### Abstract

We study interacting one-dimensional two-component mixtures of cold atoms in a random potential, and extend the results reported earlier. We construct the phase diagram of a disordered Bose-Fermi mixture as a function of the strength of the Bose-Bose and Bose-Fermi interactions, and the ratio of the bosonic sound velocity and the Fermi velocity. Performing renormalization group and variational calculations, three phases are identified: (i) a fully delocalized two-component Luttinger liquid with superfluid bosons and fermions, (ii) a fully localized phase with both components pinned by disorder, and (iii) an intermediate phase where fermions are localized but bosons are superfluid. Within the variational approach, each phase corresponds to a different level of replica symmetry breaking. In the fully localized phase we find that the bosonic and fermionic localization lengths can largely differ. We also compute the long-wavelength asymptotic behavior of the momentum distribution as well as that of the structure factor of the atoms (both experimentally accessible), and discuss how the three phases can be experimentally distinguished.

Original language | English |
---|---|

Article number | 023625 |

Journal | Physical Review A |

Volume | 85 |

Issue number | 2 |

DOIs | |

Publication status | Published - Feb 21 2012 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Physical Review A*,

*85*(2), [023625]. https://doi.org/10.1103/PhysRevA.85.023625

**Mixtures of ultracold atoms in one-dimensional disordered potentials.** / Crépin, François; Zaránd, G.; Simon, Pascal.

Research output: Contribution to journal › Article

*Physical Review A*, vol. 85, no. 2, 023625. https://doi.org/10.1103/PhysRevA.85.023625

}

TY - JOUR

T1 - Mixtures of ultracold atoms in one-dimensional disordered potentials

AU - Crépin, François

AU - Zaránd, G.

AU - Simon, Pascal

PY - 2012/2/21

Y1 - 2012/2/21

N2 - We study interacting one-dimensional two-component mixtures of cold atoms in a random potential, and extend the results reported earlier. We construct the phase diagram of a disordered Bose-Fermi mixture as a function of the strength of the Bose-Bose and Bose-Fermi interactions, and the ratio of the bosonic sound velocity and the Fermi velocity. Performing renormalization group and variational calculations, three phases are identified: (i) a fully delocalized two-component Luttinger liquid with superfluid bosons and fermions, (ii) a fully localized phase with both components pinned by disorder, and (iii) an intermediate phase where fermions are localized but bosons are superfluid. Within the variational approach, each phase corresponds to a different level of replica symmetry breaking. In the fully localized phase we find that the bosonic and fermionic localization lengths can largely differ. We also compute the long-wavelength asymptotic behavior of the momentum distribution as well as that of the structure factor of the atoms (both experimentally accessible), and discuss how the three phases can be experimentally distinguished.

AB - We study interacting one-dimensional two-component mixtures of cold atoms in a random potential, and extend the results reported earlier. We construct the phase diagram of a disordered Bose-Fermi mixture as a function of the strength of the Bose-Bose and Bose-Fermi interactions, and the ratio of the bosonic sound velocity and the Fermi velocity. Performing renormalization group and variational calculations, three phases are identified: (i) a fully delocalized two-component Luttinger liquid with superfluid bosons and fermions, (ii) a fully localized phase with both components pinned by disorder, and (iii) an intermediate phase where fermions are localized but bosons are superfluid. Within the variational approach, each phase corresponds to a different level of replica symmetry breaking. In the fully localized phase we find that the bosonic and fermionic localization lengths can largely differ. We also compute the long-wavelength asymptotic behavior of the momentum distribution as well as that of the structure factor of the atoms (both experimentally accessible), and discuss how the three phases can be experimentally distinguished.

UR - http://www.scopus.com/inward/record.url?scp=84857524159&partnerID=8YFLogxK

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U2 - 10.1103/PhysRevA.85.023625

DO - 10.1103/PhysRevA.85.023625

M3 - Article

AN - SCOPUS:84857524159

VL - 85

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 2

M1 - 023625

ER -