01855nas a2200157 4500008004100000245011400041210006900155260001500224300001100239490000700250520131500257100001801572700002001590700001901610856006801629 2016 eng d00aA Hubbard model for ultracold bosonic atoms interacting via zero-point-energy induced three-body interactions0 aHubbard model for ultracold bosonic atoms interacting via zeropo c2016/04/19 a0436160 v933 aWe show that for ultra-cold neutral bosonic atoms held in a three-dimensional periodic potential or optical lattice, a Hubbard model with dominant, attractive three-body interactions can be generated. In fact, we derive that the effect of pair-wise interactions can be made small or zero starting from the realization that collisions occur at the zero-point energy of an optical lattice site and the strength of the interactions is energy dependent from effective-range contributions. We determine the strength of the two- and three-body interactions for scattering from van-der-Waals potentials and near Fano-Feshbach resonances. For van-der-Waals potentials, which for example describe scattering of alkaline-earth atoms, we find that the pair-wise interaction can only be turned off for species with a small negative scattering length, leaving the 88Sr isotope a possible candidate. Interestingly, for collisional magnetic Feshbach resonances this restriction does not apply and there often exist magnetic fields where the two-body interaction is small. We illustrate this result for several known narrow resonances between alkali-metal atoms as well as chromium atoms. Finally, we compare the size of the three-body interaction with hopping rates and describe limits due to three-body recombination.

1 aPaul, Saurabh1 aJohnson, P., R.1 aTiesinga, Eite uhttp://journals.aps.org/pra/abstract/10.1103/PhysRevA.93.04361613859nas a2200145 45000080041000002450084000412100069001252600015001943000011002094900007002205201338100227100001813608700001913626856006813645 2016 eng d00aWannier functions using a discrete variable representation for optical lattices0 aWannier functions using a discrete variable representation for o c2016/09/07 a0336060 v943 aWe propose a numerical method using the discrete variable representation (DVR) for constructing real-valued Wannier functions localized in a unit cell for both symmetric and asymmetric periodic potentials. We apply these results to finding Wannier functions for ultracold atoms trapped in laser-generated optical lattices. Following S. Kivelson [Phys. Rev. B 26, 4269 (1982)], for a symmetric lattice with inversion symmetry, we construct Wannier functions as eigenstates of the position operators xˆ, yˆ, and zˆ restricted to single-particle Bloch functions belonging to one or more bands. To ensure that the Wannier functions are real-valued, we numerically obtain the band structure and real-valued eigenstates using a uniform Fourier grid DVR. We then show, by a comparison of tunneling energies, that the Wannier functions are accurate for both inversion-symmetric and asymmetric potentials to better than 10 significant digits when using double-precision arithmetic. The calculations are performed for an optical lattice with double-wells per unit cell with tunable asymmetry along the x axis and a single sinusoidal potential along the perpendicular directions. Localized functions at the two potential minima within each unit cell are similarly constructed, but using a superposition of single-particle solutions from the two lowest bands. We finally use these localized basis functions to determine the two-body interaction energies in the Bose-Hubbard model and show the dependence of these energies on lattice asymmetry.

1 aPaul, Saurabh1 aTiesinga, Eite uhttp://journals.aps.org/pra/abstract/10.1103/PhysRevA.94.03360601804nas a2200145 4500008004100000245007600041210006900117260001500186300001100201490000700212520133400219100001801553700001901571856006801590 2015 eng d00aLarge effective three-body interaction in a double-well optical lattice0 aLarge effective threebody interaction in a doublewell optical la c2015/08/03 a0236020 v923 a We study ultracold atoms in an optical lattice with two local minima per unit
cell and show that the low energy states of a multi-band Bose-Hubbard (BH)
Hamiltonian with only pair-wise interactions is equivalent to an effective
single-band Hamiltonian with strong three-body interactions. We focus on a
double-well optical lattice with a symmetric double well along the $x$ axis and
single well structure along the perpendicular directions. Tunneling and
two-body interaction energies are obtained from an exact band-structure
calculation and numerically-constructed Wannier functions in order to construct
a BH Hamiltonian spanning the lowest two bands. Our effective Hamiltonian is
constructed from the ground state of the $N$-atom Hamiltonian for each unit
cell obtained within the subspace spanned by the Wannier functions of two
lowest bands. The model includes hopping between ground states of neighboring
unit cells. We show that such an effective Hamiltonian has strong three-body
interactions that can be easily tuned by changing the lattice parameters.
Finally, relying on numerical mean-field simulations, we show that the
effective Hamiltonian is an excellent approximation of the two-band BH
Hamiltonian over a wide range of lattice parameters, both in the superfluid and
Mott insulator regions.
1 aPaul, Saurabh1 aTiesinga, Eite uhttp://journals.aps.org/pra/abstract/10.1103/PhysRevA.92.02360202343nas a2200133 4500008004100000245010800041210006900149260001400218490000700232520189600239100001802135700001902153856003702172 2013 eng d00aFormation and decay of Bose-Einstein condensates in an excited band of a double-well optical lattice
0 aFormation and decay of BoseEinstein condensates in an excited ba c2013/9/120 v883 a We study the formation and collision-aided decay of an ultra-cold atomic
Bose-Einstein condensate in the first excited band of a double-well 2D-optical
lattice with weak harmonic confinement in the perpendicular $z$ direction. This
lattice geometry is based on an experiment by Wirth et al. The double well is
asymmetric, with the local ground state in the shallow well nearly degenerate
with the first excited state of the adjacent deep well. We compare the band
structure obtained from a tight-binding (TB) model with that obtained
numerically using a plane wave basis. We find the TB model to be in
quantitative agreement for the lowest two bands, qualitative for next two
bands, and inadequate for even higher bands. The band widths of the excited
bands are much larger than the harmonic oscillator energy spacing in the $z$
direction. We then study the thermodynamics of a non-interacting Bose gas in
the first excited band. We estimate the condensate fraction and critical
temperature, $T_c$, as functions of lattice parameters. For typical atom
numbers, the critical energy $k_BT_c$, with $k_B$ the Boltzmann constant, is
larger than the excited band widths and harmonic oscillator energy. Using
conservation of total energy and atom number, we show that the temperature
increases after the lattice transformation. Finally, we estimate the time scale
for a two-body collision-aided decay of the condensate as a function of lattice
parameters. The decay involves two processes, the dominant one in which both
colliding atoms decay to the ground band, and the second involving excitation
of one atom to a higher band. For this estimate, we have used TB wave functions
for the lowest four bands, and numerical estimates for higher bands. The decay
rate rapidly increases with lattice depth, but stays smaller than the tunneling
rate between the $s$ and $p$ orbitals in adjacent wells.
1 aPaul, Saurabh1 aTiesinga, Eite uhttp://arxiv.org/abs/1308.4449v1