Ultracold Dipolar Gas of Fermionic ${}^{23}\mathrm{Na}{}^{40}\mathrm{K}$ Molecules in Their Absolute Ground State

We report on the creation of an ultracold dipolar gas of fermionic ${}^{23}\mathrm{Na}{}^{40}\mathrm{K}$ molecules in their absolute rovibrational and hyperfine ground state. Starting from weakly bound Feshbach molecules, we demonstrate hyperfine resolved two-photon transfer into the singlet $X\hspace{0.17em}{}^1{\mathrm{\Sigma }}^{+}|v=0,J=0⟩$ ground state, coherently bridging a binding energy difference of 0.65 eV via stimulated rapid adiabatic passage. The spin-polarized, nearly quantum degenerate molecular gas displays a lifetime longer than 2.5 s, highlighting NaK’s stability against two-body chemical reactions. A homogeneous electric field is applied to induce a dipole moment of up to 0.8 D. With these advances, the exploration of many-body physics with strongly dipolar Fermi gases of ${}^{23}\mathrm{Na}{}^{40}\mathrm{K}$ molecules is within experimental reach.

Figure 1

Two-photon pathway to the absolute ground state of ${}^{23}\mathrm{Na}{}^{40}\mathrm{K}$. (a) Relevant molecular potentials for the STIRAP transfer to the rovibrational ground state $|v=0,J=0⟩$ in the $X\hspace{0.17em}{}^1{\mathrm{\Sigma }}^{+}$ potential. Rabi frequencies of the Raman lasers are denoted by ${\mathrm{\Omega }}_1$ and ${\mathrm{\Omega }}_2$. (b) The initial Feshbach molecular state is associated with the highest vibrational state $|v=19⟩$ of the $a\hspace{0.17em}\hspace{0.17em}{}^3{\mathrm{\Sigma }}^{+}$ potential. In the excited state, spin-orbit coupling resonantly mixes the vibrational states $c\hspace{0.17em}{}^3{\mathrm{\Sigma }}^{+}|v=35,J=1⟩$ and $B\hspace{0.17em}{}^1\mathrm{\Pi }|v=12,J=1⟩$ with 64% triplet and 36% singlet character [32]. ${\delta }_2$ denotes the two-photon detuning of the Raman lasers. (c) Single-photon spectra via laser 1 resolving hyperfine states $|E1⟩$ and $|E2⟩$ of the electronically excited state. In the upper (lower) panel, the linear polarization of laser 1 is chosen to be horizontal (vertical), which is perpendicular (parallel) to the quantization axis set by a vertical magnetic field. The bars above the upper (lower) panel indicate the expected relative spectral weight of the contributing hyperfine states with $m_F=-5/2$ ($m_F=-7/2$) [32].

Figure 2

Creation of ${}^{23}\mathrm{Na}{}^{40}\mathrm{K}$ ground state molecules. (a) Observation of the rovibrational ground state using two-photon dark resonance spectroscopy. The solid line is obtained by fitting a three-level master equation model using an excited state linewidth of $\mathrm{\Gamma }=2\pi \times 9\mathrm{MHz}$. (b) The STIRAP sequence realizes coherent transfer from the Feshbach state to the rovibrational ground state and back via sinusoidal ramping of the laser intensities. (c) Evolution of the number of Feshbach molecules during the STIRAP sequence. The solid line is obtained from the master equation model using the Rabi couplings ${\mathrm{\Omega }}_1/\mathrm{\Gamma }=0.15$ and ${\mathrm{\Omega }}_2/\mathrm{\Gamma }=0.37$. The inset shows a background-free absorption image of about $4\times 10^3$ Feshbach molecules after a STIRAP round trip.

Figure 3

Hyperfine structure of the rovibrational ground state of ${}^{23}\mathrm{Na}{}^{40}\mathrm{K}$. Hyperfine states $|G1⟩$ and $|G2⟩$ are detected using STIRAP resonances via intermediate states $|E1⟩$ (a) and $|E2⟩$ (b). The ground hyperfine state $|G1⟩$ is observed via $|E1⟩$ using horizontal and vertical polarization for lasers 1 and 2, respectively, while $|G2⟩$ is accessed with both laser 1 and laser 2 vertically polarized. Solid lines are a guide for the eye. (c) Energies of all $(2I_{\mathrm{Na}}+1)(2I_{\mathrm{K}}+1)=36$ ground state hyperfine states at a magnetic field of 85.7 G. The nuclear Zeeman effect dominates, with weak influence of the scalar spin-spin interaction $c_4{\overrightarrow{I}}_{\mathrm{Na}}·{\overrightarrow{I}}_{\mathrm{K}}$ with a predicted $c_4=-466.2\mathrm{Hz}$ [40, 41]. The initial Feshbach state has $m_{F,\text{ini}}=-7/2$. Hyperfine states that can be addressed in principle from this state using a two-photon process are shown as filled dots.

Figure 4

Lifetime of ${}^{23}\mathrm{Na}{}^{40}\mathrm{K}$ in the rovibrational ground state. (a) Molecules in the absolute lowest hyperfine state $|G1⟩$ are created using STIRAP transfer via $|E1⟩$ and (b) in the hyperfine state $|G2⟩$ via $|E2⟩$. Solid lines show exponential fits $A+B{e}^{-t/\tau }$ and yield lifetimes $\tau$ of 2.5(5) and 2.7(8) s, respectively. Data points show the average of three experimental runs; the error bars denote the standard deviation of the mean. The insets show the respective STIRAP resonances, sufficiently narrow to address individual hyperfine states.

Figure 5

Creation of a strongly dipolar gas of ${}^{23}\mathrm{Na}{}^{40}\mathrm{K}$ molecules. The Stark shift in the presence of a homogeneous electric field is measured via STIRAP resonances (circles) and dark resonance spectroscopy (squares). Error bars are smaller than the point size. In a STIRAP transfer at finite electric field, strongly dipolar ground state molecules are created (see inset). The solid line corresponds to the Stark shift expected for the known permanent dipole moment $d$ and the rotational constant $B$ of the ground state. The gray shading reflects the uncertainty. The Stark shift is used to calibrate the electric field strength.