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Molecular Physics

Formation of ultralong-range fermionic Rydberg molecules in 87Sr: role of quantum statistics

J. D. Whalen, Roger Ding, S. K. Kanungo, T. C. Killian, S. Yoshida, Joachim Burgdörfer, F. B. Dunning

Published Feb 3, 2019• 12 citations
Publisher

Abstract

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.

DOI
10.1080/00268976.2019.1575485

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Synopsis The photoexcitation of ultralong-range Rydberg molecules is demonstrated as a probe of spatial cor-relations in a quantum gas on previously inaccessible length scales of 1400-3200 a 0. Measurements using cold (∼1 μK) (fermionic) 87Sr and (bosonic) 84Sr reveal the effects of quantum statistics on the pair correlation function g (2)(R).

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Creation of vibrationally-excited ultralong-range Rydberg molecules in polarized and unpolarized cold gases of 87 Sr

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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.

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Spectroscopy of ⁸⁷Sr Rydberg Atoms and Molecules

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Spectroscopy of ⁸⁷Sr Rydberg Atoms and Molecules This dissertation describes the development of an apparatus to undertake spectroscopic studies of ⁸⁷Sr Rydberg states and their application in the production of ultra-long-range Rydberg molecules (ULRRMs). Most previous spectroscopic studies of strontium have been performed with the bosonic isotope ⁸⁸Sr which has no nuclear spin (I=0), resulting in a relatively simple and well-understood Rydberg excitation spectrum. In contrast, fermionic ⁸⁷Sr has a large nuclear spin (I=9/2) that leads to strong hyperfine interactions which greatly complicate the Rydberg excitation spectrum. In order to understand the Rydberg states in ⁸⁷Sr, two-photon spectroscopy was performed to measure and identify the (5sns)³S and (5snd)³D hyperfine Rydberg states for 30≲n≲99. Working with theory collaborators, a detailed understanding of how the hyperfine interaction affects the Rydberg levels is developed and used to extract revised quantum defects. The detailed understanding of the ⁸⁷Sr hyperfine Rydberg structure was exploited to produce the first ULRRMs in a fermionic gas. Unlike traditional molecular binding mechanisms, ULRRMs comprise of one or more ground-state atoms embedded in the electron cloud of a Rydberg atom with the entire system bound together through the weak Rydberg electron-neutral atom scattering. Therefore, production of ULRRMs is dependent on both the principal quantum number (n) of the parent Rydberg atom and the initial spatial distribution of atoms. At low temperatures, the effects of quantum statistics becomes important and result in bunching (bosons) and antibunching (fermions). These differences in spatial distributions can influence the excitation rates of ULRRMs. Current progress in exploring the role of quantum statistics in the excitation of ULRRMs using cold, dense strontium gases is described, with an emphasis on ⁸⁷Sr, and how such measurements can be used to extract the pair correlation function g⁽²⁾(R).

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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.

arXiv:2301.00871•Physical Review A•Mar 20, 2023•14 citations
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.
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.
Spectroscopy of ⁸⁷Sr Rydberg Atoms and Molecules This dissertation describes the development of an apparatus to undertake spectroscopic studies of ⁸⁷Sr Rydberg states and their application in the production of ultra-long-range Rydberg molecules (ULRRMs). Most previous spectroscopic studies of strontium have been performed with the bosonic isotope ⁸⁸Sr which has no nuclear spin (I=0), resulting in a relatively simple and well-understood Rydberg excitation spectrum. In contrast, fermionic ⁸⁷Sr has a large nuclear spin (I=9/2) that leads to strong hyperfine interactions which greatly complicate the Rydberg excitation spectrum. In order to understand the Rydberg states in ⁸⁷Sr, two-photon spectroscopy was performed to measure and identify the (5sns)³S and (5snd)³D hyperfine Rydberg states for 30≲n≲99. Working with theory collaborators, a detailed understanding of how the hyperfine interaction affects the Rydberg levels is developed and used to extract revised quantum defects. The detailed understanding of the ⁸⁷Sr hyperfine Rydberg structure was exploited to produce the first ULRRMs in a fermionic gas. Unlike traditional molecular binding mechanisms, ULRRMs comprise of one or more ground-state atoms embedded in the electron cloud of a Rydberg atom with the entire system bound together through the weak Rydberg electron-neutral atom scattering. Therefore, production of ULRRMs is dependent on both the principal quantum number (n) of the parent Rydberg atom and the initial spatial distribution of atoms. At low temperatures, the effects of quantum statistics becomes important and result in bunching (bosons) and antibunching (fermions). These differences in spatial distributions can influence the excitation rates of ULRRMs. Current progress in exploring the role of quantum statistics in the excitation of ULRRMs using cold, dense strontium gases is described, with an emphasis on ⁸⁷Sr, and how such measurements can be used to extract the pair correlation function g⁽²⁾(R).
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 measure nonlocal third-order spatial correlations in nondegenerate ultracold gases of bosonic (84Sr^{84}\mathrm{Sr}84Sr) and spin-polarized fermionic (87Sr^{87}\mathrm{Sr}87Sr) 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 84Sr^{84}\mathrm{Sr}84Sr due to bunching and a marked reduction for spin-polarized fermionic 87Sr^{87}\mathrm{Sr}87Sr 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.