Dynamics of excitations in a onedimensional Bose liquid.pdf

Dynamics of excitations in a one-dimensional Bose liquid M. Khodas,1 M. Pustilnik,2 A. Kamenev,3 and L.I. Glazman1 1 William I. Fine Theoretical Physics Institute and School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455 2School of Physics, Georgia Institute of Technology, Atlanta, GA 30332 3 School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455 7 We show that the dynamic structure factor of a one-dimensional Bose liquid has a power-law 0 singularity defining the main mode of collective excitations. Using the Lieb-Liniger model, we 0 evaluate the corresponding exponent as a function of the wave vector and the interaction strength. 2 PACS numbers: 03.75.Kk, 05.30.Jp, 02.30.Ik p e S Progress in the ability to manipulate ultracold atomic one to relate the parameters of the hydrodynamic de- 4 gases stimulates the interest in fundamental properties scription [5, 6], the sound velocity v and the parameter 1 of one-dimensional (1D) Bose liquids [1]. The quan- K , to the concentration n = N/L and the dimensionless ] tity characterising the collective excitations in these sys- interaction strength γ = mc/n [9]. Finding dynamic cor- h tems, the dynamic structure factor (DSF), is now di- relation functions, such as DSF, in a closed form remains c rectly accessible experimentally using the Bragg spec- a challenge [8]. The most impressive progress so far was e troscopy technique [2]. Already the very first such mea- achieved by combining a