Correlations of stripe phase in one-dimensional spin-orbit coupled Bose gas

We investigate the effects of interaction for the stripe phase of a homogeneous one-dimensional Bose gas with laser-induced Raman spin-orbit coupling (SOC) and Zeeman splitting, for a wide range of densities. In order to account for quantum fluctuations, important in one dimension for low densities close to the Tonks-Girardeau limit, we use a variational method based on the hypernetted-chain Euler-Lagrange optimization of a Jastrow-Feenberg ansatz for the many-body wave function. For strong coupling we observe significant deviations from mean-field results not only quantitatively but also qualitatively. The main interest of this paper lies in the interplay and competition between interaction-induced pair correlations and the SOC-induced density oscillations of the stripe phase. We explain the increase in wave number of this density oscillation with increasing interaction due to an effective attraction between particles in the many-body system.