Is the 1D Bose gas superfluid?

Joachim Brand & Alexander Cherny

Max-Planck-Institut Dresden

Authors: Alexander Yu. Cherny (MPIPKS) and Joachim Brand (MPIPKS) While the one-dimensional 1D Bose gas appears to exhibit superfluid response under certain conditions, it fails the Landau criterion according to the elementary excitation spectrum calculated by Lieb. The apparent riddle is solved by calculating the dynamic structure factor (DSF) of the Lieb-Liniger 1D Bose gas. In a dual representation, strongly interacting bosons are mapped into weakly interacting fermions, which are treated in the Hartree-Fock and generalized random-phase approximations. The dynamic structure factor is calculated analytically in this approximation, which is valid to first order in $1/gamma$, where $1/gamma$ is the dimensionless interaction strength of the model. With the help of the obtained expression for the DSF, the drag force acting on a heavy impurity is calculated for arbitrary values of velocity of the impurity. The results clearly indicate a suppression of superfluidity-breaking umklapp excitations near the Tonks-gas limit. The predicted behaviour of the DSF can be directly observable by Bragg scattering in current experiments.