Stability and Phase Coherence of Trapped 1D Bose Gases

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 (TonksGirardeau) 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.PACS numbers: 03.75Fi, 05.30JpRecent success in creating quantum degenerate 1D trapped atomic gases [1,2,3] has stimulated an interest in correlation properties of these systems. The 1D regime is reached by tightly confining the radial motion of atoms in a cylindrical trap to zero point oscillations. The difference between such a kinematically 1D gas and a purely 1D gas is related only to the value of the interparticle interaction, which depends on the radial confinement.The 1D Bose gas with repulsive short-range interactions characterized by the coupling constant g > 0 exhibits remarkable properties. Counterintuitively, it becomes more non-ideal with decreasing 1D density n [4,5]. The equation of state and correlation functions depend crucially on the parameterwhere m is the atom mass. For comparatively large n, the parameter γ ≪ 1 and √ γ represents the ratio of the mean interparticle separation 1/n to the correlation length l c =h/ √ mng. In this case the gas is in the weakly interacting or Gross-Pitaevskii (GP) regime, and the amplitude of the boson field obeys the familiar Gross-Pitaevskii equation. For sufficiently low densities (or large g), one has γ ≫ 1 and the strongly interacting or Tonks-Girardeau (TG) regime is reached. In this regime the 1D gas acquires fermionic properties in the sense that the wave function strongly decreases as particles approach each other (see [4,5] and cf. [6]). For γ = ∞ any correlation function of the density can be calculated straightforwardly [7] by using the exact mapping onto the system of free fermions found by Girardeau [4].A uniform 1D system of bosons interacting via a deltafunctional potential is integrable by using the Bethe ansatz and has been a subject of extensive theoretical studies. Lieb and Liniger [5] have calculated the ground state energy and excitation spectrum for any value of the parameter γ. Yang and Yang [8] have studied thermodynamic properties of this system at finite temperatures and found no phase transition for T > 0. The absence of long-range order and true Bose-Einstein condensate in finite-temperature 1D Bose gases follows from the Bogoliubov k −2 theorem as has been expounded in [9]. The long-range order is destroyed by long-wave fluctuations of the phase leading to an exponential decay of the oneparticle density matrix at large distances [10,11]. A similar picture is found at T = 0 [12], where the density matrix undergoes a power-law decay [11,13,14]. In the past few decades, a general approach has been developed for exact calculations of one-and two-particle correla...

Tan relations in one dimension

“…At small momenta, it diverges like 1/ √ k while for large momenta it exhibits a C B /k 4 -tail as shown by Olshanii and Dunjko [1]. Using equation (25), which relates the bosonic contact to the pair correlation function at zero distance, the asymptotic behavior g (2) (0) = 4π 2 /3γ 2 B in the limit γ B ≫ 1 [37] gives rise to a universal value s B (∞) = 4 3π 2 ≃ 0.1350949 (57) of the dimensionless contact s B = C B /k 4 F , which is much smaller than that for infinitely repulsive fermions. The finiteness of the dimensionless contact s(γ) in the limit of infinite repulsion can be inferred from a simple argument.…”

Ground-state properties of ultracold trapped bosons with an immersed ionic impurity

“…Loss can result from three-body scattering which might become important in the weakly interacting regime [74], from spontaneous scattering induced by high power traps with decay times of several hundred milliseconds [75], and from atom-ion collisions which can become the dominant loss channel if the ion is not cooled to the ultracold regime [9].…”

Confinement-induced resonances in anharmonic waveguides

“…For a one-dimensional (1D) Bose gas [1][2][3], the finite-temperature correlations predicted for a Tonks-Girardeau gas [4,5] have been experimentally verified [6,7], and a cross-over to a non-equilibrium super Tonks-Girardeau gas has been realized [8]. For a twodimensional (2D) geometry, the Berezinskii-KosterlitzThouless phase transition was predicted [9,10], and subsequently observed in experiment [11].…”