Bosonizing one-dimensional cold atomic gases

Details Bosonizing one-dimensional cold atomic gases Bosonizing one-dimensional cold atomic gases

2003-07-02

arxiv.org/abs/cond-mat/0307033v2

Journal of Physics B: AMOP 37, S1-S47 (2004)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

39 pages + 14 EPS figures; typos corrected, references updated

Scientific paper

10.1088/0953-4075/37/7/051

We present results for the long-distance asymptotics of correlation functions of mesoscopic one-dimensional systems with periodic and open (Dirichlet) boundary conditions, as well as at finite temperature in the thermodynamic limit. The results are obtained using Haldane's harmonic-fluid approach (also known as ``bosonization''), and are valid for both bosons and fermions, in weakly and strongly interacting regimes. The harmonic-fluid approach and the method to compute the correlation functions using conformal transformations are explained in great detail. As an application relevant to one-dimensional systems of cold atomic gases, we consider the model of bosons interacting with a zero-range potential. The Luttinger-liquid parameters are obtained from the exact solution by solving the Bethe-ansatz equations in finite-size systems. The range of applicability of the approach is discussed, and the prefactor of the one-body density matrix of bosons is fixed by finding an appropriate parametrization of the weak-coupling result. The formula thus obtained is shown to be accurate, when compared with recent diffusion Montecarlo calculations, within less than 10%. The experimental implications of these results for Bragg scattering experiments at low and high momenta are also discussed.

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