Novel quantum phases in orbital systems in optical lattices


Optical lattices with cold atoms have become a new frontier for exploring interesting physics in strongly correlated systems. In particular, recent experiments on high orbital bands provide a wonderful new opportunity for studying orbital physics, which is characterized by orbital degeneracy and spatial anisotropy. In this work, we study new features of orbital physics in the $p$-orbital bands with bosons and fermions, which are not usually realized in solid state systems.


Orbital analogue of quantum anomalous Hall effect in $p$-band systems

We investigate the topological insulating states of the $p$-band systems in optical lattices induced by the onsite orbital angular momentum polarization, which exhibit gapless edge modes in the absence of Landau levels. This effect arises from the energy level splitting between the onsite $p_x+ip_y$ and $p_x-ip_y$ orbitals by rotating each optical lattice site around its own center. At large rotation angular velocities, this model naturally reduces to two copies of Haldane's quantum Hall model without Landau levels. The distribution of Berry curvature in the momentum space and the quantized Chern numbers are calculated. The experimental realization is also discussed.

Proposed realization of itinerant ferromagnetism in optical lattices

We propose to realize the itinerant ferromagnetism of two-component cold fermionic atoms in the $p$-orbital bands in optical lattices. The band flatness in the two-dimensional honeycomb lattice dramatically amplifies the interaction effect driving the ferromagnetic transitions even with a weak repulsive interaction. This has the advantage to maintain the system stability without decaying to the dimer-molecule state which occurs as approaching the Feshbach resonance from the side with the positive scattering length. Experimental signatures and detections are also discussed.

Orbital ordering and frustration of $p$-band Mott-insulators

We investigate the general structure of orbital exchange physics in Mott-insulating states of $p$-orbital systems in optical lattices. Orbital orders occur in both the triangular and Kagome lattices. In contrast, orbital exchange in the honeycomb lattice is frustrated as described by a novel quantum 120$^\circ$-model. Its classical ground states are mapped into configurations of the fully-packed loop model with an extra U(1) rotation degree of freedom. Quantum orbital fluctuations select a six-site plaquette ground state ordering pattern in the semiclassical limit from the ``order from disorder'' mechanism. This effect arises from the appearance of a zero energy flat-band of orbital excitations.

The $p_{x,y}$-orbital counterpart of graphene: cold atoms in the honeycomb optical lattice

We study the ground state properties of the interacting spinless fermions in the $p_{x,y}$-orbital bands in the two dimensional honeycomb optical lattice, which exhibit different novel features from those in the $p_z$-orbital system of graphene. In addition to two dispersive bands with Dirac cones, the tight-binding band structure exhibits another two completely flat bands over the entire Brillouin zone. With the realistic sinusoidal optical potential, the flat bands acquire a finite but much smaller band width compared to the dispersive bands. The band flatness dramatically enhanced interaction effects giving rise to various charge and bond ordered states at commensurate fillings of $n=\frac{i}{6} (i=1 \sim 6)$. At $n=1/6$, the many-body ground states can be exactly solved as the close packed hexagon states which can be stabilized even in the weak interacting regime. The dimerization of bonding strength occurs at both $n=1/2$ and 5/6, and the latter case is accompanied with the charge density wave of holes. The trimerization of bonding strength and charge inhomogeneity appear at $n={1/3},{2/3}$. These crystalline orders exhibit themselves in the noise correlations of the time of flight spectra.

Predicted quantum stripe ordering in optical lattices

We predict the robust existence of a novel quantum orbital stripe order in the $p$-band Bose-Hubbard model of two-dimensional triangular optical lattices with cold bosonic atoms. An orbital angular momentum moment is formed on each site exhibiting a stripe order both in the superfluid and Mottinsulating phases. The stripe order spontaneously breaks time-reversal, lattice translation, and rotation symmetries. In addition, it induces staggered plaquette bond currents in the superfluid phase. Possible signatures of this stripe order in the time of flight experiment are discussed.

Atomic matter of nonzero-momentum Bose-Einstein condensation and orbital current order

Here we propose a new quantum state where bosonic alkali-metal atoms condense at nonzero momenta. This becomes possible when the atoms are confined in the p-orbital Bloch band of an optical lattice rather than the usual s-orbital band. The new condensate simultaneously forms an order of transversely staggered orbital currents, reminiscent of orbital antiferromagnetism or d-density wave in correlated electronic systems but different in fundamental ways. We discuss several approaches of preparing atoms to the p-orbital band and propose an "energy blocking" mechanism by Feshbach resonance to protect them from decaying to the lowest s-orbital band. Such a model system seems very unique and novel to atomic gases. It suggests a new concept of quantum collective phenomena of no prior example from solid state materials.


References and talks

  • Congjun Wu, "Orbital orderings and frustrations of p-band systems in optical lattices", arxiv:08010888 .
  • Congjun Wu , and S. Das Sarma, "The $p_{x,y}$-orbital counterpart of graphene: cold atoms in the honeycomb optical lattice", arXiv:0712.4284 .
  • Congjun Wu, Doron Bergman, Leon Balents, and S. Das Sarma, "Flat bands and Wigner crystallization in the honeycomb optical lattice", Phys. Rev. Lett. 99, 70401 , see pdf file
  • Congjun Wu, W. Vincent Liu, Joel Moore, and Sankar Das Sarma, "Predicted quantum stripe ordering in optical lattices" Phys. Rev. Lett. 97, 190406 (2006) , see pdf file.
  • W. Vincent Liu, and Congjun Wu, "Atomic matter of nonzero-momentum Bose-Einstein condensation and orbital current order", Phys. Rev. A 74 , 13607 (2006), see pdf file.
  • Invited talk at Department of Physics, University of Maryland , Joint Quantum Institute seminar , "Exploring new states of matter in the p-orbital bands of optical lattices (PPT)" , Feb. 05, 2007.



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    Last modified: July 15, 2007.