians of condensed matter physics, and may also lead to the discovery of new physics. Recent study of this system has shown that strong interactions near Feshbach resonance will lead to the population of multiple lattice bands, and that collisions between atoms on neighboring sites cannot be neglected. These effects lead to a complicated Hamiltonian, but one which can be simplified to an effective single-band model equivalent to the generalized Hubbard model (GHM), which is an extension of the Hubbard model that includes correlated hopping terms. My main results concern the study of this model. The strong correlations between the particles make it difficult to definitively determine the many body physics of the GHM. As a first approach to understanding the GHM in optical lattices, I focus mainly on cases where the problem is greatly simplified by allowing interactions among only small groups of lattice sites. This restriction can be implemented in experiments using an optical superlattice potential. Our results include a proposed scheme (based on double-well superlattices) to empirically verify that the GHM describes this system and to directly measure the various parameters of this model. Other results include exact solutions on four-site square plaquettes, which demonstrate that d-wave excitations can occur in the low-energy states. By using a superlattice to give an array of weakly coupled plaquettes, one can thus produce a d-wave superfluid state. This is of relevance to the study of high-Tc superconductors, although I note certain key differences between the sort of d-wave superfluid described here and that of the superconductors.
We consider the behavior of Fermi atoms on optical superlattices with two-well structure for each node. Fermions on such lattices serve as an analog simulator of the Fermi-type Hamiltonian. We derive a mapping between fermion quantum ordering in the optical superlattices and the spin-orbital physics developed for degenerate ddd-electron compounds. The appropriate effective spin-orbital model appears to be a modification of the Kugel-Khomskii Hamiltonian. We show how different ground states of this Hamiltonian correspond to particular spin-pseudospin arrangement patterns of fermions on the lattice. The dependence of the fermion arrangement on phases of complex hopping amplitudes is illustrated.
We previously proposed [K. G. L. Pedersen, B. M. Andersen, G. M. Bruun, O. F. Sylju\aa{}sen, and A. S. S\o{}rensen, Phys. Rev. A 84, 041603 (2011)] a method to utilize a temporally dependent superlattice potential to mediate spin-selective transport and thereby probe long- and short-range magnetic correlations in optical lattices. Specifically, this can be used for detecting antiferromagnetic ordering in repulsive fermionic optical lattice systems, but more generally it can serve as a means of directly probing correlations among the atoms by measuring the mean value of an observable, the number of double occupied sites. Here we provide a detailed investigation of the physical processes that limit the effectiveness of this ``conveyer belt method.'' Furthermore, we propose a simple way to improve the procedure, resulting in an essentially perfect (error-free) probing of the magnetic correlations. These results shows that suitably constructed superlattices constitute a promising way of manipulating atoms of different spin species as well as probing their interactions.
The exchange coupling between quantum mechanical spins lies at the origin of quantum magnetism. We report on the observation of nearest-neighbor magnetic spin correlations emerging in the many-body state of a thermalized Fermi gas in an optical lattice. The key to obtaining short-range magnetic order is a local redistribution of entropy within the lattice structure. This is achieved in a tunable-geometry optical lattice, which also enables the detection of the magnetic correlations. We load a low-temperature two-component Fermi gas with repulsive interactions into either a dimerized or an anisotropic simple cubic lattice. For both systems the correlations manifest as an excess number of singlets as compared to triplets consisting of two atoms with opposite spins. For the anisotropic lattice, we determine the transverse spin correlator from the singlet-triplet imbalance and observe antiferromagnetic correlations along one spatial axis. Our work paves the way for addressing open problems in quantum magnetism using ultracold fermions in optical lattices as quantum simulators.