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Physical Review A

Frustrated tunneling of ultracold atoms in a state-dependent optical lattice

Xiang-Fa Zhou, Zhixin Chen, Zheng-Wei Zhou, Yongsheng Zhang, Guang‐Can Guo

Published Feb 9, 2010• 5 citations
Publisher

Abstract

We propose a general method to realize frustrated tunneling of ultracold atoms in a state-dependent optical lattice. Two typical lattice configurations are considered, the square lattice with competing interaction and the kagom\'e lattice with geometrical frustration. The ideal can be extended to implement frustrated tunneling of ultracold atoms in various geometries, which enable us to investigate the physics of frustration in both bosonic and spin systems. We study the mean-field phase diagrams of the considered models and the experimental situations are also discussed.

DOI
10.1103/physreva.81.021602

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We propose a general method to realize frustrated tunneling of ultracold atoms in a state-dependent optical lattice. Two typical lattice configurations are considered, the square lattice with competing interaction and the kagom'e lattice with geometrical frustration. The ideal can be extended to implement frustrated tunneling of ultracold atoms in various geometries, which enable us to investigate the physics of frustration in both bosonic and spin systems. We study the mean-field phase diagrams of the considered models and the experimental situations are also discussed.
Geometric frustration is a phenomenon where local energy constraints cannot be simultaneously satisfied because of geometric reasons. This leads to a manifold of degenerate ground states in which ordering can be highly nontrivial and exotic phases of matter could emerge. In a kagome lattice, both interaction energies of spins and kinetic energies of particles can be frustrated. In the latter case, a single-particle band structure with a flat (dispersionless) energy band results.In this dissertation, we report our experimental studies of interacting bosonic systems in kagome lattices. Such studies are performed with a quantum simulator based on ultracold atoms in optical lattices. We describe upgrades and development of the apparatus that constructs optical kagome lattices in our experiment. We briefly discuss results of an experiment studying the Bose-Hubbard model in a trimerized kagome lattice. We then report the details of an experiment investigating the interplay of kinetic frustration and interactions by probing the band structure of an optical kagome lattice with interacting ultracold bosonic atoms. Finally, we propose experimental ideas for exploring the properties of the singular band touching point in the kagome flat band.
We realize a two-dimensional kagome lattice for ultracold atoms by overlaying two commensurate triangular optical lattices generated by light at the wavelengths of 532 and 1064 nm. Stabilizing and tuning the relative position of the two lattices, we explore different lattice geometries including a kagome, a one-dimensional stripe, and a decorated triangular lattice. We characterize these geometries using Kapitza-Dirac diffraction and by analyzing the Bloch-state composition of a superfluid released suddenly from the lattice. The Bloch-state analysis also allows us to determine the ground-state distribution within the superlattice unit cell. The lattices implemented in this work offer a near-ideal realization of a paradigmatic model of many-body quantum physics, which can serve as a platform for future studies of geometric frustration.
We propose to realize the anisotropic triangular-lattice Bose-Hubbard model with positive tunneling matrix elements by using ultracold atoms in an optical lattice dressed by a fast lattice oscillation. This model exhibits frustrated antiferromagnetism at experimentally feasible temperatures; it interpolates between a classical rotor model for weak interaction, and a quantum spin-1/2 XYXYXY-model in the limit of hard-core bosons. This allows to explore experimentally gapped spin liquid phases predicted recently [Schmied et al., New J. Phys. {\bf 10}, 045017 (2008)].
We propose a scheme to implement an optical kagome lattice for ultracold atoms with controllable s-wave interactions between nearest neighbor sites and a gauge potential. The atoms occupy three different internal atomic levels with electromagnetically induced coupling between the levels. We show that by appropriately shifting the triangular lattice potentials, experienced by atoms in different levels, the kagome lattice can be realized using only two standing waves, generating a highly frustrated quantum system for the atoms.
We propose and experimentally explore a method for realizing frustrated lattice models using a Bose-Einstein condensate held in an optical square lattice. A small lattice distortion opens up an energy gap such the lowest band splits into two. Along the edge of the first Brillouin zone for both bands a nearly flat energy-momentum dispersion is realized. For the excited band a highly degenerate energy minimum arises. By loading ultracold atoms into the excited band, a classically frustrated XYXYXY model is formed, describing rotors on a square lattice with competing nearest and next nearest tunnelling couplings. Our experimental optical lattice provides a regime, where a fully coherent Bose-Einstein condensate is observed, and a regime where frustration is expected. If we adiabatically tune from the condensate regime to the regime of frustration, the momentum spectra shows a complete loss of coherence. Upon slowly tuning back to the condensate regime, coherence is largely restored. Good agreement with model calculations is obtained.
We propose a cold-atom realization of a zigzag ladder. The two legs of the ladder correspond to a "synthetic" dimension given by two internal (spin) states of the atoms, so that tunneling between them can be realized as a laser-assisted process. The zigzag geometry is achieved by employing a spin-dependent optical lattice with the site position depending on the internal atomic state, i.e., on the ladder's leg. The lattice offers a possibility to tune the single-particle dispersion from a double-well to a single-minimum configuration. In contrast to previously considered semisynthetic lattices with a square geometry, the tunneling in the synthetic dimension is accompanied by spatial displacements of atoms. Therefore, the atom-atom interactions are nonlocal and act along the diagonal (semisynthetic) direction. We investigate the ground-state properties of the system for the case of strongly interacting bosons. In particular, we find that the interplay between the frustration induced by the magnetic field and the interactions gives rise to an interesting gapped phase at fractional filling factors corresponding to one particle per magnetic unit cell.