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arXiv:cond-mat/0207338 · Physical Review Letters

Stability and Phase Coherence of Trapped 1D Bose Gases

Dimitri M. Gangardt, Gora V. Shlyapnikov

Published Jan 2, 2003• 262 citations
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Abstract

We discuss stability and phase coherence of 1D trapped Bose gases and find that inelastic decay processes, such as three-body recombination, are suppressed in the strongly interacting (Tonks-Girardeau) and intermediate regimes. This is promising for achieving these regimes with a large number of particles. "Fermionization" of the system reduces the phase coherence length, and at T=0 the gas is fully phase coherent only deeply in the weakly interacting (Gross-Pitaevskii) regime.

DOI
10.1103/physrevlett.90.010401

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We discuss stability and phase coherence of 1D trapped Bose gases and find that inelastic decay processes, such as three-body recombination, are suppressed in the strongly interacting (Tonks-Girardeau) and intermediate regimes. This is promising for achieving these regimes with a large number of particles. "Fermionization" of the system reduces the phase coherence length, and at T=0 the gas is fully phase coherent only deeply in the weakly interacting (Gross-Pitaevskii) regime.
We study the properties of strongly interacting Bose gases at the density and temperature regime when the three-body recombination rate is substantially reduced. In this regime, one can have a Bose gas with all particles in scattering states (i.e., the "upper branch") with little loss even at unitarity over the duration of the experiment. We show that because of bosonic enhancement, pair formation is shifted to the atomic side of the original resonance (where scattering length a(s)<0), opposite to the fermionic case. In a trap, a repulsive Bose gas remains mechanically stable when brought across resonance to the atomic side until it reaches a critical scattering length a(s)*<0. For a(s)<a(s)*, the density consists of a core of upper branch bosons surrounded by an outer layer of equilibrium branch. The conditions of low three-body recombination require that the particle number N<1.024(T/ω)(5/2) in a harmonic trap with frequency ω.
The loading of a Bose-Einstein condensate into a deep two-dimensional optical lattice provides a unique way to study one-dimensional Bose gases: the strong radial confinement freezes any motion in two dimensions, and for deep enough lattices, the system can be seen as an array of independent I D tubers. For our experimental parameters, the ID gas is predicted to be in an intermediate regime between the Tonks-Girardeau and the Thomas-Fermi regimes. We performed experiments showing that some long range phase coherence is present in this regime. We investigated correlation properties of these gases by studying their collective oscillations. In addition, we investigated the ID Mott transition by adiabatically loading the 1D gases into a 1D optical lattice.
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 CCC 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 investigate correlation properties of a one-dimensional interacting Bose gas by loading a magnetically trapped 87-Rb Bose-Einstein condensate into a deep two-dimensional optical lattice. We measure the three-body recombination rate for both the BEC in the magnetic trap and the BEC loaded into the optical lattice. The recombination rate coefficient is a factor of seven smaller in the lattice, which we interpret as a reduction in the local three-body correlation function in the 1D case. This is a signature of correlation intermediate between that of the uncorrelated phase coherent 1D mean-field regime and the strongly correlated Tonks-Girardeau regime.