Buffer-gas cooling, high-resolution spectroscopy, and optical cycling of barium monofluoride molecules

We demonstrate buffer-gas cooling, high-resolution spectroscopy, and cycling fluorescence of cold barium monofluoride (BaF) molecules. Our source produces an intense and internally cold molecular beam containing the different BaF isotopologues with a mean forward velocity of $190\mathrm{m}/\mathrm{s}$. For a well-collimated beam of ${}^{138}\mathrm{Ba}{}^{19}\mathrm{F}$ we observe a flux of $>{10}^{10}$ molecules ${\mathrm{sr}}^{-1}{\mathrm{pulse}}^{-1}$ in the $X{}^2\mathrm{\Sigma }$, $N=1$ state in our downstream detection region. Studying the absorption line strength of the intermediate $A^{\prime }\mathrm{\Delta }$ state we infer a lifetime of ${\tau }_{\mathrm{\Delta }}=790\pm 346\mathrm{ns}$, significantly longer than previously estimated. Finally, highly diagonal Franck-Condon factors and magnetic remixing of dark states allow us to realize a quasicycling transition in ${}^{138}\mathrm{Ba}{}^{19}\mathrm{F}$ that is suitable for future laser cooling of this heavy diatomic molecule.

Figure 1

Energy levels and laser cooling scheme for ${}^{138}\mathrm{Ba}{}^{19}\mathrm{F}$. (a) Cooling and repumping transitions (${\lambda }_{00}=859.840\text{nm}$, ${\lambda }_{10}=895.710\text{nm}$, and ${\lambda }_{21}=897.973\text{nm}$) are indicated by the red solid lines. The linewidth of the excited $A{}^2\mathrm{\Pi }$ state is ${\mathrm{\Gamma }}_{\mathrm{\Pi }}=2\pi \times 2.84\mathrm{MHz}$ [24]. Decays are indicated by dashed lines, with $q_{ij}$ denoting the respective Franck-Condon factors. The branching from both the ${\nu }^{\prime }=0$ and 1 states is highly diagonal, with the precise $q_{ij}$ values for the latter given in Appendix pp1. Overall, each molecule can scatter almost ${10}^5$ photons using only three lasers before vibrational branching into states where $\nu \ge 3$ occurs. However, additional branching from the $A{}^2{\mathrm{\Pi }}_{1/2}$ into the $A^{\prime }\mathrm{\Delta }$ state can also limit optical cycling. The corresponding branching ratio has been estimated between ${10}^{-4}$ [25] and ${10}^{-9}$ [26], with the precise value unknown. The linewidth of the narrow-line transition from the ground state to the $A^{\prime }\mathrm{\Delta }$ state (${\lambda }_{\mathrm{\Delta }}=933.111\text{nm}$, orange solid line) is estimated in this paper to be ${\mathrm{\Gamma }}_{\mathrm{\Delta }}=2\pi \times (171\pm 82)\mathrm{kHz}$. (b) As in CaF, SrF, and YO, rotational branching can be suppressed by driving a transition from the negative-parity $X{}^2\mathrm{\Sigma }$, $N=1$ state to the positive-parity $A{}^2{\mathrm{\Pi }}_{1/2}$, $J^{\prime P^{\prime }}=1/2^{+}$ state. For optical cycling, all four ground-state hyperfine levels need to be addressed simultaneously using laser sidebands. The corresponding energy shifts are roughly equidistant and lie in the MHz range. The hyperfine structure in the excited state is not resolved.

Figure 2

Experimental setup. Molecules are created by laser ablation inside a buffer-gas cell, which is attached to the 4-K stage of a cryostat. The outcoupled slow and cold molecular beam is collimated using two cryogenic copper apertures. Probing of the molecules is possible using the absorption of a retroreflected laser beam inside the buffer-gas cell or after time of flight via laser induced fluorescence.

Figure 3

(a) Absorption trace of the ablation plume expanding into vacuum. The trace shown is an average over 50 ablation pulses. (b) Molecular absorption during buffer-gas cooling. The absorption initially increases as the molecules reach the probe beam, and then decays exponentially, as expected for the diffusive motion of the molecules as they collide and thermalize with the helium atoms. Note that due to the slow diffusion the timescale is now three orders of magnitude longer than in (a). Inset: Absorption in logarithmic scale. A fit (solid red line) allows us to extract a decay time of ${\tau }_d=0.47\mathrm{ms}$, corresponding to a BaF-He collisional cross section of ${\sigma }_{\text{BaF,He}}=2.7\times {10}^{-14}{\mathrm{cm}}^2$.

Figure 4

High-resolution spectroscopy of the $X{}^2\mathrm{\Sigma }\text{−}A{}^2{\mathrm{\Pi }}_{1/2}$ band in the spectral region relevant for laser cooling. The strongest lines are due to the ${}^{138}\mathrm{Ba}{}^{19}\mathrm{F}$ isotopologue. The $P_1\left(1\right)$ and ${}^{P}Q_{12}\left(1\right)$ lines correspond to the main laser cooling transitions ${\lambda }_{00}$. Specifically, these lines result from transitions of the $N=1$, $J=3/2$, and $J=1/2$ ground states, respectively, to the $J^{\prime }=1/2^{+}$ excited state. A scan of these transitions recorded with an increased resolution is shown in the inset. The hyperfine structure of these states is not resolved due to a residual Doppler broadening of $\approx 60\mathrm{MHz}$ at $5\mathrm{K}$. A large number of weaker lines of the less abundant isotopologues are also visible in the spectrum. As an example, we have labeled the $G=1$ and 2 components of the ${}^{P}P_{1G}\left(3\right)+{}^{P}Q_{1G}\left(3\right)$ transitions of the ${}^{135}\mathrm{Ba}{}^{19}\mathrm{F}$ and ${}^{137}\mathrm{Ba}{}^{19}\mathrm{F}$ isotopologues, which we investigate in more detail in Fig. 6.

Figure 5

Peak absorption of the ${}^P{Q}_{12}\left(N\right)$ branch vs the rotational quantum number $N$. The red line is a fitted Boltzmann distribution, with a temperature of $T_{\text{rot}}=7.2\pm 3.1\mathrm{K}$.

Figure 6

(a) Absorption in the region of the ${}^{P}P_{12}\left(3\right)+{}^{P}Q_{12}\left(3\right)$ transition. Inset: High-resolution spectrum, containing many overlapping hyperfine components from ${}^{137}\mathrm{Ba}{}^{19}\mathrm{F}$ and ${}^{135}\mathrm{Ba}{}^{19}\mathrm{F}$. (b) Absorption signal at the repumping transition $X(\nu =1)\to A({\nu }^{\prime }=0)$ of ${}^{138}\mathrm{Ba}{}^{19}\mathrm{F}$. Insets: High-resolution spectrum, showing the fine-structure splitting of the transition into $P_1\left(1\right)$ and ${}^{P}Q_{12}\left(1\right)$. (c) Examples of absorption signals on the $X\text{−}A{}^2{\mathrm{\Pi }}_{1/2}$ and $X\text{−}{A}^{\prime }\mathrm{\Delta }$ transitions, as used in the analysis of the $A^{\prime }\mathrm{\Delta }$ state lifetime. The peak around $1.6\mathrm{ms}$ in all panels is caused by noise from the ablation laser. It is strongest in (c) due to less efficient filtering of the 1064-nm ablation light, when probing the $933\text{−}\mathrm{nm}X\text{−}\mathrm{\Delta }$ transition.

Figure 7

(a) Remixing of dark states enabled by magnetic fields. Laser induced fluorescence of the molecular beam passing a transversal laser beam resonant with all four hyperfine transitions. A magnetic field is used to remix dark states, which increases the observed amount of fluorescence. The magnetic fields are 8.64, 3.43, and $0.76\mathrm{G}$ from top to bottom. In all traces a constant fluorescence offset from residual ablation laser light scatter has been subtracted. Inset: Peak amplitude of the fluorescence signal as a function of the applied magnetic field. The signal saturates at a field of $\approx 5\mathrm{G}$, where the associated Larmor frequency corresponds to around twice the excited-state decay rate. The peak fluorescence increases by a factor of 1.7 with respect to the nonremixed case at zero field. (b) The addition of a repumper leads to a further increase of the fluorescence signal by a factor of 1.17.