Light scattering in inhomogeneous Tomonaga-Luttinger liquids

TL;DR

This paper derives an analytic expression for light scattering in inhomogeneous Tomonaga-Luttinger liquids, enabling experimental probing of universal scaling behaviors in confined one-dimensional quantum gases.

Contribution

It provides a simple analytic formula for the light-scattering cross section in inhomogeneous Tomonaga-Luttinger liquids based on density-dependent ground-state energy.

Findings

Universal scaling behavior identified in light scattering signals.

Application to dipolar bosonic gases in harmonic traps.

Potential for experimental detection via Bragg spectroscopy.

Abstract

We derive the dynamical structure factor for an inhomogeneous Tomonaga-Luttinger liquid as can be formed in a confined strongly interacting one-dimensional gas. In view of current experimental progress in the field, we provide a simple analytic expression for the light-scattering cross section, requiring only the knowledge of the density dependence of the ground-state energy, as they can be extracted e.g. from exact or Quantum Monte Carlo techniques, and a Thomas-Fermi description. We apply the result to the case of one-dimensional quantum bosonic gases with dipolar interaction in a harmonic trap, using an energy functional deduced from Quantum Monte Carlo computations. We find an universal scaling behavior peculiar of the Tomonaga-Luttinger liquid, a signature that can be eventually probed by Bragg spectroscopy in experimental realizations of such systems.