# Probing Nonlocal Spatial Correlations in Quantum Gases with Ultra-long-range Rydberg Molecules

## TL;DR

This paper uses ultra-long-range Rydberg molecules to probe spatial correlations in ultracold quantum gases, revealing quantum statistical effects like bunching and anti-bunching at specific length scales.

## Contribution

It introduces a method to map pair-correlation functions in quantum gases using Rydberg molecules with tunable internuclear spacing.

## Key findings

- Observed bunching in Bose gas of $^{84}$Sr.
- Detected anti-bunching in Fermi gas of $^{87}$Sr.
- Mapped pair-correlation function at length scales of 1400-3200 $a_0$.

## Abstract

We present photo-excitation of ultra-long-range Rydberg molecules as a probe of spatial correlations in quantum gases. Rydberg molecules can be created with well-defined internuclear spacing, set by the radius of the outer lobe of the Rydberg electron wavefunction $R_n$. By varying the principal quantum number $n$ of the target Rydberg state, the molecular excitation rate can be used to map the pair-correlation function of the trapped gas $g^{(2)}(R_n)$. We demonstrate this with ultracold Sr gases and probe pair-separation length scales ranging from $R_n = 1400 - 3200$ $a_0$, which are on the order of the thermal de Broglie wavelength for temperatures around 1 $\mu$K. We observe bunching for a single-component Bose gas of $^{84}$Sr and anti-bunching due to Pauli exclusion at short distances for a polarized Fermi gas of $^{87}$Sr, revealing the effects of quantum statistics.