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arXiv:1011.5002 · Journal of Physics B Atomic Molecular and Optical Physics

A three-site Bose–Fermi ring with a few atoms

Santiago F. Caballero-Benítez, Elena A. Ostrovskaya

Published Jun 14, 2011• 1 citation
arXivHTMLPDF

Abstract

We investigate a three-site ring system with a small number of quantum degenerate bosons and fermions. By means of the exact diagonalization of the Bose-Fermi-Hubbard Hamiltonian, we show that the symmetry of the ground state configuration is a function of both the boson-boson and the inter-species interaction in the system. The phase diagram of the system, constructed by computing the exact two-body spatial correlations, reveals nontrivial insulating phases that exist even in the strong bosonic tunneling limit and for incommensurate filling of bosons. These insulating phases are due to the inter-species interactions in the system and are not necessarily accompanied by the suppression of the particle number fluctuations.

DOI
10.1088/0953-4075/44/13/135301

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The superfluid-insulator transition in systems of lattice bosons is usually analyzed in the framework of the Bose-Hubbard model, and has been extensively studied by theory and simulations. Less attention has been paid to the remnants of the transition in truncated lattices, with or without periodic boundary conditions. Here we consider the hard-core limit of the extended Bose-Hubbard model on small square and triangular grids -- i.e., sections of the square and triangular lattices containing up to 13 sites. By mapping out the zero-temperature phase diagram through exact diagonalization, we find ground-state characteristics that are markedly different from those emerging in the thermodynamic limit, together with similarities. The dichotomy between superfluid-like and insulating-like behavior is then investigated in two-dimensional systems of a few interacting bosons in the continuum, subject to confining and optical-lattice potentials mimicking the 3×33\times 33×3 square grid. Using path-integral Monte Carlo simulations, we compute kinetic and potential energies, as well as superfluidity and exchange-cycle statistics, finding hints of Bose-Hubbard behavior even in systems of just five particles.
The zero-temperature phase diagram of a binary mixture of bosonic and fermionic atoms in a one-dimensional optical lattice is studied in the framework of the Bose-Fermi-Hubbard model. By exact numerical solution of the associated eigenvalue problems, ground state observables and the response to an external phase twist are evaluated. The stiffnesses under phase variations provide measures for the boson superfluid fraction and the fermionic Drude weight. Several distinct quantum phases are identified as functions of the strength of the repulsive boson-boson and the boson-fermion interactions. In addition to the bosonic Mott-insulator phase, two other insulating phases are found, where both the bosonic superfluid fraction and the fermionic Drude weight vanish simultaneously. One of these double-insulator phases exhibits a crystalline diagonal long-range order, while the other is characterized by spatial separation of the two species.
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We study the ground state phases of Bose-Fermi mixtures in one-dimensional optical lattices with quantum Monte Carlo simulations using the canonical worm algorithm. Depending on the filling of bosons and fermions, and the on-site intra- and interspecies interaction, different kinds of incompressible and superfluid phases appear. On the compressible side, correlations between bosons and fermions can lead to a distinctive behavior of the bosonic superfluid density and the fermionic stiffness, as well as of the equal-time Green functions, which allow one to identify regions where the two species exhibit anticorrelated flow. We present here complete phase diagrams for these systems at different fillings and as a function of the interaction parameters.