Ultracold Gas of Dipolar NaCs Ground State Molecules

Ian Stevenson, Aden Z. Lam, Niccolò Bigagli, Claire Warner, Weijun Yuan, Siwei Zhang, and Sebastian Will

Phys. Rev. Lett. 130, 113002 – Published 16 March 2023

Abstract

We report on the creation of bosonic NaCs molecules in their absolute rovibrational ground state via stimulated Raman adiabatic passage. We create ultracold gases with up to 22 000 dipolar NaCs molecules at a temperature of 300(50) nK and a peak density of $1.0 (4) \times 10^{12} {cm}^{- 3}$ . We demonstrate comprehensive quantum state control by preparing the molecules in a specific electronic, vibrational, rotational, and hyperfine state. We measure the ground state ac polarizability at 1064 nm along with the two-body loss rate, which we find to be universal. Employing the tunability and strength of the permanent electric dipole moment of NaCs, we induce dipole moments of up to 2.6 D at a dc electric field of $2.1 (2) kV / cm$ and demonstrate strong microwave coupling between the two lowest rotational states with a Rabi frequency of $2 π \times 45 MHz$ . A large electric dipole moment, accessible at relatively small electric fields, makes ultracold gases of NaCs molecules well suited for the exploration of strongly interacting phases of dipolar quantum matter.

Received 21 June 2022
Revised 9 September 2022
Accepted 13 February 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.113002

Physics Subject Headings (PhySH)

Cold and ultracold molecules Dipolar molecules

Bose gases Molecules Ultracold gases

Atomic, Molecular & Optical

Authors & Affiliations

Ian Stevenson , Aden Z. Lam, Niccolò Bigagli , Claire Warner , Weijun Yuan , Siwei Zhang , and Sebastian Will ^*

Department of Physics, Columbia University, New York, New York 10027, USA

^*sebastian.will@columbia.edu

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Vol. 130, Iss. 11 — 17 March 2023

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Figure 1
Two-photon pathway to the rovibrational ground state of NaCs. (a) An ultracold bulk gas of weakly bound NaCs Feshbach molecules is transferred to the ground state via STIRAP. Prior to detection, STIRAP is applied in reverse. (b) Molecular potentials of NaCs as relevant for transfer to the rovibrational ground state $X^{1} Σ^{+}$ $| v = 0, J = 0, m_{J} = 0 ⟩$ . Here, $J$ denotes the total angular momentum and $m_{J}$ its projection on the quantization axis. $Ω_{1}$ and $Ω_{2}$ denote the Rabi frequencies of the Raman lasers. The inset shows the relevant sublevels, including the $m_{F}$ quantum numbers that are accessible with the given laser polarizations. $Δ$ and $δ$ denote the one- and two-photon detuning from the excited state and the ground state, respectively. Arrows indicate light polarizations relative to the quantization axis set by the vertical magnetic field.
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Figure 2
Creation of NaCs ground state molecules. (a) Coupling to the rovibrational ground state via $B^{1} Π | v = 10 ⟩$ is observed in two-photon dark resonance spectroscopy. The solid line is a fit to a master equation model yielding Rabi frequencies $Ω_{1} / 2 π = 0.6 (1)$ and $Ω_{2} / 2 π = 8.8 (5) MHz$ . (b) STIRAP is realized via a ramp of laser intensities, giving rise to a dynamic change of the Rabi frequencies $Ω_{1}$ (red) and $Ω_{2}$ (orange) as shown. (c) Evolution of the number of Feshbach molecules (circles) during the STIRAP sequence. The black solid line shows a fit of the Feshbach molecule number to a master equation model that also yields the number of molecules in the ground state (red solid line). The inset shows a background-free absorption image of about $1.2 \times 10^{4}$ Feshbach molecules after a STIRAP round trip and 17 ms time of flight. For this data, $Ω_{1} / 2 π = 4.5$ , $Ω_{2} / 2 π = 8.4$ , $Δ / 2 π = 90$ , and $δ / 2 π = 0 MHz$ .
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Figure 3
Controlling the hyperfine state of NaCs ground state molecules. (a) Dependence of transfer efficiency on the one-photon detuning $Δ$ , while staying on resonance with the ground state ( $δ = 0$ ). Top (bottom) panel corresponds to $Ω_{1} / 2 π = 4.5$ and $Ω_{2} / 2 π = 8.4 MHz$ ( $Ω_{1} / 2 π = 4.5$ and $Ω_{2} / 2 π = 4.5 MHz$ ). (b) Accessible hyperfine states for $Δ / 2 π = - 90 MHz$ (top) and $Δ / 2 π = + 90 MHz$ (bottom) with $Ω_{1} = Ω_{2} = 2 π \times 4.5 MHz$ . Solid lines in (a) and (b) are calculated from a master equation model to be reported in Ref. [56]. (c) Energies of all $(2 I_{Na} + 1) (2 I_{Cs} + 1) = 32$ hyperfine ground states at a magnetic field of 863.84 G. The hyperfine structure is in the Paschen-Back regime, dominated by the nuclear Zeeman effect, while scalar spin-spin interactions are weak ( $c_{4} = 3941.8 Hz$ [59]). The initial Feshbach state has $m_{F} = 4$ . Hyperfine states that can be addressed in our coupling scheme are shown as red dots.
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Figure 4
Lifetime of NaCs in the rovibrational ground state measured for an initial peak density of $5 (3) \times 10^{11} {cm}^{- 3}$ and temperature of 300(50) nK. The solid line shows a fit to a two-body decay model. Data points correspond to the average of three experimental runs. The inset shows a trap frequency measurement of ground state molecules oscillating along the $y$ axis. From this we determine a ratio for the ac polarizabilities of the ground state molecules and Cs atoms of 0.77(1) in the optical dipole trap at 1064 nm.
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Figure 5
Strong dipole moment of NaCs molecules. (a) NaCs molecules in a homogeneous electric field. The Stark shift of the ground state is measured via dark resonance spectroscopy (red circles). Error bars are smaller than the point size. The solid line corresponds to the calculation of the expected Stark shift based on the known permanent dipole moment $d$ [41] and the rotational constant of the ground state. The gray shading reflects the uncertainty in the dipole moment. The Stark shift is used to calibrate the electric field strength. The inset shows the induced dipole moment $d$ versus dc electric field; the dashed rectangle indicates the dipole moments of up to 2.6 D reached in this Letter. (b) Fast Rabi oscillations between rotational states of NaCs. The population in the rotational ground state ( $J = 0$ ) is measured as a function of time. The optical dipole trap is switched off during the microwave pulse. The solid line is a sinusoidal fit yielding a Rabi frequency of 45.4(3) MHz. The microwave frequency is about 3.471 GHz. Further details on rotational spectra of NaCs will be reported elsewhere [70].
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