Abstract
The extended effective multiorbital Bose–Hubbard-type Hamiltonian which takes into account higher Bloch bands is discussed for boson systems in optical lattices, with emphasis on dynamical properties, in relation to current experiments. It is shown that the renormalization of Hamiltonian parameters depends on the dimension of the problem studied. Therefore, mean-field phase diagrams do not scale with the coordination number of the lattice. The effect of Hamiltonian parameters renormalization on the dynamics in reduced one-dimensional optical lattice potential is analyzed. We study both the quasi-adiabatic quench through the superfluid–Mott insulator transition and the absorption spectroscopy, that is, the energy absorption rate when the lattice depth is periodically modulated.
Highlights
This gave an explanation for experimental observations of the shift of the SF–MI phase transition [41] which could not be explained by single-band approaches
We take a look at the effects of the renormalization of coupling constants on the dynamics in a 1D optical lattice: both quench through the SF–MI transition and the absorption spectroscopy are analyzed
The initial state when the periodic lattice modulation starts is not the ground state, but a wavepacket dynamically created during the ramping of the lattice, the peak positions are well predicted by the effective multiorbital (EMO) model
Summary
The second quantization Hamiltonian for a dilute gas of interacting bosonic atoms in the optical lattice potential V (r ) and external trapping potential Ve(r ) is of the form. We will consider only situations where the atomic wavenumber k—being evaluated either in the lowest band or in the excited bands included in the calculation—is such that kas 1 so that only s-wave low-energy interatomic scattering is relevant This puts a limit on the number of bands used B < 20, beyond which the model is not a good approximation of the real world. Assuming that interactions are on-site only, i.e. Uiαjβklγ δ = 0 for i = j = k = l together with considering the lowest Bloch band only (α = β = γ = δ = 0) [7] leads directly to the BH Hamiltonian, equation (3), provided we chose the zero of the energy axis at E0. First we discuss the accurate numerical determination of the U and J parameters that, in itself, is a challenging problem, giving an insight into the physics involved
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