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arXiv:1203.1412 · Physical Review A

Three-body on-site interactions in ultracold bosonic atoms in optical lattices and superlattices

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

Published May 21, 2012• 38 citations
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Abstract

The Mott-insulator--superfluid transition for ultracold bosonic atoms in an optical lattice has been extensively studied in the framework of the Bose-Hubbard model with two-body on-site interactions. In this paper, we analyze the additional effect of the three-body on-site interactions on this phase transition in an optical lattice and the transitions between the various phases that arise in an optical superlattice. Using the mean-field theory and the density matrix renormalization group method, we find the phase diagrams depicting the relationships between various physical quantities in an optical lattice and superlattice. We also propose a possible experimental signature to observe the on-site three-body interactions.

DOI
10.1103/physreva.85.051604

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The Mott-insulator--superfluid transition for ultracold bosonic atoms in an optical lattice has been extensively studied in the framework of the Bose-Hubbard model with two-body on-site interactions. In this paper, we analyze the additional effect of the three-body on-site interactions on this phase transition in an optical lattice and the transitions between the various phases that arise in an optical superlattice. Using the mean-field theory and the density matrix renormalization group method, we find the phase diagrams depicting the relationships between various physical quantities in an optical lattice and superlattice. We also propose a possible experimental signature to observe the on-site three-body interactions.
A first-order type phase transition between Mott lobes has been reported in Phys. Rev. Lett. 109, 135302 (2012) for a two-dimensional Bose-Hubbard model in the presence of an attractive three-body interaction. We revisit the scenario in systems of ultracold bosons both in one- and two-dimensional lattices using the density matrix renormalization group method and the self-consistent cluster mean-field theory approach, respectively. We show that an unconventional pairing of particles occurs due to the competing repulsive two-body and attractive three-body interactions. This leads to a pair superfluid phase sandwiched between the Mott insulator lobes corresponding to densities density one and three in the strongly interacting regime. This is in contrast to the direct first-order jump as predicted before. Interestingly, the Mott to pair superfluid phase transitions are found to be continuous in nature. We also show that the pair superfluid phase is robust with respect to the ratio between the two- and three-body interaction strengths. In the end, we establish a connection between the Bose-Hubbard model presented in Phys. Rev. Lett. 109, 135302 (2012) with a more general Bose-Hubbard model and analyze the fate of the pair superfluid phase in the presence of an external trapping potential.
In this paper, the quantum phase transition between the superfluid state and the Mott-insulator state is studied based on an extended Bose-Hubbard model with two- and three-body on-site interactions. By employing the mean-field approximation we find the extension of the insulating ``lobes'' and the existence of a fixed point in three-dimensional phase space. We investigate the link between experimental parameters and theoretical variables. The possibility to observe our results through some experimental effects in optically trapped Bose-Einstein condensates is also discussed.
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.
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.
The Bose–Hubbard model with an effective off-site three-body tunneling, characterized by jumps towards one another, between one atom on a site and a pair atoms on the neighborhood site, is studied systematically on a one-dimensional (1D) lattice, by using the density matrix renormalization group method. The off-site trimer superfluid, condensing at momentum k = 0 , emerges in the softcore Bose–Hubbard model but it disappears in the hardcore Bose–Hubbard model. Our results numerically verify that the off-site trimer superfluid phase derived in the momentum space from [ Phys. Rev. A 81 , 011601(R) (2010)] is stable in the thermodynamic limit. The off-site trimer superfluid phase, the partially off-site trimer superfluid phase and the Mott insulator phase are found, as well as interesting phase transitions, such as the continuous or first-order phase transition from the trimer superfluid phase to the Mott insulator phase. Our results are helpful in realizing this novel off-site trimer superfluid phase by cold atom experiments.
Quantum phases and phase transitions of weakly to strongly interacting bosonic atoms in deep to shallow optical lattices are described by a single multiorbital mean-field approach in real space. For weakly interacting bosons in one dimension, the critical value of the superfluid to Mott insulator (MI) transition found is in excellent agreement with many-body treatments of the Bose-Hubbard model. For strongly interacting bosons, (i) additional MI phases appear, for which two (or more) atoms residing in each site undergo a Tonks-Girardeau-like transition and localize, and (ii) on-site excitation becomes the excitation lowest in energy. Experimental implications are discussed.