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arXiv:2301.00871 · Physical Review A

Measuring nonlocal three-body spatial correlations with Rydberg trimers in ultracold quantum gases

S. K. Kanungo, Y. Lu, F. B. Dunning, S. Yoshida, Joachim Burgdörfer, T. C. Killian

Published Mar 20, 2023• 14 citations

Abstract

We measure nonlocal third-order spatial correlations in nondegenerate ultracold gases of bosonic ($^{84}\mathrm{Sr}$) and spin-polarized fermionic ($^{87}\mathrm{Sr}$) strontium through studies of the formation rates for ultralong-range trimer Rydberg molecules. The trimer production rate is observed to be very sensitive to the effects of quantum statistics with a strong enhancement of up to a factor of 6 (3!), in the case of bosonic $^{84}\mathrm{Sr}$ due to bunching and a marked reduction for spin-polarized fermionic $^{87}\mathrm{Sr}$ due to antibunching. The experimental results are compared to theoretical predictions and good agreement is observed. The present approach opens the way to in situ studies of higher-order nonlocal spatial correlations in a wide array of ultracold atomic-gas systems.

DOI: 10.1103/physreva.107.033322

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We measure nonlocal third-order spatial correlations in nondegenerate ultracold gases of bosonic (

^{84}\mathrm{Sr}

) and spin-polarized fermionic (

^{87}\mathrm{Sr}

) strontium through studies of the formation rates for ultralong-range trimer Rydberg molecules. The trimer production rate is observed to be very sensitive to the effects of quantum statistics with a strong enhancement of up to a factor of 6 (3!), in the case of bosonic

^{84}\mathrm{Sr}

due to bunching and a marked reduction for spin-polarized fermionic

^{87}\mathrm{Sr}

due to antibunching. The experimental results are compared to theoretical predictions and good agreement is observed. The present approach opens the way to in situ studies of higher-order nonlocal spatial correlations in a wide array of ultracold atomic-gas systems.

We present photoexcitation of ultra-long-range Rydberg molecules as a probe of spatial correlations in bosonic and fermionic quantum gases. Rydberg molecules can be created with well-defined internuclear spacing, set by the radius of the outer lobe of the Rydberg electron wave function

{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 in the range

{R}_{n}=1400--3200

{a}_{0}

, which are on the order of the thermal de Broglie wavelength for temperatures around 1 $\ensuremath{\mu}\mathrm{K}$. We observe bunching for a single-component Bose gas of

{}^{84}\mathrm{Sr}

and antibunching due to Pauli exclusion at short distances for a polarized Fermi gas of

{}^{87}\mathrm{Sr}

, revealing the effects of quantum statistics.

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)

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)

in thermal gases, and the second on the creation of heteronuclear ultralong-range Rydberg molecules from a strongly interacting Bose mixture of

^{88}

Sr and

^{84}

Sr. Finally, we will present conclusions and a brief outlook for the future experiments utilizing this method.

Measurements of ultralong-range Rydberg molecule formation in cold gases of fermionic 87Sr atoms are presented. Measurements undertaken using polarised and unpolarised cold atom samples demonstrate that studies of Rydberg molecule formation can provide a window into the important role played by quantum statistics in determining the pair-correlation function, g(2)(R), and, more generally, can furnish a sensitive probe of spatial correlations in quantum gases that is suitable for use in a number of different applications.

Ultralong-range Rydberg trimer molecules are spectroscopically observed in an ultracold gas of Cs(nd_{3/2}) atoms. The anisotropy of the atomic Rydberg state allows for the formation of angular trimers, whose energies may not be obtained from integer multiples of dimer energies. These nonadditive trimers coexist with Rydberg dimers. The existence of such effective three-body interactions is confirmed with the observation of asymmetric line profiles and interpreted by a theoretical approach that includes relativistic spin interactions. Simulations of the observed spectra with and without angular trimer lines lend convincing support to the existence of effective three-body interactions.