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arXiv:1903.11526 · Physical Review A

Probing nonlocal spatial correlations in quantum gases with ultra-long-range Rydberg molecules

J. D. Whalen, S. K. Kanungo, Roger Ding, M. Wagner, Richard Schmidt, H. R. Sadeghpour, S. Yoshida, Joachim Burgdörfer, F. B. Dunning, T. C. Killian

Published Jul 22, 2019• 35 citations

Abstract

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.

DOI: 10.1103/physreva.100.011402

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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.

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.

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.

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.

Abstract Photoexcitation rates for creation of ultralong-range Rydberg molecules with 31 ≲ n ≲ 41 in both ground and excited vibrational levels in cold ( T ∼ 900 nK) gases of polarized and unpolarized 87 Sr are presented. The measured production rates of the ν = 0, 1 and 2 vibrational levels reveal rather different n dependences which are analyzed by evaluating the Franck–Condon factors associated with excitation of the different vibrational levels and molecular rotational states. In particular, for gases of spin-polarized fermions, only Rydberg dimers with odd rotational quantum numbers are excited due to the requirement that their wave functions be anti-symmetric with respect to exchange. The data also demonstrate that measurements of the formation of vibrationally-excited ν = 1 molecules can furnish a probe of pair correlations over intermediate length scales.