Non-Luttinger quantum liquid of one-dimensional spin-orbit-coupled bosons

We show that the synthetic spin-orbit coupling created in current ultracold atom experiments provides physicists a unique tool to control the Luttinger liquid parameter $K$ of weakly interacting bosons in one dimension. At a critical value of the Raman coupling strength ${\Omega }_c$, $K$ is suppressed down to zero, and the characteristic quasi-long-range order for ordinary one-dimensional quantum systems disappears. Consequently, the single-particle correlation function decays exponentially at the ground state, signifying the rise of a one-dimensional quantum many-body state beyond the standard Luttinger liquid paradigm. Momentum distribution, as well as scaling relations for various quantities in the vicinity of the critical point, can be used as a direct diagnosis of this non-Luttinger quantum liquid.

Figure 1

(a) From top to bottom, single-particle dispersion for $\Omega <{\Omega }_c^0$, $\Omega ={\Omega }_c^0$, and $\Omega >{\Omega }_c^0$. (b) Semilogarithmic plots of the single-particle correlation function at different values of $\Omega$. Triangles, circles, and boxes are numerical results for different values of $\delta$ with ${\rho }_0=5\lambda$, $g_s=-0.1g_0$, and $2m{g}_0/{\rho }_0=0.2$ which corresponds to $K_0=7$. Red solid lines are exponential fits and blue dashed curves are power-law fits in different spatial regions, respectively. For $\Omega ={\Omega }_c$, the correlation function becomes exponential even when $x\to \infty$. Curves for $\Omega =(1\pm 0.1){\Omega }_c$ have been offset by $\pm 0.3$ for clarity. (c) Luttinger liquid parameter $K$ (black solid), the correlation length $\xi$ (red dashed), and the characteristic length scale $x^{*}$ (blue dash-dotted) as functions of $\delta =\Omega -{\Omega }_c$.