Probing ultra-cold Fermi atoms with a single ion

TL;DR

This paper proposes an in situ method using a single trapped ion as a microscopic probe to measure the local energy and spin distributions in a degenerate Fermi gas with nanometer resolution.

Contribution

It adapts the ionic microscope setup to directly measure the local single-particle energy distribution in a Fermi gas via photo-association rates.

Findings

Photo-association rate correlates with local energy distribution.

Method enables spatially resolved measurements of Fermi gas properties.

Proposes experimental setup for local energy and spin-state probing.

Abstract

We show that the recently proposed ionic microscope set-up [Kollath et.al, PRA, \textbf{76}, 063602 (2007)] could be adapted to measure the \textit {local single-particle energy distribution} of a degenerate Fermi gas \textit{in situ} with the resolution on the nanometer scale. We study an ion held in a Paul trap in an atomic Fermi gas and compute the two-photon Raman photo-association rate of the ion and an atom. We show that, as a function of the detunings between the frequencies of the two incident lasers and energies in the atom-ion system, the photo-association rate directly measures the single-particle energy distribution in the Fermi gas around the ion. We describe an experiment to measure the photo-association rate of a trapped ion and argue that, as the position of the ion can be scanned through the Fermi gas, this experiment directly probes the local energy and spin-state distribution of the Fermi gas.