Observation of Interference between Resonant and Detuned stirap in the Adiabatic Creation of $^{23}\mathrm{Na}^{40}\mathrm{K}$ Molecules

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Observation of Interference between Resonant and Detuned stirap in the Adiabatic Creation of ${}^{23}{Na} {}^{40}K$ Molecules

Lan Liu, De-Chao Zhang, Huan Yang, Ya-Xiong Liu, Jue Nan, Jun Rui, Bo Zhao, and Jian-Wei Pan

Phys. Rev. Lett. 122, 253201 – Published 25 June 2019

Abstract

Stimulated Raman adiabatic passage (stirap) allows efficiently transferring the populations between two discrete quantum states and has been used to prepare molecules in their rovibrational ground state. In realistic molecules, a well-resolved intermediate state is usually selected to implement the resonant stirap. Because of the complex molecular level structures, the detuned stirap always coexists with the resonant stirap and may cause unexpected interference phenomenon. However, it is generally accepted that the detuned stirap can be neglected if compared with the resonant stirap. Here we report on the first observation of interference between the resonant and detuned stirap in the adiabatic creation of ${}^{23}{Na} {}^{40}K$ ground-state molecules. The interference is identified by observing that the number of Feshbach molecules after a round-trip stirap oscillates as a function of the hold time, with a visibility of about 90%. This occurs even if the intermediate excited states are well resolved, and the single-photon detuning of the detuned stirap is about 1 order of magnitude larger than the linewidth of the excited state and the Rabi frequencies of the stirap lasers. Moreover, the observed interference indicates that if more than one hyperfine level of the ground state is populated, the stirap prepares a coherent superposition state among them, but not an incoherent mixed state. Further, the purity of the hyperfine levels of the created ground state can be quantitatively determined by the visibility of the oscillation.

Received 3 March 2019

DOI:https://doi.org/10.1103/PhysRevLett.122.253201

Physics Subject Headings (PhySH)

Cold and ultracold molecules Stimulated Raman adiabatic passage

Molecules Ultracold gases

Coherent control

Atomic, Molecular & Optical

Authors & Affiliations

Lan Liu^1,2, De-Chao Zhang^1,2, Huan Yang^1,2, Ya-Xiong Liu^1,2, Jue Nan^1,2, Jun Rui^1,2, Bo Zhao^1,2, and Jian-Wei Pan^1,2

¹Hefei National Laboratory for Physical Sciences at 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

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Vol. 122, Iss. 25 — 28 June 2019

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Figure 1
(a) Illustration of stimulated Raman adiabatic passage (stirap) in the adiabatic creation of the ${}^{23}{Na} {}^{40}K$ molecule. The $| E_{r} ⟩$ , $| E_{d} ⟩$ , and $| E_{n} ⟩$ states are the hyperfine levels of the electronic excited state, and the $| G_{r} ⟩$ , $| G_{d} ⟩$ , and $| G_{n} ⟩$ states are the hyperfine levels of the rovibrational ground state. The $| E_{r} ⟩$ state is well-separated from the other hyperfine excited states. The pump light resonantly couples the Feshbach state $| F ⟩$ and the intermediate electronic state $| E_{r} ⟩$ , and the Stokes light resonantly couples the ground state $| G_{r} ⟩$ and $| E_{r} ⟩$ . (b) Two-photon dark-state spectroscopy. (c) The pulse sequence of the round-trip stirap. The number of Feshbach molecules during the stirap process is measured by truncating the laser pulses. Error bars represent $\pm 1$ SD.
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Figure 2
(a) The stirap spectrum is measured as a function of the frequency of the pump laser. The solid line is a theoretical fit to the shape of the data (see text). The two vertical dashed lines represent two-photon resonances between the Feshbach state $| F ⟩$ and the hyperfine levels $| G_{r} ⟩$ and $| G_{d} ⟩$ of the ground state, respectively. The pulse sequence is shown in the inset. (b) The number of Feshbach molecules after a round-trip stirap as a function of hold time between the forward and reverse stirap oscillates with a visibility of 90% and a frequency of about 123 kHz. The pump laser frequency used for this measurement is marked by the arrow in (a). (c) The stirap spectrum is measured for a hold time of $300 μ s$ . The pulse sequence is shown in the inset. (d) The number of Feshbach molecules after a round-trip stirap as a function of hold time. The pump laser frequency used for this measurement is marked by the arrow in (c). Error bars represent $\pm 1$ SD.
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Figure 3
Increase of the purity by reducing the Rabi frequencies of the stirap lasers. (a) The stirap spectrum and (b) the measured oscillation with $Ω_{P}$ , $Ω_{S} \approx 2 π \times 4.6 MHz$ . The estimated purity of the hyperfine ground state is about 90%. (c) The stirap spectrum and (d) the measured oscillation with $Ω_{P}$ , $Ω_{S} \approx 2 π \times 3.3 MHz$ . There is no obvious oscillation in (d). The estimated purity of the hyperfine level of the ground state is about 99%. Error bars represent $\pm 1$ SD.
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Figure 4
The coherence between the $| G_{r} ⟩$ and the $| G_{d} ⟩$ state is measured for a long hold time. We fit the data points with a single oscillation function, which gives a frequency of 123.080(1) kHz. The oscillation can be clearly observed for 150 ms, which corresponds to more than $10^{4}$ oscillations. The pulse sequence is shown in the inset. Error bars represent $\pm 1$ SD.
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Physical Review Letters

Observation of Interference between Resonant and Detuned stirap in the Adiabatic Creation of Na23K40 Molecules

Lan Liu, De-Chao Zhang, Huan Yang, Ya-Xiong Liu, Jue Nan, Jun Rui, Bo Zhao, and Jian-Wei Pan

Phys. Rev. Lett. 122, 253201 – Published 25 June 2019

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Observation of Interference between Resonant and Detuned stirap in the Adiabatic Creation of ${}^{23}{Na} {}^{40}K$ Molecules