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arXiv:1403.2744 · Journal of the Optical Society of America B

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

H. H. Jen, Daw-Wei Wang

Published Oct 30, 2014• 1 citation
arXivHTMLPDF

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 can be reconstructed by the measurements of frequency moments in EIT spectroscopy. 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 we demonstrate the reconstruction steps of Green’s function for the examples of three-dimensional Mott-insulator phase and one-dimensional Luttinger liquid.

DOI
10.1364/josab.31.002931

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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 can be reconstructed by the measurements of frequency moments in EIT spectroscopy. 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 we demonstrate the reconstruction steps of Green’s function for the examples of three-dimensional Mott-insulator phase and one-dimensional Luttinger liquid.
We develop a general theory to study the electromagnetically induced transparency (EIT) in ultracold quantum gases, applicable for both Bose and Fermi gases with an arbitrary interparticle interaction strength. We show that, in the weak probe field limit, the EIT spectrum is solely determined by the single-particle Green's function of the ground-state atoms, and reflects interesting quantum many-body effects when atoms are virtually coupled to the low-lying Rydberg states. As an example, we apply our theory to a one-dimensional Luttinger liquid, a Bose-Mott insulator state, and the superfluid state of two-component Fermi gases, and show how the many-body features can be observed nondestructively in the unconventional EIT spectrum.
We develop a general theory to study the electromagnetically induced transparency (EIT) in ultracold quantum gases, applicable for both Bose and Fermi gases with arbitrary inter-particle interaction strength. We show that, in the weak probe field limit, the EIT spectrum is solely determined by the single particle Green's function of the ground state atoms, and reflects interesting quantum many-body effects when atoms are virtually coupled to the low-lying Rydberg states. As an example, we apply our theory to 1D Luttinger liquid, Bose-Mott insulator state, and the superfluid state of two-component Fermi gases, and show how the many-body features can be observed non-destructively in the unconventional EIT spectrum.
We report on systematic numerical and experimental investigations of electromagnetically induced transparency (EIT) to determine temperatures in an ultracold atomic gas. The technique relies on the strong dependence of EIT on atomic motion (i.e., Doppler shifts), when the relevant atomic transitions are driven with counterpropagating probe and control laser beams. Electromagnetically induced transparency permits thermometry with satisfactory precision over a large temperature range, which can be addressed by the appropriate choice of Rabi frequency in the control beam. In contrast to time-of-flight techniques, thermometry by EIT is fast and nondestructive, i.e., essentially it does not affect the ultracold medium. In an experimental demonstration we apply both EIT and time-of-flight measurements to determine temperatures along different symmetry axes of an anisotropic ultracold gas. As an interesting feature we find that the temperatures in the anisotropic atom cloud vary in different directions.
Abstract We present combined measurements of the spatially resolved optical spectrum and the total excited-atom number in an ultracold gas of three-level atoms under electromagnetically induced transparency conditions involving high-lying Rydberg states. The observed optical transmission of a weak probe laser at the center of the coupling region exhibits a double peaked spectrum as a function of detuning, while the Rydberg atom number shows a comparatively narrow single resonance. By imaging the transmitted light onto a charge-coupled-device camera, we record hundreds of spectra in parallel, which are used to map out the spatial profile of Rabi frequencies of the coupling laser. Using all the information available we can reconstruct the full one-body density matrix of the three-level system, which provides the optical susceptibility and the Rydberg density as a function of spatial position. These results help elucidate the connection between three-level interference phenomena, including the interplay of matter and light degrees of freedom and will facilitate new studies of many-body effects in optically driven Rydberg gases.
An optical spectroscopic method based on the principle of electromagnetically induced transparency (EIT) is proposed as quite a generic probing tool that provides valuable insights into the nature of Fermi paring in ultracold Fermi gases of two hyperfine states. This technique has the capability of allowing spectroscopic response to be determined in a nearly nondestructive manner and the whole spectrum may be obtained by scanning the probe-laser frequency faster than the lifetime of the sample without re-preparing the atomic sample repeatedly. A quasiparticle picture is constructed to facilitate a simple physical explanation of the pairing signature in the EIT spectra.
In condensed-matter physics, inelastic light-scattering provides a powerful method to investigate the system under study. It allows accessing the correlation functions which could identify dierent many-body states. We will report on the investigation of ultracold atoms in optical potentials, which have proved to be an excellent way of realizing simplied models of condensed-matter physics theory in experimental practice. In particular, we studied the modication of the response of an array of one-dimensional samples of 87Rb in a periodic potential across the superfluid to Mott-insulator transition, extracting information about both the dynamical spectral function and the one-particle spectral function.