Pair Correlations in a Finite-Temperature 1D Bose Gas

Abstract

We calculate the two-particle local correlation for an interacting 1D Bose gas at finite temperature and classify various physical regimes. We present the exact numerical solution by using the Yang-Yang equations and Hellmann-Feynman theorem and develop analytical approaches. Our results draw prospects for identifying the regimes of coherent output of an atom laser, and of finitetemperature "fermionization" through the measurement of the rates of two-body inelastic processes, such as photo-association. The knowledge of the exact solutions to the 1D models allows us to go far beyond the mean-field Bogoliubov approximation. In the current stage of studies of experimentally feasible 1D Bose gases, one of the most important issues that requires such an approach is understanding the correlation properties in the various regimes at finite temperatures.In this Letter we give an exact calculation of the finitetemperature two-particle local correlation for an interacting uniform 1D Bose gas,is the field operator and n = Ψ † (x)Ψ(x) is the linear (1D) density. As a result, we identify and classify various finite-temperature regimes of the 1D Bose gas. Aside from this, the pair correlations are responsible for the rates of inelastic collisional processes [9], and are of particular importance for the studies of coherence properties of atom "lasers" produced in 1D waveguides.At T = 0, the local two-and three-particle correlations of a uniform 1D Bose gas have recently been calculated in Ref. [10]. Here one has two well-known and physically distinct regimes of quantum degeneracy. For weak couplings or high densities, the gas is in a coherent or Gross-Pitaevskii (GP) regime with g (2) → 1. In this regime, long-range order is destroyed by longwavelength phase fluctuations [11] and the equilibrium state is a quasi-condensate characterized by suppressed density fluctuations. For strong couplings or low densities, the gas reaches the strongly interacting or TonksGirardeau (TG) regime and undergoes "fermionization" [3,4]: the wave function strongly decreases as particles approach each other, and g (2) → 0.At the non-zero temperatures studied here, one has to further extend the classification of different regimes. For strong enough couplings or low densities, we obtain the TG regime with g (2) → 0 not only at low temperatures, but also at high temperatures. In addition, and in contrast to previous T = 0 results, we find a weak-coupling or high-density regime in which fluctuations are enhanced. Asymptotically, they reach the non-interacting Bose gas level of g (2) → 2 (rather than g (2) → 1), for any finite temperature T .The emergence of this behavior at low temperatures implies that one can identify three physically distinct regimes of quantum degeneracy: the strong-coupling TG regime of "fermionization" with g (2) → 0, a coherent GP regime with g (2) ≃ 1 at intermediate coupling strength, and a fully decoherent quantum (DQ) regime with g (2) ≃ 2 at very weak couplings. In the GP regime, where the density fluctuations are suppresse...

Equilibrium thermodynamic properties of interacting two-component bosons in one dimension

“…The values of and T are chosen such that in each case the ratio T goes from less to more than 1. Following the qualitative description of [48,49] for the single-component case, the regimes of the gas are identified by the two dimensionless parameters γ = c n 1 +n 2 and τ = T (n 1 +n 2 ) 2 , respectively, the interaction strength and the reduced temperature. As results presented hereafter are made for the fixed interaction parameter (c), the ratio τ γ 2 = T c 2 is then constant and the regime is identified by the position on the γ axis.…”

Fock-state dynamics in Raman photoassociation of Bose-Einstein condensates

“…The different dynamics of the Fock state cannot be ascribed to the initial spatial intensity correlation, g ͑2͒ ͑x , x͒ (see Refs. [12,31]), as this between 1 −1/N for a Fock state, 1 for a coherent state, and 1.04 at the center for the crescent state. As demonstrated previously [11,12], the more uncertainty in phase that a given state has by comparison with a coherent state, the more difference we see in the dynamics.…”

Effective interactions, Fermi–Bose duality, and ground states of ultracold atomic vapors in tight de Broglie waveguides

“…Note that the density n is in the numerator, whereas it is in the denominator of the bosonic analog γ B = mg B 1D /n 2 . For γ F ≫ 1 one has a "fermionic TG gas" [35], a fermionic analog of the impenetrable Bose gas, called the "Tonks-Girardeau" (TG) gas in recent literature [14,18,25,29,[37][38][39][40][41][42][43][44][45][46][47][48]. As previously noted, a F 1D → −∞ in the fermionic TG limit, implying an interaction-free exterior wave function.…”