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arXiv:1806.02277 · Physical Review A

Manipulating the Mott lobes: Optical lattice bosons coupled to an array of atomic quantum dots

Damian Wozniak, Florian Magnus Dobler, Anna Posazhennikova

Published Nov 26, 2018• 1 citation
arXivHTMLPDF

Abstract

We analyze quantum phase transitions in a system of optical lattice bosons coupled to an array of atomic quantum dots. Atomic quantum dots are represented by hard-core bosons of different hyperfine species and therefore can be mapped onto pseudospins 1/2. The system parallels the Bose-Hubbard model with an additional assisted tunneling via coupling to the atomic quantum dots. We calculate the phase diagram of the combined system, numerically within the Gutzwiller ansatz and analytically using the mean-field decoupling approximation. The result of the assisted Bose-Hubbard model is that the Mott-superfluid transition still takes place; however, the Mott lobes strongly depend on the system parameters such as the detuning. One can even reverse the usual hierarchy of the lobes with the first lobe becoming the smallest. The phase transition in the bosonic subsystem is accompanied by a magnetization rotation in the pseudospin subsystem with the tilting angle being an effective order parameter. When direct tunneling is taken into account, the Mott lobes can be made to disappear and the bosonic subsystem becomes superfluid throughout.

DOI
10.1103/physreva.98.053628

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We investigate properties of an ultracold, two-component bosonic gas in a square optical lattice at unit filling. In addition to density-density interactions, the atoms are subject to coherent light-matter interactions that couple different internal states. We examine the influence of this coherent coupling on the system and its quantum phases by using Gutzwiller mean-field theory as well as bosonic dynamical mean-field theory. We find that the interplay of strong interspecies repulsion and coherent coupling affects the Mott insulator to superfluid transition and shifts the tip of the Mott lobe toward higher values of the tunneling amplitude. In the strongly interacting Mott regime, the resulting Bose-Hubbard model can be mapped onto an effective spin Hamiltonian that offers additional insights into the observed phenomena.
We study the ground-state phase diagram of spinless and spin-1 bosons in optical superlattices using a Bose-Hubbard Hamiltonian that includes spin-dependent interactions. We decouple the unit cells of the superlattice via a mean-field approach and take into account the dynamics within the unit cell exactly. The system supports Mott-insulating as well as superfluid phases. The transitions between these phases are second order for spinless bosons and second or first order for spin-1 bosons. Antiferromagnetic interactions energetically penalize high-spin configurations and elongate all Mott lobes, especially the ones corresponding to an even atom number on each lattice site. We find that the quadratic Zeeman effect lifts the degeneracy between different polar superfluid phases leading to additional metastable phases and first-order phase transitions. Finally, we show that an energy offset between the two sites of the unit cell induces a staircase of single-atom tunneling resonances, which surprisingly survives well into the superfluid regime.
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.
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We present an analytic description of the finite-temperature phase diagram of the Bose-Hubbard model, successfully describing the physics of cold bosonic atoms trapped in optical lattices and superlattices. Based on a standard statistical mechanics approach, we provide the exact expression for the boundary between the superfluid and the normal fluid by solving the self-consistency equations involved in the mean-field approximation to the Bose-Hubbard model. The zero-temperature limit of such a result supplies an analytic expression for the Mott lobes of superlattices, characterized by a critical fractional filling.
We investigate the superfluid--Mott-insulator quantum phase transition of spin-1 bosons in an optical lattice created by pairs of counterpropagating linearly polarized laser beams, driving an Fg=1{F}_{g}=1Fg​=1 to Fe=1{F}_{e}=1Fe​=1 internal atomic transition. The whole parameter space of the resulting two-component Bose-Hubbard model is studied. We find that the phase transition is not always second order as in the case of spinless bosons, but can be first order in certain regions of the parameter space. The calculations are done in the mean-field approximation by means of exact numerical diagonalization as well as within the framework of perturbation theory.