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Journal of the Physical Society of Japan

Quasi-Long-Range-Order in Mott State of Bose–Fermi Mixtures on One-Dimensional Optical Lattice

Akiko Masaki, Sota Tsukada, 弘之 森

Published Jun 10, 2009• 1 citation
Publisher

Abstract

We numerically studied internal structure of Mott insulating state of Bose–Fermi mixture systems on a one-dimensional optical lattice by using quantum Monte Carlo simulations. We looked for Mott state carefully adjusting various parameters to prevent phase separation. From the calculation of density–density correlation functions we found a quasi long-range order in the particle distribution in the Mott state. The order was strongly dependent of the ratio of the number of the bosons to that of the fermions. For example, the bosons and the fermions showed a tendency of aligning alternately when equal number of the bosons and fermions are introduced in the system. The observation of the quasi long-range order in the one-dimensional system indicates the presence of true long-range order in Bose–Fermi mixtures on a three-dimensional optical lattice.

DOI
10.1143/jpsj.78.064303

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We numerically studied internal structure of Mott insulating state of Bose–Fermi mixture systems on a one-dimensional optical lattice by using quantum Monte Carlo simulations. We looked for Mott state carefully adjusting various parameters to prevent phase separation. From the calculation of density–density correlation functions we found a quasi long-range order in the particle distribution in the Mott state. The order was strongly dependent of the ratio of the number of the bosons to that of the fermions. For example, the bosons and the fermions showed a tendency of aligning alternately when equal number of the bosons and fermions are introduced in the system. The observation of the quasi long-range order in the one-dimensional system indicates the presence of true long-range order in Bose–Fermi mixtures on a three-dimensional optical lattice.
We study distinctive features of local Mott insulator of trapped Bose-Fermi mixture systems on an optical lattice by using Monte-Carlo simulations of one-dimensional Bose-Fermi-Hubbard model. It was found that each species of the bosons and the fermions in a Mott insulator state had a finite stiffness but the density correlation function exhibited a quasi-long-range-order. This strongly suggested that in actual experiments the bosons and fermions of a commensurate filling with the lattice sites would form a Mott insulator state under strong interatomic interactions and have an order in their positional configuration.
We performed quantum Monte Carlo calculations to investigate the detail of local Mott states formed in Bose–Fermi mixtures confined in an optical lattice. The density profile of Bose–Fermi mixtures confined in an optical lattice could have some flat density domains, known as Mott plateaus, when the local density meets a certain criterion. By looking into the domains, we found an interesting tendency that the ratio of the density of the bosons to that of the fermions within the domains was given by a ratio of simple integers. We discuss the implications of the tendency.
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.
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.
Confinement of atoms by laser technology has opened up a new field of physics. Following the realization of Bose– Einstein condensation (BEC) of bosonic atoms, fermionic atom systems and even boson–fermion mixture systems were successfully trapped and cooled. Application of a periodic potential, so called optical lattice, could also unveil interesting nature of the atoms. One of the interesting phenomena of the atoms on optical lattice is Mott transition. Although there is a long history of the study on bosons or fermions on lattice, coexistence of bosons and fermions on lattice is a rather new topic to study. In particular, we have little knowledge about strongly-correlated bosons and fermions on lattice. In our previous works we performed numerical simulations of Bose–Fermi mixtures to clarify the phase diagram and the effect of the confinement potential. When the total number of bosonic and fermionic atoms per site takes an integer value and interatomic interactions are sufficiently strong, the system would undergo Mott transition where the local atom density is fixed to the integer value. A characteristic of this Mott insulating phase is that a boson and fermion located next to each other can exchange their positions by going through a virtual doubly-occupied state with the atom exchange energy t ’ tbtf=Ubf where tb and tf are the hopping energy of the bosons and fermions respectively and Ubf denotes the on-site interaction between the boson and the fermion. Although there still remain a number of open questions on the Mott state of Bose–Fermi mixtures, the property of superfluid state of the strongly-correlated bosons and fermions has yet to be revealed. In this short note we would like to focus on strongly-correlated Bose–Fermi mixtures at commensurate filling in a three-dimensional periodical potential and see characteristic behaviors, if any, of the superfluid phase close to the phase boundary to the Mott insulating phase. In the following analysis we assume uniformity of the system and thus neglect the possibility of the emergence of so-called supersolid where superfluidity and structural long-range order coexist. For simplicity we ignore all the internal degree of freedom of the atoms and the influence of the trap potential which in fact creates a nonuniform density profile of the bosons and fermions. For the system at commensurate filling on optical lattice, we assume that the interatomic interactions are weak enough to avoid formation of Mott state but strong enough to allow us to expect that there are only few empty or doublyoccupied sites and most sites are singly occupied. Namely we analyze the system that stays in a superfluid phase but lies close to the boundary to the Mott phase. Since a boson and fermion located next to each other can exchange their positions as stated above, the energy of the superfluid state of the mixture system is given mostly by the kinetic energy of the bosons and fermions exchanging their positions. We therefore express the Hamiltonian in the following form, ignoring the kinetic energy of the atoms at the empty sites and the interaction energy at the doubly-occupied sites:
The ground state phase diagram of the one-dimensional Bose-Fermi Hubbard model is studied in the canonical ensemble using a quantum Monte Carlo method. We focus on the case where both species have half filling in order to maximize the pairing correlations between the bosons and the fermions. In case of equal hopping we distinguish among phase separation, a Luttinger liquid phase, and a phase characterized by strong singlet pairing between the species. True long-range density waves exist with unequal hopping amplitudes.