Rydberg blockade in an ultracold strontium gas revealed by two-photon excitation dynamics

Chang Qiao, Canzhu Tan, Julia Siegl, Fachao Hu, Zhijing Niu, Yuhai Jiang, Matthias Weidemüller, and Bing Zhu

Phys. Rev. A 103, 063313 – Published 21 June 2021

Abstract

We demonstrate the interaction-induced blockade effect in an ultracold ${}^{88}{Sr}$ gas via studying the time dynamics of a two-photon excitation to the triplet Rydberg series $5 s n s^{3} S_{1}$ for five different principal quantum numbers $n$ ranging from 19 to 37. By using a multipulse excitation sequence to increase the detection sensitivity, we could identify Rydberg-excitation-induced atom losses as low as $< 1 %$ . Based on an optical Bloch equation formalism, treating the Rydberg-Rydberg interaction on a mean-field level, the van der Waals coefficients are extracted from the observed dynamics, which agree fairly well with ab initio calculations.

Received 8 March 2021
Accepted 11 June 2021
Corrected 30 June 2021

DOI:https://doi.org/10.1103/PhysRevA.103.063313

Physics Subject Headings (PhySH)

Long-range interactions

Rydberg atoms & molecules Ultracold gases

Atomic, Molecular & Optical

Corrections

30 June 2021

Correction: The equal-contribution statement for the first two authors was moved during production and has been restored as a byline footnote. The abbreviation ${}^{88}{Sr}$ was typeset incorrectly during production in the abstract and two locations in text and has been fixed.

Authors & Affiliations

Chang Qiao^1,2,*, Canzhu Tan^1,2,*, Julia Siegl^1,3, Fachao Hu^1,2, Zhijing Niu^1,2, Yuhai Jiang ^4,2,†, Matthias Weidemüller ^1,2,3,‡, and Bing Zhu ^3,2,§

¹Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
²Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
³Physikalisches Institut, Universität Heidelberg, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany
⁴Shanghai Advanced Research Institute, Chinese Academy of Sciences, Shanghai 201210, China

^*These authors contributed equally to this work.
^†jiangyh@sari.ac.cn
^‡weidemueller@uni-heidelberg.de
^§bzhu@physi.uni-heidelberg.de

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Vol. 103, Iss. 6 — June 2021

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Images

Figure 1
Two-photon pulsed excitation to the $5 s n s {}^{3}S_{1}$ states. (a) Schematic view of the experimental setup. The abbreviations are: HWP—half-wave plate, QWP—quarter-wave plate, PBS—polarizing beam splitter, EOM—electro-optic modulator, AOM—accousto-optic modulator, and ULE—ultralow expansion. Many optical elements are omitted here, like lenses. See text for detailed descriptions. (b) The relevant energy levels. The Rydberg state $| r 〉$ is addressed via a two-photon process from the ground state $| g 〉$ via an intermediate state $| e 〉$ . $Ω_{e r}$ ( $Ω_{g e}$ ) represents the Rabi frequency driving the $| e 〉 − | r 〉$ ( $| g 〉 − | e 〉$ ) transition and $Δ$ ( $δ$ ) is the one-photon (two-photon) detuning. Atoms at $| g 〉$ are detected by absorption imaging with the broad $| g 〉 − | i 〉$ transition. $γ_{g, e, i}$ are the natural linewidths of the corresponding states and the branching ratio from $| r 〉$ to $| e 〉$ ( $| l 〉$ ) is $1 - b$ ( $b$ ). Here $| l 〉$ represents the low-lying states that $| r 〉$ decays to, except $| e 〉$ . (c) The $N$ -pulse sequence. The two beams are operated simultaneously with $N$ pulses, each of equal duration $t_{d}$ and equally separated by $t_{s}$ . The ODT is temporarily switched off during the excitation pules.
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Figure 2
Measurements of the loss fraction per pulse $p_{d}$ for $n = 19$ and $n = 23$ . (a) and (b) The remaining fraction of atoms $f_{N}$ as a function of the pulse number $N$ for these two states at two different atomic densities (see Table 1). The solid curves are fits to Eq. (5) to extract $p_{d}$ and the shaded areas mark the $95 %$ confidence level. See text for detailed discussions. (c) and (d) $p_{d}$ as a function of the single-pulse length $t_{d}$ . In (c) the black, red, and blue curves are parameter-free calculations for the $n = 19$ state with $V / h = 0.62$ , 0.10, and 0 (see text), respectively. In (d) the solid curves are fits of the high- and low-density data to the mean-field model [47], from which we obtain $γ_{e r} / 2 π = 0.98 (36) MHz, V^{e} / 2 π = - 71 (10) MHz$ for the high-density measurement (black curve), and $γ_{e r} / 2 π = 0.10 (9) MHz, V^{e} / 2 π = - 3.4 (7) MHz$ for the low-density data (red curve). The fitted parameters are listed in Table 1. As a comparison, the blue dashed line represents the noninteracting case ( $V = 0$ ) with $γ_{e r} / 2 π = 0.10 MHz$ .
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Figure 3
The vdW coefficients $C_{6}$ . The black and red points are from fits to the experimental data at high and low densities, respectively, while the blue ones are from Ref. [33]. See text for more details.
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Figure 4
Calibrations of Rabi frequencies. (a) Rabi oscillation between $| g 〉$ and $| e 〉$ . The solid lines are fits to a damped cosinusoidal function (see text) and the obtained fitting parameters are: $Ω_{g e} / 2 π = 784 (5) kHz, τ = 3.0 (3) μ s$ , and $t_{0} = 0.05 (2) μ s$ . (b) ATS caused by the UV light measured via absorption imaging on the red transition. The data is fitted to the analytic expression in Eq. (A1), from which we obtain: $Ω_{e r} / 2 π = 1235 (13) kHz$ and the UV detuning $δ_{e r} / 2 π = 86 (7) kHz$ .
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Figure 5
Comparison between the experimental data (blue and red points) from Fig. 1(b) of Ref. [32] and our mean-field calculation (solid curves). See text for descriptions.
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Figure 6
Comparison between the experimental data from Figs. 8 and 9 of Ref. [38] and our mean-field calculation. The black curves represent the case of including the Rydberg interaction term while the red dashed ones are free of interaction ( $V = 0$ ). See text for more details.
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