Extracting dynamical Green’s function of ultracold quantum gases via electromagnetically induced transparency

Abstract

The essential quantum many-body physics of an ultracold quantum gas relies on the single-particle Green's functions. We demonstrate that it can be extracted by the spectrum of electromagnetically induced transparency (EIT). The single-particle Green's function depends on the convolution of EIT spectroscopy and the functional laser parameters. This optical measurement provides an efficient and nondestructive method to reveal the many-body properties, and we propose an experimental setup to realize it. Finite temperature and finite size effects are discussed, and the examples of three-dimensional Mott-insulator phase and one-dimensional Luttinger liquid are demonstrated.