Session Y6: Novel Orbital Quantum Phases in Cold Atom Optical Lattices

Dynamics of ultracold atoms in higher lattice orbitals

Ultracold quantum gases in far detuned optical lattices have enabled many intriguing experiments studying a new regime of strongly correlated quantum systems. So far, such experiments have mostly concentrated on atoms in the vibrational ground state of the lattice band structure. Here, we report on the realization of a multiorbital system with ultracold atoms in the excited bands of a 3D optical lattice by selectively controlling the band population along a given lattice direction. The lifetime of the atoms in the excited band is found to be considerably longer (10-100 times) than the characteristic time scale for intersite tunneling, thus opening the path for orbital selective many-body physics with ultracold atoms in optical lattices. Upon exciting the atoms from an initial lowest band Mott-insulating state to higher lying bands, we observe the dynamical emergence of long-range coherence in 1D (and also 2D) at nonzero quasimomentum, providing a possible route for Bose-Einstein condensation to nonzero momentum.   

Control of Bosons in a 2D optical lattice with checkerboard staggered field.

I will describe experiments to control the vibrational and spin degrees of freedom of ultra-cold Rb atoms in a novel 2D optical lattice. This unit cell of the lattice can be dynamically transformed between a single-site and two-site configuration, allowing us to manipulate the vibrational degree of freedom of atoms in the unit cell, and merge separated atoms into the same site. In addition, the vector light shift of the optical lattice acts as a Zeeman field for the atoms on every other site of the lattice, providing a checkerboard staggered field. We use this field to control the spins on the two sub-lattices separately. I will also discuss the possibility of using this field to prepare low entropy anti-ferromagnetic states.   

Non-zero momentum Bose-Einstein condensation of orbital atoms

Bose-Einstein condensation (BEC) is often associated with zero momentum to which a macroscopic fraction of bosons condense. Here we propose a new class of meta-stable quantum states where bosons condense at non-zero momenta, defying the paradigm. This becomes possible when bosonic atoms are confined in the $p$-orbital Bloch bands of an optical lattice rather than the usual $s$-orbital. A recent experiment at Mainz confirmed the discovery of such an exotic BEC with alkali-metal atoms in a 3D cubic lattice with anisotropic optical potentials. Non-zero momentum suggests crystalline order. Our theoretical studies further found that such non-zero momentum BECs are also naturally orbital ordered superfluids due to the fascinating, less studied center-of-mass $p$-wave symmetry (e.g., a vortex-like $p_x+ip_y$ condensate). Varying with the geometry from standard optical lattices to double-well lattices, the interesting orderings include staggered orbital currents, stripes of angular momenta, and modulated super-current density wave. Different than a phase of coexisting orders such as supersolidity, this new class of states is characterized by a single order parameter. Work done in collaboration with J. Moore, S. Das Sarma, V. M. Stojanovic, C. Wu, and E. Zhao. \\[4pt] References:\\[0pt] [1] W. V. Liu, C. Wu, Phys. Rev. A {\bf 74}, 013607 (2006). \\[0pt] [2] C. Wu, W. V. Liu, J. Moore, S. Das Sarma, Phys. Rev. Lett. {\bf 97}, 190406 (2006). \\[0pt] [3] V. M. Stojanovic, C. Wu, W. V. Liu, S. Das Sarma, Phys. Rev. Lett. {\bf 101}, 125301 (2008). \\[0pt] [4] E. Zhao and W. V. Liu, Phys. Rev. Lett. {\bf 100}, 160403 (2008).   

Novel orbital physics with fermions in optical lattices

Orbitals, a degree of freedom characterized by orbital degeneracy and spatial anisotropy and independent of change and spin, play important roles in magnetism and superconductivity in transition metal oxides. In this talk, we will show that the rapid progress of cold atom physics has opened up an opportunity to study novel features of orbital physics, which do not appear usual solid state systems. In particular, the p$_{x;y}$-orbital system of the honeycomb lattice exhibits amazingly rich and fundamentally different behavior from that in the $p_z$-orbital system of graphene. Its flat band structure dramatically amplifies interaction effects, providing a natural way to study non-perturbative strong correlation phenomena such as Wigner crystallization, and ferromagnetism which is an important field in condensed matter physics but has not attracted much attention in the cold atom community. Furthermore, in the Mott-insulating states, the orbital degree of freedom enables superexchange interactions as spin does. We will show how spatial anisotropy generates frustration in such systems, which leads to a promising way to the exciting orbital liquid states. At last, we will present that a topological insulating phase occurs in the presence of the lattice rotation, as an orbital analogy of the quantum anomalous Hall effect of electron systems. \\[3pt] References:\\[0pt] 1. Congjun Wu, ``Orbital analogue of quantum anomalous Hall effect in $p$-band systems,'' Phys. Rev. Lett. 101, 186807 (2008). \\[0pt] 2. Shizhong Zhang, Congjun Wu, ``Proposed realization of itinerant ferromagnetism in optical lattices,'' arXiv:0805.3031. \\[0pt] 3. Congjun Wu, ``Orbital orderings and frustrations of p-band systems in optical lattices,'' Phys. Rev. Lett. 100, 200406 (2008).\\[0pt] 4. Congjun Wu , and S. Das Sarma, ``The $p_{x,y}$-orbital counterpart of graphene: cold atoms in the honeycomb optical lattice,'' Phys. Rev. B 77, 235107 (2008).\\[0pt] 5. Congjun Wu, Doron Bergman, Leon Balents, and S. Das Sarma, ``Flat bands and Wigner crystallization in the honeycomb optical attice,'' Phys. Rev. Lett. 99, 70401 (2007).   

Realization of Extended Hubbard Models with Tailored Orbitals in Optical Lattices

Optical lattices containing cold atoms represent nearly ideal manifestations of Hubbard models free from disorder, defects, impurities and lattice phonons. Experiments with bosonic alkali atoms confined to the lowest optical lattice band demonstrate strongly correlated phases including the superfluid and Mott insulator that arise from a real space contact interaction between atoms. Can other quantum condensed phases of matter be observed in these systems? We show that promoting bosons to higher bands effectively extends the range of the contact interaction. Quasi-localized orbitals in higher bands overlap with nearest neighbors. They can be modeled with extended Bose-Hubbard models that harbor density wave and supersolid phases. Bosons promoted to higher bands can decay but the purity of optical lattice systems limits possible decay mechanisms (e.g. phonons). We propose that long-lived metastable states of bosons promoted to higher bands of optical lattices may therefore provide a route to a novel class of extended Hubbard models.