Evidence for orbital superfluidity in the P-band of a bipartite optical square lattice

Abstract

The successful emulation of the Hubbard model [1] in optical lattices [2,3] has stimulated world wide efforts to extend their scope to also capture more complex, incompletely understood scenarios of many-body physics [4,5]. Unfortunately, for bosons, Feynmans fundamental "nonode" theorem [6] under very general circumstances predicts a positive definite ground state wave function with limited relevance for manybody systems of interest.A promising way around Feynmans statement is to consider higher bands in optical lattices with more than one dimension [7], where the orbital degree of freedom with its intrinsic anisotropy due to multiple orbital orientations gives rise to a structural diversity, highly relevant, for example, in the area of strongly correlated electronic matter. In homogeneous two-dimensional optical lattices, lifetimes of excited bands on the order of a hundred milliseconds are possible [8,9] but the tunneling dynamics appears not to support cross-dimensional coherence [8,10]. Here we report the first observation of a superfluid in the P -band of a bipartite optical square lattice with S-orbits and P -orbits arranged in a chequerboard pattern. This permits us to establish full cross-dimensional coherence with a life-time of several ten milliseconds. Depending on a small adjustable anisotropy of the lattice, we can realize real-valued striped superfluid order parameters with different orientations P x ± P y or a complex-valued P x ± iP y order parameter, which breaks time reversal symmetry and resembles the π-flux model proposed in the context of high temperature superconductors [11]. Our experiment opens up the realms of orbital superfluids to investigations with optical lattice models.Orbital optical lattices permit to prepare exciting new many-body scenarios with relevant counterparts in the area of strongly correlated electronic matter, where the orbital degree of freedom with its rich structure of possible orientations gives rise to a wealth of interesting phenomena. For example, in the transition-metal oxides orbital physics is believed to be a key element for understanding their metal-insulator transitions, superconductivity, or colossal magnetoresistance. Recent theoretical proposals have considered, for example, the formation of multiflavor and multiorbital systems [8,9,12,13], supersolid quantum phases in cubic lattices [14,15], quantum stripe ordering in triangular lattices [16], or Wigner crystallization in honeycomb lattices [17]. The recent prediction, that the life time of atoms in higher Bloch bands can be unexpectedly long, has further strengthened the potential significance of orbital physics in optical lattices [8,9]. Previous experiments have demonstrated that the excitation of higher Bloch bands is in fact possible [18,19]. In a recent experiment, investigating a homogeneous quasi one-dimensional (1D) lattice of bosons, transient partial coherence in the P -band has been observed [10]. In an extension to a two-dimensional square lattice, however, no cross-coherence could be est...

Topological states in a ladder-like optical lattice containing ultracold atoms in higher orbital bands

“…Topologically nontrivial band structure of this sp orbital ladder, which shall be shown analytically next, may be heuristically speculated from the following comparison: the staggered quantum tunnelling t sp P j ½C w j ð À is y ÞC j þ 1 þ h:c: resembles spin-orbit interaction [18][19][20][21]23 , when the s and p orbital states are mapped to pseudo-spin-(1/2) states. Such a staggered tunnelling can also naturally arise in the checkerboard optical lattice already engineered in the experiment 6 by increasing the laser strength in one direction to reach the quasi-1D limit. The physics of the sp orbital ladder is also connected to the more familiar frustrated ladder with magnetic flux 24 , but the sp orbital ladder appears much easier to realize experimentally.…”

“…The relative well depth of the two legs is controlled by the phase f and further by the ratio V 2 /V 1 . We will focus on a situation, similar to the setup in the experiment 6 , where the s orbital of leg A has roughly the same energy as the p x orbital of leg B (other p orbitals have much higher energy). For example, one can choose…”

“…We now consider a single species of fermions occupying these orbitals, with the low-lying s orbital of leg B completely filled. Alternatively fermions can be directly loaded into the p x orbital of leg B, leaving the low-lying s empty, by techniques developed in recent experiments 4,6,10 . With these techniques, long-lived meta-stable states of atoms in high orbitals with life time on the order of several hundred milliseconds are demonstrated achievable 6 .…”

“…In the context of ultracold quantum gases, optical lattices engineered with interfering laser beams can realize specific configurations of potentials of single or multiple periods not found in nature. For instance, doublewell superlattices 1,2 have matured into a powerful tool for manipulating orbital degrees of freedom [3][4][5][6][7][8][9][10] . Controls of atoms in the s and p orbitals of the checkerboard 6 and hexagonal 8 optical lattices have also been demonstrated, and correlation between these orbitals tends to give exotic quantum states 6,8,[11][12][13] .…”

Proposed formation and dynamical signature of a chiral Bose liquid in an optical lattice

“…Our work is motivated by recent experiments that have successfully prepared long-lived metastable phases of weakly interacting 87 Rb atoms in p orbitals 21,27 . In the deep lattice regime, this experimental system is well approximated by a tight binding model on a checkerboard optical lattice with bosons in the p x , p y and s orbital degrees of freedom (see Fig.…”