Confinedp-band Bose-Einstein condensates

Abstract

We study bosonic atoms on the p band of a two-dimensional optical square lattice in the presence of a confining trapping potential. Using a mean-field approach, we show how the anisotropic tunneling for p-band particles affects the cloud of condensed atoms by characterizing the ground-state density and the coherence properties of the atomic states both between sites and atomic flavors. In contrast to the usual results based on the local-density approximation, the atomic density can become anisotropic. This anisotropic effect is especially pronounced in the limit of weak atom-atom interactions and of weak lattice amplitudes, i.e., when the properties of the ground state are mainly driven by the kinetic energies. We also investigate how the trap influences known properties of the nontrapped case. In particular, we focus on the behavior of the antiferromagnetic vortex-antivortex order, which for the confined system is shown to disappear at the edges of the condensed cloud.

XYZQuantum Heisenberg Models withp-Orbital Bosons

“…Within the local density approximation, the trap renormalizes the couplings so that they become spatially dependent [30], but this effect can be negligible if the orbitals are small compared to the length scale of the trap. In the regime of strong repulsion, the main effect of the trap is instead that it gives rise to "wedding cake" structures with Mott regions of integer filling.…”

Tunneling-Induced Restoration of the Degeneracy and the Time-Reversal Symmetry Breaking in Optical Lattices

“…when going beyond the HA approximation. However, it was shown that anharmonicity may have important consequences when one studies p-band physics [16,21,22]. In our Letter, we demonstrate that the apparently technical and quantitatively small change of harmonically approximated on-site functions to the true orthonormal basis of Wannier states may substantially change the phase diagram and many-body physics in a nonperturbative way.…”

“…Note that our potential does not take into account the slowly spatially varying harmonic trap typically present in experiments, which may affect the properties of p-band states [22]. In the following, we shall assume a uniform filling of sites, thus explicitly excluding the additional trapping.…”

“…Such states can be prepared by loading ultracold atoms into the higher bands [8][9][10][11] or via interactioninduced interorbital transfer [12][13][14][15][16]. Atoms in such excited bands can give rise to a zoo of exotic phases, such as exotic superfluidity with broken time-reversal symmetry (TRS) [9][10][11][12][17][18][19][20][21][22] In a theoretical treatment of Bose-Hubbard models the harmonic approximation (HA) is often used to get the first most important insight into the physics of the system. Simplifying the Hamiltonian using a Gaussian basis is the simplest route to checking for the possible phases of the system.…”

Theoretical studies of Bose-Hubbard and discrete nonlinear Schrödinger models : Localization, vortices, and quantum-classical correspondence

“…This introduces new degrees of freedom for the bosons, e.g. that the orbitals can point in different directions, which leads to anisotropic tunneling and interactions [194].…”