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Title: Luther-Emery Phase and Atomic-Density Waves in a Trapped Fermion Gas

Abstract

The Luther-Emery liquid is a state of matter that is predicted to occur in one-dimensional systems of interacting fermions and is characterized by a gapless charge spectrum and a gapped spin spectrum. In this Letter we discuss a realization of the Luther-Emery phase in a trapped cold-atom gas. We study by means of the density-matrix renormalization-group technique a two-component atomic Fermi gas with attractive interactions subject to parabolic trapping inside an optical lattice. We demonstrate how this system exhibits compound phases characterized by the coexistence of spin pairing and atomic-density waves. A smooth crossover occurs with increasing magnitude of the atom-atom attraction to a state in which tightly bound spin-singlet dimers occupy the center of the trap. The existence of atomic-density waves could be detected in the elastic contribution to the light-scattering diffraction pattern.

Authors:
; ; ;  [1];  [2];  [3];  [4];  [5]
  1. NEST-CNR-INFM and Scuola Normale Superiore, I-56126 Pisa (Italy)
  2. International School for Advanced Studies (SISSA), via Beirut 2-4, I-34014 Trieste (Italy)
  3. (Italy)
  4. Centro Internacional de Fisica da Materia Condensada, Universidade de Brasilia, Caixa Postal 04513, 70919-970 Brasilia (Brazil)
  5. Departamento de Fisica e Informatica, Instituto de Fisica de Sao Carlos, Universidade de Sao Paulo, Caixa Postal 369, 13560-970 Sao Carlos, Sao Paulo (Brazil)
Publication Date:
OSTI Identifier:
20861609
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review Letters; Journal Volume: 98; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevLett.98.030404; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ATOMS; DENSITY; DENSITY MATRIX; DIFFRACTION; DIMERS; FERMI GAS; FERMIONS; LIGHT SCATTERING; LIQUIDS; MATTER; ONE-DIMENSIONAL CALCULATIONS; RENORMALIZATION; SPECTRA; SPIN; TRAPPING; TRAPS

Citation Formats

Gao Xianlong, Rizzi, M., Polini, Marco, Tosi, M. P., Fazio, Rosario, NEST-CNR-INFM and Scuola Normale Superiore, I-56126 Pisa, Campo, V. L. Jr., and Capelle, K. Luther-Emery Phase and Atomic-Density Waves in a Trapped Fermion Gas. United States: N. p., 2007. Web. doi:10.1103/PHYSREVLETT.98.030404.
Gao Xianlong, Rizzi, M., Polini, Marco, Tosi, M. P., Fazio, Rosario, NEST-CNR-INFM and Scuola Normale Superiore, I-56126 Pisa, Campo, V. L. Jr., & Capelle, K. Luther-Emery Phase and Atomic-Density Waves in a Trapped Fermion Gas. United States. doi:10.1103/PHYSREVLETT.98.030404.
Gao Xianlong, Rizzi, M., Polini, Marco, Tosi, M. P., Fazio, Rosario, NEST-CNR-INFM and Scuola Normale Superiore, I-56126 Pisa, Campo, V. L. Jr., and Capelle, K. Fri . "Luther-Emery Phase and Atomic-Density Waves in a Trapped Fermion Gas". United States. doi:10.1103/PHYSREVLETT.98.030404.
@article{osti_20861609,
title = {Luther-Emery Phase and Atomic-Density Waves in a Trapped Fermion Gas},
author = {Gao Xianlong and Rizzi, M. and Polini, Marco and Tosi, M. P. and Fazio, Rosario and NEST-CNR-INFM and Scuola Normale Superiore, I-56126 Pisa and Campo, V. L. Jr. and Capelle, K.},
abstractNote = {The Luther-Emery liquid is a state of matter that is predicted to occur in one-dimensional systems of interacting fermions and is characterized by a gapless charge spectrum and a gapped spin spectrum. In this Letter we discuss a realization of the Luther-Emery phase in a trapped cold-atom gas. We study by means of the density-matrix renormalization-group technique a two-component atomic Fermi gas with attractive interactions subject to parabolic trapping inside an optical lattice. We demonstrate how this system exhibits compound phases characterized by the coexistence of spin pairing and atomic-density waves. A smooth crossover occurs with increasing magnitude of the atom-atom attraction to a state in which tightly bound spin-singlet dimers occupy the center of the trap. The existence of atomic-density waves could be detected in the elastic contribution to the light-scattering diffraction pattern.},
doi = {10.1103/PHYSREVLETT.98.030404},
journal = {Physical Review Letters},
number = 3,
volume = 98,
place = {United States},
year = {Fri Jan 19 00:00:00 EST 2007},
month = {Fri Jan 19 00:00:00 EST 2007}
}
  • We study the quasi-one-dimensional (Q1D) spin-polarized Bose-Fermi mixture of atomic gases at zero temperature. Bosonic excitation spectra are calculated in the random phase approximation on the ground state with uniform Bose-Einstein condensates (BEC's) and the Peierls instabilities are shown to appear in bosonic collective excitation modes with wave number 2k{sub F} by the coupling between the Bogoliubov-phonon mode of bosonic atoms and the fermion particle-hole excitations. The ground-state properties are calculated in the variational method, and, corresponding to the Peierls instability, the state with a periodic BEC and fermionic density waves with the period {pi}/k{sub F} are shown to havemore » a lower energy than the uniform one. We also briefly discuss the Q1D system confined in a harmonic oscillator potential and derive the Peierls instability condition for it.« less
  • We show that the degeneracy parameter of a trapped Bose gas can be changed adiabatically in a reversible way, both in the Boltzmann regime and in the degenerate Bose regime. We have performed measurements on spin-polarized atomic hydrogen in the Boltzmann regime, demonstrating reversible changes of the degeneracy parameter (phase-space density) by more than a factor of 2. This result is in good agreement with theory. By extending our theoretical analysis to the quantum degenerate regime we predict that, starting close enough to the Bose-Einstein phase transition, one can cross the transition by an adiabatic change of the trap shape.more » {copyright} {ital 1997} {ital The American Physical Society}« less
  • A Comment on the Letter by T. Mizushima, K. Machida, and M. Ichioka, Phys. Rev. Lett. 94, 060404 (2005)
  • Density-wave structures are studied in a quasi-one-dimensional atomic gas mixture of one-component bosons and two-component fermions using the mean-field approximation at zero temperature. Owing to the Peierls instability in the fermion system, the ground state of the system shows a fermion density wave and periodic Bose-Einstein condensation induced by the boson-fermion interatomic interaction. For the two-component fermions, two density waves appear in each component, and their phase difference distinguishes two types of ground states, the in-phase and the out-phase density waves. In this paper, a self-consistent method is presented to treat the density-wave states in a boson-fermion mixture with two-componentmore » fermions. The analysis of the effective potential and the interaction energies shows that the density waves appearing in the ground state are in phase or out of phase depending on the strength of the interfermion interaction. It is also shown that the periodic Bose-Einstein condensate coexists with the in-phase density wave of fermions, but, in the case of out of phase, only the uniform condensate appears. The phase diagram of the system is given for the effective coupling constants.« less
  • We present a theoretical study of the dynamical behavior of a gas made of ultracold fermionic atoms, which during their motions can collide with a much smaller number of thermal bosonic impurities. The atoms are confined inside harmonic traps and the interactions between the two species are treated as due to s-wave scattering with a negative scattering length modeling the {sup 40}K-{sup 87}Rb fermion-boson system. We set the fermions into motion by giving a small shift to their trap center and examine two alternative types of initial conditions, referring to (i) a close-to-equilibrium situation in which the two species aremore » at the same temperature (well below the Fermi temperature and well above the Bose-Einstein condensation temperature); and (ii) a far-from-equilibrium case in which the impurities are given a Boltzmann distribution of momenta while the fermions are at very low temperatures. The dynamics of the gas is evaluated by the numerical solution of the Vlasov-Landau equations for the one-body distribution functions, supported by some analytical results on the collisional properties of a fermion gas. We find that the trapped gaseous mixture is close to the collisionless regime for values of the parameters corresponding to current experiments, but can be driven towards a collisional regime even without increasing the strength of the interactions, either by going over to heavier impurity masses or by matching the width of the momentum distribution of the impurities to the Fermi momentum of the fermion gas.« less