Molecular beam study of the $a{}^3{\Sigma }^{+}$ state of NaK up to the dissociation limit

We provide spectroscopic data for the $a{}^3{\Sigma }^{+}$ state of the ${}^{23}\mathrm{Na}{}^{39}\mathrm{K}$ molecule. The experiment is done in an ultrasonic beam apparatus, starting from the ground state $X{}^1{\Sigma }^{+}$ and driving the population to the $a{}^3{\Sigma }^{+}$ state, using a $\Lambda$ scheme with fixed pump and scanning dump laser. The signals are observed as dips of the total fluorescence. The intermediate level is chosen to be strongly perturbed by the $B{}^1\Pi /c{}^3{\Sigma }^{+}$ states mixing to overcome the singlet-triplet transfer prohibition. We observed highly resolved hyperfine spectra of various rovibrational levels of the $a{}^3{\Sigma }^{+}$ state from $v_a=2$ up to the highest vibrational levels for rotational quantum numbers $N_a=4,6,8$. By the typical experimental linewidth of 17 MHz, the vibrational dependence of the hyperfine splitting is clearly revealed for NaK. The absolute frequency measurements of the vibrational levels are used for improvement of the $a{}^3{\Sigma }^{+}$ potential curve and of the derived scattering length of all natural isotope combinations. Applying the $\Lambda$ scheme in the reverse direction can provide a pathway for efficient transfer of ultracold ${}^{23}\mathrm{Na}{}^{39}\mathrm{K}$ molecules from the $\text{Na}\left(3s\right)+\text{K}\left(4s\right)$ asymptote to the lowest levels of the ground state. We show spectra that couple the absolute ground state $v_X=0,J=0$ with an appropriate intermediate state for direct realization of the reverse path. The refined theoretical model of the coupled excited states of the $\text{Na}\left(3s\right)+\text{K}\left(4p\right)$ asymptote allows predictions of efficient paths for ${}^{23}\mathrm{Na}{}^{40}\mathrm{K}$; one example is calculated.

Figure 1

Potential scheme of NaK including the pump-dump steps. The pump laser connects an intermediate level of the $B{}^1\Pi$ state strongly coupled to the $c{}^3{\Sigma }^{+}$ state with the state $X{}^1{\Sigma }^{+}$. The dump laser connects the same intermediate level with various vibrational levels of the $a{}^3{\Sigma }^{+}$ state. The signals are observed as a dip in the fluorescence to the $X{}^1{\Sigma }^{+}$ state during a scan (tuning knob indicated by a small dashed arrow) of the dump laser when it crosses a $B{}^1\Pi /c{}^3{\Sigma }^{+}\text{−}a{}^3{\Sigma }^{+}$ resonance while the frequency of the pump laser is kept fixed.

Figure 2

Simplified scheme of the experimental setup. The molecular beam is crossed perpendicularly by two laser beams from the dye and the Ti:sapphire laser running parallel, focused, and overlapped by the beam forming optics. The resulting fluorescence is observed by the photomultiplier (PM). The absolute frequencies of the two lasers, together with the reference HeNe laser, are monitored by the wavemeter WS7 via an optical multiplexer. The frequency of the dye laser is long-term stabilized by a servo system involving the wavemeter for setting the laser to the requested frequency. A confocal cavity gives relative frequency markers when the Ti:sapphire laser is tuned. The data are collected and recorded by the data acquisition system via a buffer box.

Figure 3

Laser excitation spectra of the perturbed lines ${}^{R}Q\left(6\right)(8/30–0)$ and $Q\left(6\right)(8/30–0)$ of the $X{}^1{\Sigma }^{+}–B{}^1\Pi /c{}^3{\Sigma }^{+}$ band. The quartet structure is caused by the hyperfine structure of the ${}^{23}\mathrm{Na}$ nucleus with sodium nuclear spin $i_{\mathrm{Na}}=3/2$. Due to the coupling scheme ${\vec{F}}_1=\vec{J}+{\vec{i}}_{\mathrm{Na}}$, intermediate quantum numbers $F_1=15/2,13/2,11/2,9/2$ are assigned to the lines of the quartet. The hyperfine splitting due to the coupling scheme $\vec{F}={\vec{F}}_1+{\vec{i}}_{\mathrm{K}}$ of the ${}^{39}\mathrm{K}$ nucleus is not resolved.

Figure 4

Hyperfine structure of the state $a{}^3{\Sigma }^{+}$ for vibrational levels $v_a=5,17,18$ and $N_a=6$. The line ${}^{R}Q\left(6\right)$ with hyperfine component $F_1=15/2$ of the mixed levels $B{}^1\Pi (v_B=8,J_B=6)/c{}^3{\Sigma }^{+}(v_c=30,J_c=6)$ was pumped.

Figure 5

Comparison between the experimental and the calculated spectrum for $N_a=6,v_a=5$. The calculated frequency of each allowed hyperfine component is given as a red vertical bar at the bottom of the diagram. The intermediate level was $J_c=6,F_1=15/2$.

Figure 6

Observed low $J$ transitions in the $8/30–0$ band of $B{}^1\Pi /c{}^3{\Sigma }^{+}\text{−}X{}^1{\Sigma }^{+}$ for ${}^{23}\mathrm{Na}{}^{39}\mathrm{K}$ in the molecular beam with dominant amplitude of (a) the $B{}^1\Pi$ state and (b) the $c{}^3{\Sigma }^{+}$ state.