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arXiv:1103.0523 · Physical Review A

Quantum phases of ultracold bosonic atoms in a one-dimensional optical superlattice

Arya Dhar, Tapan Mishra, Ramesh V. Pai, Bhanu Pratap Das

Published May 20, 2011• 21 citations
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Abstract

We analyze various quantum phases of ultracold bosonic atoms in a periodic one-dimensional optical superlattice. Our studies have been performed using the finite-size density-matrix renormalization group method in the framework of the Bose-Hubbard model. Calculations have been carried out for a wide range of densities and the energy shifts due to the superlattice potential. At commensurate fillings, we find the Mott insulator and the superfluid phases as well as Mott insulators induced by the superlattice. At a particular incommensurate density, the system is found to be in the superfluid phase coexisting with density oscillations for a certain range of parameters of the system.

DOI
10.1103/physreva.83.053621

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We analyze various quantum phases of ultracold bosonic atoms in a periodic one-dimensional optical superlattice. Our studies have been performed using the finite-size density-matrix renormalization group method in the framework of the Bose-Hubbard model. Calculations have been carried out for a wide range of densities and the energy shifts due to the superlattice potential. At commensurate fillings, we find the Mott insulator and the superfluid phases as well as Mott insulators induced by the superlattice. At a particular incommensurate density, the system is found to be in the superfluid phase coexisting with density oscillations for a certain range of parameters of the system.
We report our findings on the quantum phase transitions in cold bosonic atoms in a one-dimensional optical lattice using the finite-size density-matrix renormalization-group method in the framework of the extended Bose-Hubbard model. We consider wide ranges of values for the filling factors and the nearest-neighbor interactions. At commensurate fillings, we obtain two different types of charge-density wave phases and a Mott insulator phase. However, departure from commensurate fillings yields the exotic supersolid phase where both the crystalline and the superfluid orders coexist. In addition, we obtain the signatures for the solitary waves and the superfluid phase.
In this paper, we analyze superfluid, insulator and various magnetic phases of ultracold spin-1 bosonic atoms in two-dimensional optical superlattices. Our studies have been performed using Cluster Mean Field Theory. Calculations have been carried out for a wide range of densities and the energy shifts due to the superlattice potential. We find superlattice potential do not change the symmetry of the polar superfluid phases. Superlattice potentials induce Mott insulator phases with half-integer densities. The phase diagram is obtained using superfluid density, nematic order and singlet density. Second order Rényi entanglement entropy is also calculated in different phases. The results show that Rényi entanglement entropy is large in the nematic Mott insulator phase.
The dynamics of an ultracold dilute gas of bosonic atoms in an optical lattice can be described by a Bose-Hubbard model where the system parameters are controlled by laser light. We study the continuous (zero temperature) quantum phase transition from the superfluid to the Mott insulator phase induced by varying the depth of the optical potential, where the Mott insulator phase corresponds to a commensurate filling of the lattice (``optical crystal''). Examples for formation of Mott structures in optical lattices with a superimposed harmonic trap and in optical superlattices are presented.
Ultracold atomic gases in optical lattices provide an unique framework to study quantum phenomena in strongly correlated systems. In addition to the precise control over all relevant parameters in the experiment, these experiments can be mapped to a fundamental model from solid-state physics. For the bosonic version of this model, the so-called Bose-Hubbard model, a phase transition from a superfluid to a Mott insulator was theoretically predicted and later experimentally observed in an ultracold gas of Rb-87 atoms in three-dimensional as well as in one-dimensional optical lattices. Apart from homogeneous optical lattices one can introduce more complex lattice topologies such as two-color superlattices which give rise to a rich phase diagram including more exotic phases like the Bose-glass. We employ various powerful many-body techniques like exact diagonalization in complete and truncated Hilbert spaces and the Density-Matrix Renormalization Group (DMRG) algorithm to study the phase diagrams of the one-dimensional Bose-Hubbard and the one-dimensional Bose-Fermi-Hubbard Hamiltonian. Most theoretical studies of these systems discuss the phase diagrams with respect to the generic parameters of the Hubbard model. These Hubbard parameters, however, depend non-trivially on the control parameters used in experiments. The focus of this work is on the ab-initio calculation of the phase diagram of ultracold Rb-87 in one-dimensional optical superlattices starting directly from the experimental setup. To this end, we first employ band-structure calculations to extract the Hubbard parameters from the experimental parameters. Then, we use state-of-the-art DMRG techniques to solve the many-body problem for realistic particle numbers and lattice sizes that occur in experiments. Our results show that by using the intensities of the two laser fields forming the two-color superlattice as control parameters while keeping all other experimental parameters fixed, it is possible to access all relevant quantum phases of the system. Furthermore, we found out that the critical values of the laser intensities for the different phase transitions depend strongly on a third parameter that has to be included for a realistic description of the experiment. This third parameter is the strength of a harmonic trapping potential which accounts for the Gaussian shape of the laser fields and an additional magnetic potential used to confine the atoms in the center of the trap.
We study quantum phases of ultracold bosonic atoms in a two-dimensional optical superlattice. The extended Bose–Hubbard model derived from the system of ultracold bosonic atoms in an optical superlattice is solved numerically with the Gutzwiller approach. We find that the modulated superfluid (MS), Mott-insulator (MI) and density-wave (DW) phases appear in some regimes of parameters. The experimental detection of the first-order correlations and the second-order correlations of different quantum phases with time-of-flight and noise-correlation techniques is proposed.