skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Commensurate mixtures of ultracold atoms in one dimension

Abstract

We study binary mixtures of ultracold atoms, confined to one dimension in an optical lattice, with commensurate densities. Within a Luttinger liquid description, which treats various mixtures on equal footing, we derive a system of renormalization group equations at second order, from which we determine the rich phase diagrams of these mixtures. These phases include charge and spin density wave orders, singlet and triplet pairings, polaron pairing [L. Mathey et al., Phys. Rev. Lett. 93, 120404 (2004)], and a supersolid phase. Various methods to detect our results experimentally are discussed.

Authors:
 [1]
  1. Physics Department, Harvard University, Cambridge, Massachusetts 02138 (United States)
Publication Date:
OSTI Identifier:
20957804
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. B, Condensed Matter and Materials Physics; Journal Volume: 75; Journal Issue: 14; Other Information: DOI: 10.1103/PhysRevB.75.144510; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; ATOMS; BINARY MIXTURES; CHARGE DENSITY; DENSITY; EQUATIONS; LIQUIDS; PHASE DIAGRAMS; POLARONS; RENORMALIZATION; SPIN; TRIPLETS

Citation Formats

Mathey, L. Commensurate mixtures of ultracold atoms in one dimension. United States: N. p., 2007. Web. doi:10.1103/PHYSREVB.75.144510.
Mathey, L. Commensurate mixtures of ultracold atoms in one dimension. United States. doi:10.1103/PHYSREVB.75.144510.
Mathey, L. Sun . "Commensurate mixtures of ultracold atoms in one dimension". United States. doi:10.1103/PHYSREVB.75.144510.
@article{osti_20957804,
title = {Commensurate mixtures of ultracold atoms in one dimension},
author = {Mathey, L.},
abstractNote = {We study binary mixtures of ultracold atoms, confined to one dimension in an optical lattice, with commensurate densities. Within a Luttinger liquid description, which treats various mixtures on equal footing, we derive a system of renormalization group equations at second order, from which we determine the rich phase diagrams of these mixtures. These phases include charge and spin density wave orders, singlet and triplet pairings, polaron pairing [L. Mathey et al., Phys. Rev. Lett. 93, 120404 (2004)], and a supersolid phase. Various methods to detect our results experimentally are discussed.},
doi = {10.1103/PHYSREVB.75.144510},
journal = {Physical Review. B, Condensed Matter and Materials Physics},
number = 14,
volume = 75,
place = {United States},
year = {Sun Apr 01 00:00:00 EDT 2007},
month = {Sun Apr 01 00:00:00 EDT 2007}
}
  • We investigate many-body phase diagrams of atomic boson-fermion mixtures loaded in the two-dimensional optical lattice. Bosons mediate an attractive, finite-range interaction between fermions, leading to fermion pairing phases of different orbital symmetries. Specifically, we show that by properly tuning atomic and lattice parameters it is possible to create superfluids with s-, p-, and d-wave pairing symmetry as well as spin and charge density wave phases. These phases and their stability are analyzed within the mean-field approximation for systems of {sup 40}K-{sup 87}Rb and {sup 40}K-{sup 23}Na mixtures. For the experimentally accessible regime of parameters, superfluids with unconventional fermion pairing havemore » transition temperature around a percent of the Fermi energy.« less
  • We study quadrupole collective oscillations in the bose-fermi mixtures of ultracold atomic gases of Yb isotopes, which are realized by Kyoto group. Three kinds of combinations are chosen, {sup 170}Yb-{sup 171}Yb, {sup 170}Yb-{sup 173}Yb and {sup 174}Yb-{sup 173}Yb, where boson-fermion interactions are weakly repulsive, strongly attractive and strongly repulsive respectively. Collective oscillations in these mixtures are calculated in a dynamical time-evolution approach with the time-dependent Gross-Pitaevskii and the Vlasov equations. The boson oscillations are shown to have one collective mode, and the fermions are shown to have the boson-forced and two intrinsic modes, which correspond to the inside- and outside-fermionmore » oscillations for the boson-distributed regions. The oscillations obtained in the dynamical approach show discrepancies from the results obtained in the small-amplitude approximations, e.g., the random phase approximation, except in the case of weak boson-fermion interactions. We also analyze these discrepancies, and show that they originated in the change of the fermion distributions through oscillation.« less
  • The momentum distribution is one of the most important quantities which provides information about interactions in many-body systems. At the same time it is a quantity that can easily be accessed in experiments on ultracold atoms. In this paper, we consider mixtures of light- and heavy-fermionic atoms in an optical lattice described effectively by the Falicov-Kimball model. Using a Monte Carlo method, we study how different ordered density-wave phases can be detected by measurement of the momentum distribution of the light atoms. We also demonstrate that ordered phases can be seen in Bragg scattering experiments. Our results indicate that themore » main factor that determines the momentum distribution of the light atoms is the trap confinement. On the other hand, the pattern formed by the heavy atoms seen in the Bragg scattering experiments is very sensitive to the temperature and possibly can be used in low-temperature thermometry.« less
  • The prospects of sympathetic cooling of polar molecules with magnetically cotrapped alkali-metal atoms are generally considered poor due to strongly anisotropic atom-molecule interactions leading to large spin relaxation rates. Using rigorous quantum scattering calculations based on ab initio interaction potentials, we show that inelastic spin relaxation in low-temperature collisions of CaH({sup 2}{Sigma}) molecules with Li and Mg atoms occurs at a slow rate despite the strongly anisotropic interactions. This unexpected result, which we rationalize using multichannel quantum-defect theory, opens up the possibility of sympathetic cooling of polar {sup 2}{Sigma} molecules with alkali-metal atoms in a magnetic trap and with alkaline-earth-metalmore » atoms in an optical dipole trap.« less
  • We study the three-body problem for both fermionic and bosonic cold-atom gases in a parabolic transverse trap of length scale a{sub perpendicular}. For this quasi-one-dimensional (quasi-1D) problem, there is a two-body bound state (dimer) for any sign of the 3D scattering length a and a confinement-induced scattering resonance. The fermionic three-body problem is universal and characterized by two atom-dimer scattering lengths a{sub ad} and b{sub ad}. In the tightly bound 'dimer limit' a{sub perpendicular}/a{yields}{infinity}, we find b{sub ad}=0 and a{sub ad} is linked to the 3D atom-dimer scattering length. In the weakly bound 'BCS limit' a{sub perpendicular}/a{yields}-{infinity}, a connection tomore » the Bethe ansatz is established, which allows for exact results. The full crossover is obtained numerically. The bosonic three-body problem, however, is nonuniversal: a{sub ad} and b{sub ad} depend both on a{sub perpendicular}/a and on a parameter R* related to the sharpness of the resonance. Scattering solutions are qualitatively similar to fermionic ones. We predict the existence of a single confinement-induced three-body bound state (trimer) for bosons.« less