We study the three-fermion problem within a 1D model of a Feshbach resonance in order to gain insight into how the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-like state at small negative scattering lengths evolves into a Bose-Fermi mixture at small positive scattering lengths. The FFLO state possesses an oscillating superfluid correlation function, while in a Bose-Fermi mixture correlations are monotonic. We find that this behavior is already present at the three-body level. We present an exact study of the three-body problem and gain extra insights by considering world lines of a path-integral Monte Carlo calculation.We study the three-fermion problem within a 1D model of a Feshbach resonance in order to gain insight into how the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-like state at small negative scattering lengths evolves into a Bose-Fermi mixture at small positive scattering lengths. The FFLO state possesses an oscillating superfluid correlation function, while in a Bose-Fermi mixture correlations are monotonic. We find that this behavior is already present at the three-body level. We present an exact study of the three-body problem and gain extra insights by considering world lines of a path-integral Monte Carlo calculation.

arXiv:0902.4653Physical Review AMar 31, 201017 citations

Exact results for the 1D mixed Bose-Fermi interacting gas

Murray T. Batchelor, Michael Bortz, Xi-Wen Guan +1 more

Jun 20, 20050 citations

Fermionization of a strongly interacting Bose-Fermi mixture in a one-dimensional harmonic trap

Bess Fang, Patrizia Vignolo, Christian Miniatura +1 more

We consider a strongly interacting one-dimensional (1D) Bose-Fermi mixture confined in a harmonic trap. It consists of a Tonks-Girardeau (TG) gas (1D Bose gas with repulsive hard-core interactions) and of a noninteracting Fermi gas (1D spin-aligned Fermi gas), both species interacting through hard-core repulsive interactions. Using a generalized Bose-Fermi mapping, we determine the one-body density matrices, exact particle density profiles, momentum distributions, and behavior of the mixture under 1D expansion when opening the trap. In real space, bosons and fermions do not display any phase separation: the respective density profiles extend over the same region and they both present a number of peaks equal to the total number of particles in the trap. In momentum space the bosonic component has the typical narrow TG profile, while the fermionic component shows a broad distribution with fermionic oscillations at small momenta. Due to the large boson-fermion repulsive interactions, both the bosonic and the fermionic momentum distributions decay as $C{p}^{\ensuremath{-}4}$ at large momenta, like in the case of a pure bosonic TG gas. The coefficient $C$ is related to the two-body density matrix and to the bosonic concentration in the mixture. When opening the trap, both momentum distributions ``fermionize'' under expansion and turn into that of a Fermi gas with a particle number equal to the total number of particles in the mixture.We consider a strongly interacting one-dimensional (1D) Bose-Fermi mixture confined in a harmonic trap. It consists of a Tonks-Girardeau (TG) gas (1D Bose gas with repulsive hard-core interactions) and of a noninteracting Fermi gas (1D spin-aligned Fermi gas), both species interacting through hard-core repulsive interactions. Using a generalized Bose-Fermi mapping, we determine the one-body density matrices, exact particle density profiles, momentum distributions, and behavior of the mixture under 1D expansion when opening the trap. In real space, bosons and fermions do not display any phase separation: the respective density profiles extend over the same region and they both present a number of peaks equal to the total number of particles in the trap. In momentum space the bosonic component has the typical narrow TG profile, while the fermionic component shows a broad distribution with fermionic oscillations at small momenta. Due to the large boson-fermion repulsive interactions, both the bosonic and the fermionic momentum distributions decay as $C{p}^{\ensuremath{-}4}$ at large momenta, like in the case of a pure bosonic TG gas. The coefficient $C$ is related to the two-body density matrix and to the bosonic concentration in the mixture. When opening the trap, both momentum distributions ``fermionize'' under expansion and turn into that of a Fermi gas with a particle number equal to the total number of particles in the mixture.

arXiv:0809.4419Physical Review AFeb 26, 200920 citations

C

is related to the two-body density matrix and to the bosonic concentration in the mixture. When opening the trap, both momentum distributions ``fermionize'' under expansion and turn into that of a Fermi gas with a particle number equal to the total number of particles in the mixture.