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Physical Review A

Nonlocal spatial correlations in an interacting atomic gas

C. Wang, Ang Li, Y. Lu, S. K. Kanungo, S. Yoshida, F. B. Dunning, T. C. Killian

Published Jan 13, 2026• 0 citations
Publisher

Abstract

We report measurements of the nonlocal two-body spatial correlation function g ( 2 ) ( R ) in an ultracold Bose gas with strong interactions using photoassociation of ultra-long-range Rydberg molecules (ULRRMs) as a spatially selective probe. This technique provides access to g ( 2 ) ( R ) on length scales from 60 to 180 nm, bridging the gap between short-range and long-range correlation measurements. The large s -wave scattering length of Sr 86 ( a = 811 a 0 ) enables exploration of the universal regime where g ( 2 ) ( R ) is governed solely by two-body interactions. Comparison with a weakly interacting isotope, Sr 84 , highlights interaction-induced suppression of pair correlations. The measured correlation functions agree quantitatively with calculations based on the two-body reduced density matrix, without adjustable parameters. Our results establish Rydberg molecular photoassociation as a powerful tool for probing nonlocal correlations in strongly interacting quantum gases.

DOI
10.1103/2q22-grqy

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We report measurements of the nonlocal two-body spatial correlation function g ( 2 ) ( R ) in an ultracold Bose gas with strong interactions using photoassociation of ultra-long-range Rydberg molecules (ULRRMs) as a spatially selective probe. This technique provides access to g ( 2 ) ( R ) on length scales from 60 to 180 nm, bridging the gap between short-range and long-range correlation measurements. The large s -wave scattering length of Sr 86 ( a = 811 a 0 ) enables exploration of the universal regime where g ( 2 ) ( R ) is governed solely by two-body interactions. Comparison with a weakly interacting isotope, Sr 84 , highlights interaction-induced suppression of pair correlations. The measured correlation functions agree quantitatively with calculations based on the two-body reduced density matrix, without adjustable parameters. Our results establish Rydberg molecular photoassociation as a powerful tool for probing nonlocal correlations in strongly interacting quantum gases.
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Ultracold atomic systems provide pristine environments for creating and manipulating strongly-interacting quantum systems. The flexibility and utility of ultracold atomic systems comes at the cost of isolation of the quantum system away from environmental perturbations inside of an ultra-high vacuum chamber. This isolation reduces the number of ways that these systems can be probed, in particular, there are relatively few ways to probe correlations in these systems at mesoscopic length scales. In this thesis we present a new technique for probing correlations in ultracold atomic gases using ultralong-range Rydberg molecules. We will present a description of the relevant experimental apparatus and techniques developed for laser cooling and trapping ultracold mixtures of Sr, and a brief theoretical discussion on the relationship between the pair correlation function g(2)(R)g^{(2)}(R)g(2)(R) and the excitation rates of ultralong-range Rydberg molecules. We present two publications: the first on using ultralong-range Rydberg molecules to probe g(2)(R)g^{(2)}(R)g(2)(R) in thermal gases, and the second on the creation of heteronuclear ultralong-range Rydberg molecules from a strongly interacting Bose mixture of 88^{88}88Sr and 84^{84}84Sr. Finally, we will present conclusions and a brief outlook for the future experiments utilizing this method.
We report experimental observations of the rotational structure in photoassociative spectroscopy of ultralong-range Rydberg molecules (ULRRMs) in an ultracold gas of 86Sr^{86}\mathrm{Sr}86Sr. ULRRM spectroscopy probes scattering wave functions at much larger internuclear separations than photoassociative spectroscopy of low-lying electronic states. At such separations photon recoil momentum can lead to the transfer of significant angular momentum to the Rydberg molecule, evidence of which is provided through the distribution of excited rotational states. The visibility of the rotational structure is enhanced because, for collisions between ground-state 86Sr^{86}\mathrm{Sr}86Sr atoms, the large, near-resonant s-wave scattering length approaches the size of the ULRRM. Similar enhancement is not seen for 84Sr^{84}\mathrm{Sr}84Sr, which has a much smaller scattering length. Results are interpreted with the aid of a theory that accounts for the recoil momentum associated with photoexcitation and the large sss-wave scattering length in the entrance channel. While the observed rotational splittings and the qualitative trends in the relative intensities of the spectral features are well described by theory, the effects of recoil momentum are more prominent in the measured data than in the theory.
We analytically calculate the spatial nonlocal pair correlation function for an interacting uniform 1D Bose gas at finite temperature and propose an experimental method to measure nonlocal correlations. Our results span six different physical realms, including the weakly and strongly interacting regimes. We show explicitly that the characteristic correlation lengths are given by one of four length scales: the thermal de Broglie wavelength, the mean interparticle separation, the healing length, or the phase coherence length. In all regimes, we identify the profound role of interactions and find that under certain conditions the pair correlation may develop a global maximum at a finite interparticle separation due to the competition between repulsive interactions and thermal effects.
Locally probing pairing in fermionic superfluids, ranging from micro- to macroscopic scales, has been a long-standing challenge. Here, we investigate a new approach that uses Rydberg impurities as a spectroscopic sensor of the surrounding strongly correlated state of ultracold paired fermions. The extended wave function of the Rydberg electron induces a finite-range potential that can bind atoms from the BCS medium, forming molecular states. As a consequence, the optical absorption spectrum of the impurity encodes key many-body properties. Using the functional determinant approach, we provide a direct measure of the superfluid gap through frequency shifts of dimer and trimer peaks. The spectra also reveal whether the Cooper pairs are broken or trapped intact. For static Rydberg atoms, we relate this signature of pairing to the suppression of the orthogonality catastrophe due to the superconducting gap resulting in the formation of well-defined polaron quasiparticles. Our Letter establishes Rydberg atom spectroscopy as a powerful local probe of strongly correlated matter.