Complex and real unconventional Bose-Einstein condensations in high orbital bands

Abstract

We perform the theoretical study on the unconventional Bose-Einstein condensations (UBEC) in the high bands of optical lattices observed by Hemmerich's group. These exotic states are characterized by complex-valued condensate wavefunctions with nodal points, or real-valued ones with nodal lines, thus are beyond the "no-node" paradigm of the conventional BECs. A quantum phase transition is driven by the competition between the single particle band and interaction energies. The complex UBECs spontaneously break time-reversal symmetry, exhibiting a vortex-antivortex lattice structure.

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

“…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] . The spatial symmetry of the orbital wavefunction dictates the complex hopping amplitudes between nearby sites.…”

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

“…4), are all nucleated by strong correlation effects in a multi-orbital setting 5 . For ultracold atomic gases, interaction effects combined with the band topology of p orbitals 6 have been argued to lead to exotic topological or superfluid (SF) phases for fermions [7][8][9][10][11][12][13] as well as bosons [14][15][16][17][18][19][20][21][22][23][24][25] . Interactions are predicted to drive a semi-metal to topological insulator quantum phase transition in two-dimensions (2D) for fermions in p x , p y and d x 2 À y 2 orbitals 12 , while interacting p-orbital atomic fermions in three-dimensions (3D) could lead to axial orbital order 26 .…”

Formation and decay of Bose-Einstein condensates in an excited band of a double-well optical lattice

“…, where the energy of the 2 nd band is minimal, and the coefficient η K0 = 1/ √ 2 when the momentum in the x and y direction has the same sign and is i/ √ 2 otherwise [1], [13]. The positive integer n(K, m ) is the number of atoms in quasi momentum K and harmonic oscillator level m given by the Bose distribution.…”

“…In addition, for these bands with nearly degenerate excited orbitals, tunneling can be "anisotropic" in that different orbitals tunnel preferably along different primitive lattice vectors. This has lead to several proposals of unconventional Bose-Einstein condensates in optical lattices and predictions of rich orbital physics in higher bands [8][9][10][11][12][13]. For example, Wirth et al [1] explores orbital superfluidity in sp−hybridized orbital bands in which condensation occurs at non-zero quasi momentum at the edge of the first Brillouin zone.…”