Ultracold Gas of Bosonic ${}^{23}\mathrm{Na}{}^{39}\mathrm{K}$ Ground-State Molecules

We report the creation of ultracold bosonic dipolar ${}^{23}\mathrm{Na}{}^{39}\mathrm{K}$ molecules in their absolute rovibrational ground state. Starting from weakly bound molecules immersed in an ultracold atomic mixture, we coherently transfer the dimers to the rovibrational ground state using an adiabatic Raman passage. We analyze the two-body decay in a pure molecular sample and in molecule-atom mixtures and find an unexpectedly low two-body decay coefficient for collisions between molecules and ${}^{39}\mathrm{K}$ atoms in a selected hyperfine state. The preparation of bosonic ${}^{23}\mathrm{Na}{}^{39}\mathrm{K}$ molecules opens the way for future comparisons between fermionic and bosonic ultracold ground-state molecules of the same chemical species.

Figure 1

(a) Potential energy curves of the ${}^{23}\mathrm{Na}{}^{39}\mathrm{K}$ molecule. The energy is shown in ${\mathrm{cm}}^{-1}$ as function of the internuclear distance. The solid green curve corresponds to the electronic $X^1{\mathrm{\Sigma }}^{+}$, the dotted light blue to the $a^3{\mathrm{\Sigma }}^{+}$, and the dashed lines to the $c^3{\mathrm{\Sigma }}^{+}$ and $B^1\mathrm{\Pi }$ potentials. Wave functions are shown as black lines with the corresponding shading. Amplitudes of the wave functions are not to scale. The black arrows indicate the STIRAP transitions and the one- ($\mathrm{\Delta }$) and two- ($\delta$) photon detunings. The inset shows the magnetic field dependence of the pump transition to the excited states from the model in Ref. [24]. (b) Magnetic field dependence of the ground-state hyperfine energy structure. The green lines are the states with $M_{\mathrm{F}}=-2$ and the black dashed line is the one with $M_{\mathrm{F}}=-3$. As the states enter the Paschen-Back regime the four branches for different $m_{i,\mathrm{Na}}$ become visible. The magnetic field, where the molecule creation process is performed, is marked with a cross on the axis.

Figure 2

EIT and time evolution of STIRAP. (a) EIT measurement together with a theory curve. The points are the remaining Feshbach molecule fraction normalized to the initial Feshbach molecule number. The solid black line is the theory curve from a three-level master equation and the dashed lines with the enclosed shaded gray area correspond to the uncertainty of the Rabi frequencies. (b) Time evolution of the Feshbach and ground-state population during a round-trip STIRAP. Data points in the upper panel are the observed Feshbach molecule number normalized to the initial molecule number. The solid green (dashed black) line is a theory curve for the ground-state (Feshbach molecule-state) population using the model described in the text and the pulses from the lower panel. The pulse duration for both lasers is $10\mu \mathrm{s}$. The ramping-up of the pump pulse starts $1\mu \mathrm{s}$ before the ramp-down of the Stokes pulse begins. The lower panel shows the pulse sequence of the pump and Stokes laser during the STIRAP. Rabi frequencies are obtained from one-photon loss measurements (not shown here). Error bars are the standard deviation coming from different experimental runs.

Figure 3

One- and two-photon detuning for STIRAP. The round-trip efficiency for STIRAP is shown as a function of the one-photon detuning $\mathrm{\Delta }$. The pulse sequence and laser intensities for these measurements were kept constant corresponding to the optimal values given in the text. The vertical solid blue (dashed red) [dotted red] line is the position of the $|e_{0(1)[2]}⟩$ state deduced from measurements and the model developed in Ref. [24]. The solid black curve is a fit using the five-level master equation model and the individual couplings of the Stokes laser to the $|e_{1,2}⟩$ states as free parameters. The dashed gray curve is a theory curve from a three-level model using the same set of parameters. The inset shows the STIRAP round-trip efficiency dependent on the two-photon detuning $\delta$ with a phenomenological Gaussian fit. The error bars for both plots are the standard error coming from different experimental cycles.

Figure 4

Loss measurements of pure ground-state molecules and with remaining atoms. The open triangles are measurements without atom removal. The fast loss originates from the chemical reaction with ${}^{23}\mathrm{Na}$ atoms. The gray circles are measurements with only ${}^{23}\mathrm{Na}$ removed while still ${}^{39}\mathrm{K}$ atoms remain in the trap. The solid circles are measurements performed with a pure molecular ensemble. The data are normalized to the molecule number without holding time obtained from the individual fits. The curves are fits using a coupled differential equation system for modeling the losses. For the corresponding loss rate coefficients, see text. All error bars are the standard deviation resulting from different experimental runs.