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arXiv:1108.0691 · Physical Review A

Localization of a Bose-Fermi mixture in a bichromatic optical lattice

Yongshan Cheng, Sadhan K. Adhikari

Published Aug 25, 2011• 23 citations
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Abstract

We study the localization of a cigar-shaped superfluid Bose-Fermi mixture in a quasiperiodic bichromatic optical lattice (OL) for interspecies attraction and intraspecies repulsion. The mixture is described by the Gross-Pitaevskii equation for the bosons, coupled to a hydrodynamic mean-field equation for fermions at unitarity. We confirm the existence of the symbiotic localized states in the Bose-Fermi mixture and Anderson localization of the Bose component in the interacting Bose-Fermi mixture on a bichromatic OL. The phase diagram in boson and fermion numbers showing the regions of the symbiotic and Anderson localization of the Bose component is presented. Finally, the stability of symbiotic and Anderson localized states is established under small perturbations.

DOI
10.1103/physreva.84.023632

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We study the localization of a cigar-shaped superfluid Bose-Fermi mixture in a quasiperiodic bichromatic optical lattice (OL) for interspecies attraction and intraspecies repulsion. The mixture is described by the Gross-Pitaevskii equation for the bosons, coupled to a hydrodynamic mean-field equation for fermions at unitarity. We confirm the existence of the symbiotic localized states in the Bose-Fermi mixture and Anderson localization of the Bose component in the interacting Bose-Fermi mixture on a bichromatic OL. The phase diagram in boson and fermion numbers showing the regions of the symbiotic and Anderson localization of the Bose component is presented. Finally, the stability of symbiotic and Anderson localized states is established under small perturbations.
By direct numerical simulation of the time-dependent Gross-Pitaevskii equation using the split-step Fourier spectral method, we study different aspects of the localization of a cigar-shaped interacting binary (two-component) Bose-Einstein condensate (BEC) in a one-dimensional bichromatic quasiperiodic optical-lattice potential, as used in a recent experiment on the localization of a BEC [Roati et al., Nature 453, 895 (2008)]. We consider two types of localized states: (i) when both localized components have a maximum of density at the origin x=0x=0x=0, and (ii) when the first component has a maximum of density and the second a minimum of density at x=0x=0x=0. In the noninteracting case, the density profiles are symmetric around x=0x=0x=0. We numerically study the breakdown of this symmetry due to interspecies and intraspecies interactions acting on the two components. Where possible, we have compared the numerical results with a time-dependent variational analysis. We also demonstrate the stability of the localized symmetry-broken BEC states under small perturbation.
By numerical simulation of the time-dependent Gross-Pitaevskii equation we show that a weakly interacting or noninteracting Bose-Einstein condensate (BEC) vortex can be localized in a three-dimensional bichromatic quasiperiodic optical-lattice (OL) potential generated by the superposition of two standing-wave polarized laser beams with incommensurate wavelengths. We also study the localization of a (nonrotating) BEC in two and three dimensions by bichromatic OL potentials along orthogonal directions. This is a generalization of the localization of a BEC in a one-dimensional bichromatic OL as studied in a recent experiment [Roati et al., Nature 453, 895 (2008)]. We demonstrate the stability of the localized state by considering its time evolution in the form of a stable breathing oscillation in a slightly altered potential for a large period of time. Finally, we consider the localization of a BEC in a random one-dimensional potential in the form of several identical repulsive spikes arbitrarily distributed in space.
By numerical simulation and variational analysis of the Gross–Pitaevskii equation we study the localization, with an exponential tail, of a dipolar Bose–Einstein condensate (DBEC) of 52 Cr atoms in a three-dimensional bichromatic optical lattice (OL) generated by two monochromatic OLs of incommensurate wavelengths along three orthogonal directions. For a fixed dipole–dipole interaction, a localized state of a small number of atoms (∼1000) could be obtained when the short-range interaction is not too attractive or not too repulsive. A phase diagram showing the region of stability of a DBEC with a short-range interaction and dipole–dipole interaction is given.
We study the localization of a noninteracting and weakly interacting Bose-Einstein condensate (BEC) with spin-orbit coupling loaded in a quasiperiodic bichromatic optical lattice potential using the numerical solution and variational approximation of a binary mean-field Gross-Pitaevskii equation with two pseudospin components. We confirm the existence of the stationary localized states in the presence of the spin-orbit and Rabi couplings for an equal distribution of atoms in the two components. We find that the interaction between the spin-orbit and Rabi couplings favors the localization or delocalization of the BEC depending on the phase difference between the components. We also studied the oscillation dynamics of the localized states for an initial population imbalance between the two components.
By direct numerical simulation of the time-dependent Gross-Pitaevskii equation using the split-step Fourier spectral method we study the double-humped localization of a cigar-shaped Bose-Einstein condensate (BEC) in a one-dimensional bichromatic quasi-periodic optical-lattice potential, as used in a recent experiment on the localization of a BEC [G. Roati et al., Nature 453 , 895 (2008)]. Such states are spatially antisymmetric and are excited modes of Anderson localization. Where possible, we have compared the numerical results with a variational analysis. We also demonstrate the stability of the localized double-humped BEC states under small perturbation.
We studied the localization property of Bose-Fermi mixture systems on incommensurate optical lattices by using quantum Monte-Carlo simulations. We found a characteristic behavior of the superfluid density when changing the Bose-Bose interactions and Bose-Fermi interactions over a wide range. The superfluidity of the bosons was enhanced in the presence of the fermions by the repulsive Bose-Fermi interactions which counteracted the localization of the bosons. With attractive Bose-Fermi interactions, on the other hand, the superfluidity is also enhanced by a different mechanism when the number of the bosons is much larger than that of the fermions.