# Cryogenic Buffer Gas beams of AlF, CaF, MgF, YbF, Al, Ca, Yb and NO – a
comparison

Sidney C. Wright1,a, Maximilian Doppelbauer1,a, Simon Hofsäss1, H. Christian
Schewe1,*, Boris Sartakov1, Gerard Meijer1, Stefan Truppe1,$\dagger$ 1Fritz
Haber Institute of the Max Planck Society, Faradayweg 4-6, 14195 Berlin,
Germany
*Current Address: Institute of Organic Chemistry and Biochemistry of the Czech Academy of Sciences, Flemingovo nám. 2, 166 10 Prague 6, Czech Republic
$\dagger$Current Address: Centre for Cold Matter, Blackett Laboratory,
Imperial College London, Prince Consort Road, London SW7 2AZ, United Kingdom

###### Abstract

Cryogenic buffer gas beams are central to many cold molecule experiments.
Here, we use absorption and fluorescence spectroscopy to directly compare
molecular beams of AlF, CaF, MgF, and YbF molecules, produced by chemical
reaction of laser ablated atoms with fluorine rich reagents. The beam
brightness for AlF is measured as $2\times 10^{12}$ molecules per steradian
per pulse in a single rotational state, comparable to an Al atomic beam
produced in the same setup. The CaF, MgF and YbF beams show an order of
magnitude lower brightness than AlF, and far below the brightness of Ca and Yb
beams. The addition of either NF3 or SF6 to the cell extinguishes the Al
atomic beam, but has a minimal effect on the Ca and Yb beams. NF3 reacts more
efficiently than SF6, as a significantly lower flow rate is required to
maximise the molecule production, which is particularly beneficial for long-
term stability of the AlF beam. We use NO as a proxy for the reactant gas as
it can be optically detected. We demonstrate that a cold, rotationally pure NO
beam can be generated by laser desorption, thereby gaining insight into the
dynamics of the reactant gas inside the buffer gas cell.

###### keywords:

Ultracold molecules; cryogenic buffer gas cooling; gas phase chemistry;

††articletype: JOURNAL ARTICLE

##  1 Introduction

††a These authors contributed equally to this work.

Cryogenic buffer gas cooling is a versatile technique to produce intense
atomic and molecular beams with a low forward velocity [1, 2, 3, 4] and allows
efficient cooling of the rotational and vibrational degrees of freedom in
molecules. Buffer gas cooling is now routinely used for precision spectroscopy
and measurements [5, 6, 7, 8], to trap molecules using magnetic fields [9, 10,
11] and electric fields [12], to study collisions at low temperatures [13, 14,
15, 16], and to provide slow atoms and molecules for magneto-optical [17, 18,
19, 20, 21, 22, 23, 24] and electro-optical traps [25], in which the particles
can be cooled to $\text{\,}\mathrm{\SIUnitSymbolMicro K}$ temperatures.

The species that have been cooled using a cryogenic buffer gas range from
light atoms such as Li [26] and K [23] to heavy atoms such as Yb [27], exotic
atoms such as Tm, Er and Ho [17], diatomic molecules [28, 29], including
radicals [2, 30, 27, 31], small polyatomic molecules [32, 33, 34, 35] and
large, complex molecules such as functionalised arenes [36], Nile Red [37],
and C60 [38]. Diatomic metal fluoride molecules with a ${}^{2}\Sigma^{+}$
electronic ground-state, such as MgF, CaF, SrF, BaF and YbF have attracted
attention due to their suitability for direct laser cooling [39, 40, 41, 42]
and precision measurements [43, 7]. Buffer gas molecular beams of these
molecules have been reported and characterised [44, 4, 43, 13]. Recently, the
molecules AlF and AlCl, which have ${}^{1}\Sigma^{+}$ electronic ground
states, have been produced for the first time in buffer gas sources and are
now the subject of laser cooling efforts [45, 46, 47, 48, 49]. These molecules
are fundamentally different to the ${}^{2}\Sigma^{+}$ ground state molecules
that have been laser cooled thus far, and we recently reported a bright
molecular beam of AlF and fast optical cycling on its
A${}^{1}\Pi\leftarrow$X${}^{1}\Sigma^{+}$ transition [46].

It is often challenging to determine whether molecular yield in one experiment
differs from another because of the choice of molecule, the detection method
or conditions of the molecular beam source which may deteriorate over time.
Here, we investigate beams of AlF, CaF, MgF, YbF, NO, Al, Ca and Yb in the
same apparatus and use absorption and laser induced fluorescence spectroscopy
to characterise them. By comparing the brightness of the molecular and atomic
beams, we gain new insight in the production efficiency for the various
species. We also describe observations which we consistently find produce
desirable molecular beam properties and better long term performance.

##  2 Experimental Setup

###  2.1 Molecular Beam Source

Figure 1a shows a sketch of the molecular beam source. We use a two-stage
closed-cycle He cryocooler (Sumitomo RDK-415DP (with helium pot) with F-50H
compressor) to cool the source to about $2.5\text{\,}\mathrm{K}$. The first
stage cools the aluminium radiation shields to about $40\text{\,}\mathrm{K}$.
The buffer gas cell, shown in Figure 1c and d, is attached to the second stage
and surrounded by a copper box, whose internal walls are coated with activated
charcoal. The charcoal acts as an efficient sorption pump for helium gas at
temperatures below $10\text{\,}\mathrm{K}$. The operating pressure of the
source chamber under cryogenic conditions is about $1\times$10-8 mbar,
measured outside the radiation shields, and typically increases to
3$\times$10-8 mbar when 2 standard cubic centimetres per minute
($\text{\,}\mathrm{s}\mathrm{c}\mathrm{c}\mathrm{m}$) of helium is flowed
through the cell.

Figure 1: (a): A diagram of the molecular beam source. The molecular beam
travels into the page. The front plates have been omitted to give a complete
view of the inside of the source chamber. (b): Cut through the charcoal-coated
shield along the direction of the molecular beam. (c): Cut through the buffer
gas cell, perpendicular to the molecular beam direction, showing the region
where the metal is ablated and reacts with a fluorine donor gas. The inset is
a photograph of the multi-species metal target. (d): cut along the molecular
beam direction showing the path of the He buffer gas.

To increase the effective pumping area, we attach charcoal-coated copper fins
to the top internal face of the copper box. An additional single fin is
mounted along the molecular beam direction (shown in Figure 1b). While the
top-fins have only a minor influence on the beam properties, the fin along the
molecular beam helps maintaining a high molecular beam flux. Saturation of the
activated charcoal with reaction products and “ablation dust” — indicated by a
discoloration of the charcoal around the aperture — can reduce the downstream
flux by up to a factor of ten, without noticeably changing absorption outside
the cell. In this case, the fin can be easily replaced. Increasing the
distance between the cell and the first charcoal-coated surface mitigates this
problem without affecting the downstream flux considerably. Cartridge heaters
can be used to heat the set-up to room temperature within about five hours.

A sketch of the buffer gas cell is shown in Figure 1c and d. It is based on
the design presented by Truppe et al. [4], with minor changes to facilitate
machining and cleaning. The cell is machined from oxygen-free copper, has a
circular bore with a 10 mm diameter, and its length is variable between 30 and
$60\text{\,}\mathrm{mm}$, using extension pieces. Windows on the extensions
allow in-cell absorption spectroscopy. For the experiments presented in this
study, we used a $40\text{\,}\mathrm{mm}$ long cell. The exit aperture of the
cell has a diameter of $4\text{\,}\mathrm{m}\mathrm{m}$. The multi-species
metal ablation target is attached to a copper adaptor with a fine thread,
which enables rotation of the target via a mechanical vacuum feed-through. We
find that translating the target is superior to translating the ablation-laser
beam and results in more consistent molecular beam properties. The relatively
small bore size of the cell results in a short extraction time for molecules
and thus short molecular pulses [50, 4], ideal for Stark deceleration and
chirped laser slowing. The helium gas is pre-cooled in two copper pipe bobbins
that are attached to each of the two cooling stages (see Figure 1a). With a
buffer gas flow rate of $1\text{\,}\mathrm{s}\mathrm{c}\mathrm{c}\mathrm{m}$
the in-cell helium density is $7\times 10^{14}$\text{\,}{\mathrm{cm}}^{-3}$$,
where we assumed an ideal vacuum conductance of the exit aperture.

The output of a pulsed Nd:YAG laser (Continuum Minilite II) with a pulse
energy of up to $40\text{\,}\mathrm{mJ}$ and a pulse-length of
5-$7\text{\,}\mathrm{ns}$ is gently focused to produce a
$0.7\text{\,}\mathrm{m}\mathrm{m}$ diameter spot size on the target. The
Nd:YAG fires with a repetition rate of $1\text{\,}\mathrm{Hz}$ for all
measurements in this study, and firing the ablation light defines $t=0$ for
each molecular pulse. A higher repetition rate leads to an increased heat
load, resulting in an increase of the rotational temperature of the molecular
beams. We ablate a metal target and introduce a fluorine donor gas (SF6, NF3,
CF4, XeF2) into the cell through a copper capillary that is thermally
insulated from the cell. We also use this capillary to inject NO molecules.
The temperature of the capillary is kept at about $120\text{\,}\mathrm{K}$.

We found over the course of our experiments that the beam properties of AlF
are sensitive to the cell having clean internal surfaces. In particular,
cleaning the cell in an ultrasonic bath with Citranox acidic detergent
(Alconox, Inc.) results consistently in a slow beam, with a small spread of
arrival times seen in downstream fluorescence. With increasing number of
ablation laser pulses, the time-of-flight broadens, and secondary higher
velocity peaks appear. Removal of ablation products by wiping the inside of
the cell leads to some recovery, but the efficacy of this method reduces
gradually. Recovery of the original behaviour is reliably achieved by
ultrasonic cleaning to expose the metal surface. We show examples of this
behaviour for AlF in Figure 2. Coating the surfaces of the cell with a thin
layer of gold to ensure a chemically inert surface was unsuccessful at
preventing the observed degradation.

Figure 2: Fluorescence time of flight (TOF) traces of AlF with a buffer gas
cell after different periods of use. From bottom to top: Cell freshly cleaned
with Citranox detergent; same cell after one day of operation using the same
ablation spot; same cell geometry after weeks of operation. Figure 3: (a):
Schematic view of the experimental setup used in this study to characterise
the atomic and molecular beams. A photodiode (PD) is used for absorption and
photomultiplier tubes (PMTs) for fluorescence spectroscopy. P marks the first
downstream position where optical pumping can occur. Closer to the buffer gas
cell collisions with helium redistribute the rotational state populations.
(b): Optical layout of the fluorescence detector.

A schematic of the full experimental setup used for this study is shown in
Figure 3a. We use a multi-species target to quickly change the metal at the
ablation spot, and therefore the species observed in the buffer gas beam. We
can probe the atoms and molecules by absorption spectroscopy with a weak laser
beam, both inside the cell and at a variable distance
0-$2\text{\,}\mathrm{cm}$ from the exit aperture, detecting the transmitted
light with a photodiode. The extraction efficiency as measured from the peak
absorption of CaF, AlF and MgF inside and directly outside the cell is about
$10-15\%$. The Doppler width measured inside and outside the cell is the same,
but downstream of the cell, an increase of about a factor two in the
transverse velocity spread is observed. We discuss the implications of this
broadening for beam brightness measurements later.

Two laser-induced fluorescence (LIF) detectors enable us to measure the
brightness of the collimated molecular beam, its velocity distribution and the
rotational state distribution. The first detector, LIF-1, is located at
$L_{1}=$23\text{\,}\mathrm{cm}$$ downstream of the cell exit. It is primarily
used as a region for optical pumping, for instance to determine the velocity
of the molecules using a pump-probe method [46]. The second zone, LIF-2, is
located $L_{2}=$44\text{\,}\mathrm{cm}$$ downstream of the cell exit and is
used for spectroscopy and beam brightness measurements. The entrance to LIF-2
is restricted by a square aperture of size
2$\times$$2\text{\,}{\mathrm{mm}}^{2}$ to reduce the transverse velocity
spread of the molecular beam to about
$1.5\text{\,}\mathrm{m}\text{\,}{\mathrm{s}}^{-1}$. This reduces the Doppler
broadening in our fluorescence excitation spectra and defines the interaction
volume with the probe laser beam.

Figure 3b shows the collection optics of LIF-2. The fluorescence of the
molecular beam is collimated by a $50\text{\,}\mathrm{m}\mathrm{m}$ plano-
convex lens and concave mirror mounted in vacuum, and focussed onto a
Hamamatsu R928 photomultiplier tube (PMT) by a second externally mounted lens.
We collimate the excitation laser light to a $e^{-2}$ intensity diameter of
2-$3\text{\,}\mathrm{mm}$, to ensure that all molecules that enter the
detection zone are addressed by the excitation laser light. The aperture of
the detector subtends a solid angle $\delta\Omega=2.1\times 10^{-5}$
$\text{\,}\mathrm{sr}$ at the buffer gas cell exit and the peak optical power
reaching the PMT when probing the brightest atomic beam is about
$1\text{\,}\mathrm{nW}$. The PMT photocurrent is sent to a transimpedance
amplifier with a current-to-voltage conversion factor of $10^{5}$
$\text{\,}\mathrm{V}\text{\,}{\mathrm{A}}^{-1}$.

We use the same optical setup in the fluorescence detector for all species.
The wavelengths of the fluorescence light span from 227 to
$606\text{\,}\mathrm{nm}$ and the collection efficiency of the LIF detector
varies across this range due to differences in the PMT quantum efficiency and
chromatic aberration of the detection optics. To compare the detection
efficiency of the PMT across the range of emission wavelengths, we illuminated
the PMT directly with about $1\text{\,}\mathrm{nW}$ of laser light at 227,
360, 452 and 606 nm. This was done by calibrating a $\sim 10^{-3}$ neutral
density filter at incident powers of order $1\text{\,}\mathrm{m}\mathrm{W}$,
and then using the filter to attenuate to
$1\text{\,}\mathrm{\SIUnitSymbolMicro W}$, measured using a calibrated optical
power meter. To account for differences in collection efficiency, we use ray
tracing simulations combined with the measured transmission and reflection
losses of the optical components.

###  2.2 Molecular Beam Brightness Measurement

The figure of merit for this study is the number of molecules produced per
unit solid angle per pulse, in a given rovibrational level. To estimate this
for the different species, we use both absorption and fluorescence
measurements.

Absorption measurements have the advantage of directly measuring the column
density of the species of interest, but sufficient density is only available
inside or near the exit of the buffer gas cell. The Lambert-Beer law relates
the density, $n(t)$, to the measured absorption,

$-\ln(I_{t}/I_{0})=n(t)\sigma(\nu)z,$ (1)

Here, $\sigma(\nu)$ is the absorption cross-section, $z$ is the interaction
length, and $I_{t}$ and $I_{0}$ are the intensity transmitted with and without
the absorbing species present, respectively. In the absence of Doppler or
hyperfine broadening, the maximum value of $\sigma(\nu)$ is the resonant
absorption cross section $\sigma_{0}$, which for a transition
$J^{\prime}\leftarrow J$ is given by [51]

$\sigma_{0}=\frac{\lambda^{2}}{2\pi}\frac{2J^{\prime}+1}{2J+1}\frac{A_{ij}}{\Gamma}\hskip
2.84544pt.$ (2)

Here, $J$ and $J^{\prime}$ are the ground and excited state total electronic
angular momentum quantum numbers for atoms and the total electronic angular
momentum including the end-over-end rotation for molecules, $A_{ij}$ is the
Einstein A-coefficient of the resonant transition, and $\Gamma$ is the total
spontaneous decay rate. In the presence of broadening mechanisms, the peak
absorption cross-section $\sigma_{D}$ can be calculated using the relation
$\int\sigma(\nu)d\nu=\sigma_{0}\Gamma\frac{\pi}{2}$, where the integral over
frequency $\nu$ covers the full absorption spectrum.

We estimate the total number, $N$, by integrating the flux outside the cell
over time,

$N=v_{f}a_{aperture}\int
n(t)dt=\frac{v_{f}a_{aperture}}{z\sigma_{D}}\int-\ln(I_{t}/I_{0})dt\hskip
2.84544pt,$ (3)

where $a_{aperture}$ is the area of the exit aperture of the cell, $z$ is
assumed to be the aperture diameter, and $v_{f}$ is the forward velocity which
can be estimated from measurements downstream of the source. The brightness of
the beam in absorption, $\mathcal{B}_{\mathrm{abs}}$, is then calculated as,

$\mathcal{B}_{\mathrm{abs}}=\frac{N}{\Delta\theta^{2}}$ (4)

with $\Delta\theta=2\tan^{-1}(v_{t}/2v_{f})$ the angular divergence of the
beam, and $v_{t}$ the full-width at half maximum (FWHM) of the transverse
velocity distribution, which is obtained from the absorption spectrum.

Fluorescence measurements, on the other hand, are much more sensitive and can
be carried out far from the cell, but are typically difficult to calibrate on
an absolute scale. For an optically closed transition, the number of photons
scattered depends on the effective intensity and interaction time of the
laser, and is thus sensitive to the laser beam profile and velocity of the
species of interest. If the fluorescence can be saturated by optically pumping
population to another state, a known number of photons $\mathcal{N}$ is
absorbed and only the overall detection efficiency $\epsilon(\lambda)$ remains
uncertain. When exciting from an initial state $i$ to an excited state $j$,
$\mathcal{N}$ is given by,

$\mathcal{N}=\frac{\Gamma}{\Gamma-A_{ji}},$ (5)

where $A_{ji}$ is the Einstein-$A$ coefficient for decay back to the initial
state and $\Gamma=\Sigma_{n}A_{jn}$ for all states $n$ is the total decay rate
of the excited state $j$. If $N$ molecules enter the fluorescence detector,
the number of photons detected is then simply $N\mathcal{N}\epsilon(\lambda)$.
The on-axis brightness is then calculated as,

$\mathcal{B}_{\mathrm{f}}=\frac{N}{\delta\Omega}\hskip 2.84544pt,$ (6)

This method can be easily applied to diatomic molecules with diagonal Franck-
Condon factors, where it is straightforward to optically pump molecules using
rotationally open electronic transitions, and $\mathcal{N}$ can be predicted
with knowledge of the relevant Hönl-London factors. For atoms, optically open
electronic transitions are commonly available, but often the coefficients
$A_{ji}$ are not known accurately.

###  2.3 Laser Systems

We use two different continuous laser systems for this study. To detect Al,
Ca, Yb, AlF, MgF and NO, we use a Ti:Sapphire laser (MSquared Solstis), whose
output is frequency doubled in successive enhancement resonators containing a
nonlinear optical crystal. The linewidth of the fundamental light is less than
400 kHz. A single stage of frequency doubling is sufficient to generate light
near $360\text{\,}\mathrm{nm}$ (MgF) and $399\text{\,}\mathrm{nm}$ (Yb), and
we use two successive doubling stages to generate UV light near
$227\text{\,}\mathrm{nm}$ (AlF, NO, Al, Ca). The second laser system is a
Coherent 899 ring dye laser (RDL) which generates light near
$606\text{\,}\mathrm{nm}$ for detection of CaF and near
$552\text{\,}\mathrm{nm}$ for the detection of YbF. The laser linewidth is
around $1\text{\,}\mathrm{M}\mathrm{H}\mathrm{z}$. The laser frequencies are
monitored with a HighFinesse WS8-10 wavemeter calibrated using a temperature-
stabilised HeNe laser. Details on the absolute accuracy of the wavemeter can
be found in reference [52]111Probing the Mg atoms would require light at 285
nm to excite the ${}^{1}P_{1}\leftarrow{}^{1}S_{0}$ transition, which was not
available for this study..

##  3 Atomic beam measurements

We first discuss measurements on the atomic buffer gas beams of Ca, Al, and
Yb. These provide an important reference when comparing with the molecular
beams.

###  3.1 Aluminium

To characterise the Al atomic beam, we use the
$(3s^{2}5d)^{2}D_{3/2}\leftarrow(3s^{2}3p)^{2}P_{1/2}$ transition near
$226.4\text{\,}\mathrm{nm}$, conveniently close to the
A${}^{1}\Pi\leftarrow$X${}^{1}\Sigma^{+}$ transition in AlF. Due to the fine
structure splitting of the electronic ground state, there exists a
$(3s^{2}3p)^{2}P_{3/2}$ state approximately $112\text{\,}{\mathrm{cm}}^{-1}$
($\sim 160$ K) above the ground state. By probing the nearby
$(3s^{2}5d)^{2}D_{5/2}\leftarrow(3s^{2}3p)^{2}P_{3/2}$ transition, we find
that about 1% of the Al atoms exiting the source initially occupy the
${}^{2}P_{3/2}$ state, and they appear only with high velocities greater than
$500\text{\,}\mathrm{m}\text{\,}{\mathrm{s}}^{-1}$. We searched for evidence
of Al2 dimers by probing the E
${}^{3}\Sigma_{g}^{-}\leftarrow$X${}^{3}\Pi_{0u}$ transition near
$366.6\text{\,}\mathrm{n}\mathrm{m}$ [53]. We therefore assume the population
in the $(3s^{2}3p)^{2}P_{1/2}$ state represents the full atomic population.

The lifetime of the $(3s^{2}5d)^{2}D_{3/2}$ excited state,
$\tau_{\mathrm{ex}}$ is $12.3\text{\,}\mathrm{ns}$
($\Gamma/2\pi=$12.8\text{\,}\mathrm{MHz}$$) [54], but to our knowledge the
hyperfine structure of the
$(3s^{2}5d)^{2}D_{3/2}\leftarrow(3s^{2}3p)^{2}P_{1/2}$ transition has not been
measured. The nuclear spin $\mathbf{I}(I_{Al}=5/2)$, couples with the
electronic total angular momentum $\mathbf{J}$ to give eigenstates labelled by
the total angular momentum quantum number $F$. Figure 4a shows a hyperfine-
resolved experimental spectrum of the
$(3s^{2}5d)^{2}D_{3/2}\leftarrow(3s^{2}3p)^{2}P_{1/2}$ transition, obtained
using about $100\text{\,}\mathrm{\SIUnitSymbolMicro W}$ of linearly polarised
laser light. The larger splitting $\sim 1.5$ GHz arises from the known ground
state hyperfine interaction, and the interaction in the excited state leads to
a further splitting of a few hundred MHz. The hyperfine levels are shown in
Figure 5. We fit the hyperfine energies, $E_{i}(J,I,F)$, to the equation [55]

$E_{i}=\frac{A_{i}C}{2}+B_{i}\frac{\frac{3}{4}C(C+1)-I(I+1)J(J+1)}{2I(2I-1)J(2J-1)},$
(7)

where $A_{i}$ is the interaction strength between the nuclear spin
$\mathbf{I}$ and the electronic angular momentum $\mathbf{J}$, $B_{i}$ is the
quadrupole interaction coefficient, necessarily zero for $J<1$, and
$C=F(F+1)-I(I+1)-J(J+1)$. The index $i$ labels the electronic state. For the
ground state we find $A=501.6(1.2)$ MHz, consistent with the literature value
[56]. For the excited state, we determined $A=-33.9(4)$ MHz and $B=1.9(2.5)$
MHz. Shown pointing downwards in red in Figure 4 is a simulated spectrum using
the known natural linewidth, where we assumed equal population of the ground
state Zeeman sub-levels and isotropic emission of the fluorescence light.
Under this assumption, the relative intensities of the $F^{\prime},F$
hyperfine lines $l_{F^{\prime},F}$ are given by,

$l_{F^{\prime},F}=|\sqrt{(2F^{\prime}+1)(2F+1)}\times\begin{Bmatrix}J^{\prime}&F^{\prime}&I\\\
F&J&1\\\ \end{Bmatrix}|^{2}\hskip 2.84544pt.$ (8)

This formula describes the data well. The fitted FWHM of the lines is found as
$19\text{\,}\mathrm{M}\mathrm{H}\mathrm{z}$, slightly larger than the measured
linewidth, which we attribute to Doppler broadening, residual Zeeman shifts
due to a small ambient magnetic field ($\sim 1$ G) in the detection region,
and the effect of optical pumping.

The measured hyperfine structure can then be used to determine the Doppler
broadening present in absorption measurements. Figure 4b shows two such
absorption spectra, directly outside the exit of the buffer gas cell and
$10\text{\,}\mathrm{mm}$ further downstream. There and in the following
absorption plots, we show the optical depth
-$\mathrm{ln}(I_{\mathrm{t}}/I_{0})$ on the $y$-axis. We fit the data using
the measured excited state hyperfine structure convolved with a Doppler
broadening term with FWHM $\Gamma_{D}$. The transverse velocity width,
$v_{t}=\Gamma_{D}\lambda/(2\pi)$, is approximately
$90\text{\,}\mathrm{m}\text{\,}{\mathrm{s}}^{-1}$ at
$z=$0\text{\,}\mathrm{mm}$$ and
$150\text{\,}\mathrm{m}\text{\,}{\mathrm{s}}^{-1}$ at
$z=$10\text{\,}\mathrm{mm}$$. This increase of about a factor 1.7 indicates
collisions of the Al atoms with (somewhat hotter) He buffer gas outside the
cell, increasing the divergence of the beam. Using the downstream value for
the transverse velocity spread, we estimate the brightness of the atomic beam
as $4.1\text{\times}{10}^{12}\text{\,}$.

To measure the Al beam brightness in fluorescence, we use the scheme shown in
Figure 5. We excite the $F^{\prime}=4\leftarrow F=3$ hyperfine line, which
optically pumps 95% of the population to the $(3s^{2}3p)^{2}P_{3/2}$ state.
The remaining 5% of the atomic population is pumped to higher lying ${}^{2}P$
and ${}^{2}F$ electronic states, which cannot directly decay back to the
electronic ground state by dipole allowed transitions. We neglect the effect
of these states other than the fact that they slightly increase the optical
pumping probability. From the ratio of the Einstein $A$-coefficients of these
transitions, we calculate that we optically pump population in the $F=3$
hyperfine level after absorbing on average $6.1(1.1)$ photons. In Figure 4c,
the fluorescence signal on this transition in LIF-2 is plotted against the
laser intensity expressed in terms of the two-level saturation intensity
$I_{\textrm{sat}}=\pi hc\Gamma/(3\lambda^{3})$, where $\Gamma$ is the
spontaneous decay rate and $\lambda$ is the transition wavelength. The
fluorescence saturates, demonstrating that we can use this transition to
accurately determine the average number of photons emitted by the atoms. The
inset shows the change in the fluorescence signal when the same laser light is
used in LIF-1 to optically pump the atoms before detecting the remaining atoms
in LIF-2. The pumping efficiency is approximately 90%, increasing with arrival
time at the detector. After accounting for the $F=2$ ground state population
which is not detected, we arrive at a total brightness of Al atoms of
$3.0\text{\times}{10}^{12}\text{\,}$$\text{\,}{\mathrm{sr}}^{-1}$ per pulse.
This is within $25\%$ of the number derived from absorption measurements in
the source when we assume the transverse velocity as measured
$10\text{\,}\mathrm{mm}$ downstream from the source. If, instead, we used the
transverse velocity spread as measured right outside the cell, we would
overestimate the beam brightness by a factor of 3.5. This clearly shows that
absorption measurements close to the cell can be misleading, and typically
will provide an upper bound to the beam brightness observed downstream.

Figure 4: (a): Hyperfine-resolved LIF spectrum of the
$(3s^{2}5d)^{2}D_{3/2}\leftarrow(3s^{2}3p)^{2}P_{1/2}$ transition of Al near
227.6 nm. The experimental spectrum is shown in blue. A simulated spectrum
using equations 7 and 8 and the known linewidth of $12.8$ MHz is shown in red.
The ground-state ($F$) and excited-state ($F^{\prime}$) hyperfine quantum
numbers of the transitions are given below the simulated spectrum. (b):
Aluminium absorption spectra recorded directly outside the cell exit and
$10\text{\,}\mathrm{mm}$ downstream (magnified by a factor five). The solid
curves in red and black are fits to the data (blue) using the known
spectroscopic constants and a Gaussian lineshape to determine the Doppler
broadening. The Doppler broadening increases for the downstream position. (c):
Fluorescence saturation curve of the
$(3s^{2}5d)^{2}D_{3/2},F^{\prime}=4\leftarrow(3s^{2}3p)^{2}P_{1/2},F=3$ line
of Al, demonstrating that we can saturate the fluorescence by optical pumping.
The inset shows the LIF TOF without (blue) and with (red) a pumping laser on
the same transition in LIF-1. (d): Time of flight traces of the Al beam under
saturated fluorescence of the
$(3s^{2}5d)^{2}D_{3/2},F^{\prime}=4\leftarrow(3s^{2}3p)^{2}P_{1/2},F=3$
transition to determine the total flux through a $2\times 2$
$\text{\,}{\mathrm{mm}}^{2}$ aperture $440\text{\,}\mathrm{mm}$ from the
source aperture. The inset shows the absorption trace directly outside the
cell. Figure 5: Scheme of the relevant electronic states and hyperfine levels
of Al. Electronic energies are not to scale, the relative hyperfine splittings
are shown to scale. We use the
2D${}_{3/2},F^{\prime}=4\leftarrow^{2}$P${}_{1/2},F=3$ transition to detect Al
atoms.

###  3.2 Calcium

To detect calcium, we use the
$(3p^{6}4snp)^{1}P_{1}\leftarrow(3p^{6}4s^{2})^{1}S_{0}$ transition at
$227.6\text{\,}\mathrm{nm}$. In Figure 6a, the relevant energy levels for our
study of the Ca atomic beam are shown. Exciting the atoms to the ${}^{1}P_{1}$
state primarily pumps the population to the metastable $(3p^{6}3d4s)^{1}D_{2}$
state, with emission of a $452$ nm photon. There are additional decay channels
to higher lying ${}^{1}S$ and ${}^{2}D$ states, but these emit at wavelengths
longer than $940$ nm, outside the detection range of the PMT. The direct decay
channel back to the ${}^{1}P_{0}$ state emits a photon at 227.6 nm. The
Einstein-$A$ coefficient for this decay channel has been measured as
$A(^{1}S_{0})=2.84(39)\times 10^{7}$$\text{\,}{\mathrm{s}}^{-1}$ [57]. We
collect both $227$ nm and $452$ nm photons and account for the detector
sensitivity at the different wavelengths. The two decay paths have different
fluorescence emission patterns, which is demonstrated by monitoring the LIF as
a function of the angle of linearly polarised excitation light, $\theta$.
Figure 6b shows the detected fluorescence against $\theta$ with and without a
filter blocking the visible light covering the PMT. The emission pattern of
the $227$ nm decay is proportional to $\sin^{2}\theta$, whereas the $452$ nm
emission is proportional to $1+\frac{1}{6}\sin^{2}\theta$, and almost
isotropic. This leads to the reduced contrast in the fluorescence as a
function of $\theta$ when detecting both the visible and UV fluorescence
compared to the UV alone. From these measurements and the detector
efficiencies, we estimated that the ratio of Einstein A-coefficients of the
two transitions, $A(^{1}D_{2})/A(^{1}S_{0})=2\pm 0.3$. Using the measured
value for $A(^{1}S_{0})$, we find a total decay rate of
$A(^{1}S_{0})+A(^{1}D_{2})=8.5(1.4)\times 10^{7}$$\text{\,}{\mathrm{s}}^{-1}$,
larger than the measured spontaneous emission rate of
$\Gamma=1/\tau=6.37\times 10^{7}$$\text{\,}{\mathrm{s}}^{-1}$ [58]. We assume
that atoms in the Ca beam emit on average $\mathcal{N}_{227}=0.5$ and
$\mathcal{N}_{452}=1$ photons at the two detection wavelengths when the
fluorescence is saturated, but note that these values are approximate.

The fluorescence spectrum is shown in Figure 7a, where we clearly resolve four
naturally abundant Ca isotopes. The transitions of the two low-abundance
bosonic isotopes, 42Ca and 44Ca, are shifted relative to 40Ca by $+1.43(1)$
GHz and $+2.755(8)$ GHz respectively. We hereon focus on 40Ca, which is
relevant for comparison with 40CaF.

Figure 6: (a): Scheme of the relevant energy levels of calcium. (b):
Polarisation dependence of fluorescence of the Ca atomic beam. The UV
fluorescence, isolated with a 227 nm bandpass filter, shows strong anisotropy
due to the dipole emission pattern. The combined fluorescence in the UV and
visible shows reduced emission anisotropy as the visible light emission is
nearly isotropic. Figure 7: (a): LIF spectrum of the
$(3p^{6}4snp)^{1}P_{1}\leftarrow(3p^{6}4s^{2})^{1}S_{0}$ line of Ca. The
observed isotope peaks are labelled. (b): Absorption spectra of the
$(3p^{6}4snp)^{1}P_{1}\leftarrow(3p^{6}4s^{2})^{1}S_{0}$ transition in 40Ca,
recorded directly outside the cell exit (Gaussian fit shown in red) and
$20\text{\,}\mathrm{mm}$ downstream (black). (c): Fluorescence saturation
curve of the $(3p^{6}4snp)^{1}P_{1}\leftarrow(3p^{6}4s^{2})^{1}S_{0}$
transition of Ca. The inset shows the LIF TOF without (blue) and with (red) a
pumping laser tuned the same transition frequency. (d): Fluorescence and
absorption TOF traces of the Ca beam, using light resonant with the
$(3p^{6}4snp)^{1}P_{1}\leftarrow(3p^{6}4s^{2})^{1}S_{0}$ transition of 40Ca.

In Figure 7b, absorption spectra of the most abundant isotope peak of the
$(3p^{6}4snp)^{1}P_{1}\leftarrow(3p^{6}4s^{2})^{1}S_{0}$ transition are shown
directly at the cell orifice and $20\text{\,}\mathrm{mm}$ downstream. We again
observe an increase in the transverse velocity width at the downstream
position, from $75\text{\,}\mathrm{m}\text{\,}{\mathrm{s}}^{-1}$ to
$120\text{\,}\mathrm{m}\text{\,}{\mathrm{s}}^{-1}$.

In Figure 7c, the fluorescence signal in LIF-2 is plotted against peak laser
intensity, demonstrating saturation of the fluorescence. The inset to the
figure shows a pump-probe measurement, from which it appears that we are only
able to pump $70\%$ of the atoms. However, the finite lifetime of the
${}^{1}D_{2}$ state of $1.71\text{\,}\mathrm{ms}$ [59] is comparable to the
flight time between the detectors. Partial repopulation of the ground state
then occurs via the ${}^{3}P_{1}$ state, which is populated with a probability
of 83% and decays to the ${}^{1}S_{0}$ state with a lifetime of
$0.331\text{\,}\mathrm{ms}$. Consistent with this, the pumping efficiency
increases for earlier arrival times at the detector, where the flight time
between pump and probe is shorter. We therefore conclude that the population
can be fully optically pumped for the purposes of measuring the beam
brightness.

Figure 7d shows a time of flight trace of the Ca atoms in LIF-2. We calculate
that $1.9\times 10^{8}$ atoms pass through the detector, corresponding to an
on-axis brightness of $9.2\times 10^{12}$ sr-1 per pulse. Using the absorption
measurement (shown in the inset of Figure 7d), we find
$7.4\text{\times}{10}^{12}\text{\,}$ per pulse, in reasonable agreement. We
conclude that the Ca atomic beam is brighter than the Al atomic beam, by about
a factor 2.5.

###  3.3 Ytterbium

Figure 8: (a): Absorption spectrum of the
$(6s6p)^{1}P_{1}\leftarrow(6s^{2})^{1}S_{0}$ transition, for all stable
isotopes of ytterbium. The inset shows a zoom-in on the 168Yb peak. The red
line is a fit to determine the Doppler width against the background absorption
of more abundant isotopes. (b): Fluorescence TOF traces of the ytterbium beam,
using light resonant with the $(6s6p)^{1}P_{1}\leftarrow(6s^{2})^{1}S_{0}$
transition for the 174Yb beam. Because the transition is optically closed, we
show the PMT count rate which is proportional to the atomic density inside the
detection volume. The inset shows an absorption trace for the 168Yb isotope
taken directly outside the cell exit.

We use the $(6s6p)^{1}P_{1}\leftarrow(6s^{2})^{1}S_{0}$ transition near
$399\text{\,}\mathrm{nm}$ to study the Yb atomic beam. The excited state
lifetime $\tau_{\mathrm{Yb}}=$5.464\text{\,}\mathrm{ns}$$
$(\Gamma/2\pi=$29.13\text{\,}\mathrm{MHz}$)$ [60]. An absorption spectrum
taken outside the cell is shown in Figure 8a. Ablation of Yb metal is highly
efficient and the absorption saturates for the most abundant isotopes. We are
able to measure the absorption of the 168Yb isotope (Figure 8a, inset), and
use this to estimate the number of atoms and to extract the Doppler width of
the beam. The transverse velocity width FWHM at the cell orifice is
$42\text{\,}\mathrm{m}\text{\,}{\mathrm{s}}^{-1}$, and
$60\text{\,}\mathrm{m}\text{\,}{\mathrm{s}}^{-1}$ when measured
$18\text{\,}\mathrm{mm}$ downstream. After taking into account the relative
natural abundances of 168Yb$:^{174}$Yb (1:245), we estimate the brightness of
the 174Yb isotope in absorption is $1.2\times 10^{13}$ sr-1 per pulse.

Figure 8b shows a time-of-flight profile obtained when probing the 174Yb
isotope with $40\text{\,}\mathrm{\SIUnitSymbolMicro W}$ of laser power, to be
compared later with the 174YbF molecule. The
$(6s6p)^{1}P_{1}\leftarrow(6s^{2})^{1}S_{0}$ transition is optically closed,
and therefore not suitable for precise fluorescence measurements of the beam
brightness. We simply estimate the brightness observed downstream by modelling
the interaction of atoms with the mean forward velocity with the intensity
profile of the probe light. Assuming a velocity of
$150\text{\,}\mathrm{m}\text{\,}{\mathrm{s}}^{-1}$, we estimate the beam
brightness as $5.0\times 10^{12}$ sr-1 per pulse, in LIF-2, in reasonable
agreement with the absorption measurements. We note that the total brightness
considering all isotopes is at least $1.6\times 10^{13}$ per steradian per
pulse, making the Yb beam the brightest of the three atomic species tested.

###  3.4 Addition of Fluorine Donor Gases

Figure 9 shows the fluorescence TOF profiles of the atomic beams before and
directly after introducing a flow of
$0.002\text{\,}\mathrm{s}\mathrm{c}\mathrm{c}\mathrm{m}$ NF3 to the cell. For
the Al atoms, there is an evident loss in signal, especially for the atoms
with late arrival times in the detector. We typically observe a reduction of
around 80% in the total number of atoms reaching the detector in LIF-2. For Ca
and Yb, the effect of the reactant gas is much less pronounced. We observe a
20% and 10% reduction in the atomic signal, respectively and obtain
qualitatively similar results when using SF6 as the reactant gas. However, the
atomic beam speeds up upon excess addition of SF6; we discuss observable
effects on the molecular beam thermalisation later. Excited state chemistry
can increase the yield of the species of interest in the source. This has been
demonstrated for the reaction of Yb and Ca with water and alcohols to form
YbOH and CaOH [61, 62, 24] and for the reaction of carbon atoms with hydrogen
molecules to form CH [63]. We found no influence on CaF production when
exciting the Ca atoms with
$40\text{\,}\mathrm{m}\mathrm{W}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}$
of $(3p^{6}4snp)^{1}P_{1}\leftarrow(3p^{6}4s^{2})^{1}S_{0}$ light
longitudinally through the cell.

Figure 9: LIF signal traces of the Al, Ca and Yb atom beams without (blue) and
with (red) NF3 flow into the buffer gas cell, demonstrating the strong effect
of a fluorine donor gas on the number of aluminium atoms in the beam.

The exact process through which the reaction between the atoms and the
reactant gas happens is largely unknown, but available experimental data
provides some useful information. The activation energies of the reactions Al
$+$ NF3 $\rightarrow$ AlF $+$ NF2 and Al $+$ SF6 $\rightarrow$ AlF $+$ SF5
have been experimentally measured as 2990 K and 4800 K respectively [64]. This
can be compared to the kinetic energy of the ablated Al atoms, which decreases
exponentially with the number of Al-He collisions [3]. Measurements of the
Doppler width of the Al atoms in the absence of the buffer gas suggested an
initial temperature of $3400\pm$1000\text{\,}\mathrm{K}$$. Even assuming an
initial Al temperature of $10^{4}$ K, the typical energy for the reaction
falls below the activation energy after 4 (SF6) and 7 (NF3) Al-He collisions.
This suggests that for a two-body gas phase reaction, the reaction must be
highly efficient to generate an appreciable number of molecules.

A number of observations suggest that the reactant gas in fact remains frozen
in the cell, and is brought into the gas phase in the ablation process.
Firstly, removing the flow of reactant gas into the cell with a tap results in
a slow drop of the molecular beam signal, over 200 shots, but never fully to
zero. However, this requires active ablation of the target; if both the
ablation light and the reactant gas flow are removed for several hundred
shots, and the ablation light is then introduced again, the signal decay
begins from its original value. We have often observed a sizeable fraction of
signal for $\sim 30$ minutes of continued operation with the reactant gas tap
completely shut.

To investigate this further, we replaced the flow of reactant gas with
$0.01\text{\,}\mathrm{s}\mathrm{c}\mathrm{c}\mathrm{m}$ of nitric oxide (NO),
and fired the ablation laser at the metal target to reproduce the usual
conditions in the cell. NO can be optically detected via the
A${}^{2}\Sigma^{+},v^{\prime}=0\leftarrow$ X${}^{2}\Pi_{1/2},v=0$ transition
near 226.2 nm, and its freezing point (109 K) is intermediate between SF6 (223
K) and NF3 (66 K). The hyperfine structure of this transition has been
resolved in a number of studies [65, 66, 67, 68, 69], and absorption
spectroscopy in a room-temperature cell was recently used to measure hyperfine
structure of high-$J$ lines of the A${}^{2}\Sigma^{+},v^{\prime}=0\leftarrow$
X${}^{2}\Pi_{3/2},v=0$ transition [70]. Here, we probe the two lowest energy
levels of the X${}^{2}\Pi_{1/2},v=0$, clearly resolving the hyperfine
structure. A level scheme for NO is shown in Figure 10a. The Franck-Condon
matrix for this transition is highly non-diagonal [65], and to a good
approximation we can assume a single photon absorption will optically pump an
NO molecule to other rovibrational levels of the X${}^{2}\Pi$ state.

With the buffer gas cell cooled to $2.5$ K, we observe a beam of buffer gas
cooled, ground-state NO molecules, which we assume are desorbed upon firing
the ablation laser (Figure 10b). The mean forward velocity of this beam is
about $120\text{\,}\mathrm{m}\text{\,}{\mathrm{s}}^{-1}$ and we estimate the
brightness as $10^{12}$ molecules per steradian per pulse, with a stability of
better than $10\%$ (standard deviation). The signal in the $J=3/2$ first
rotationally excited state is a factor 50 lower. We note that this method of
generating an intense beam of slow, rotationally pure NO molecules may be of
use in cold collision experiments [71, 72].

We also observe a bright, continuous beam of cold NO molecules without
ablation light, provided the second stage of the cryocooler is heated to above
about 60 K; below this temperature the signal completely disappeared. Spectra
of the R1/Q${}_{12}(1/2)$ lines taken with the desorbed and continuous beams
are shown in Figure 10c. Stick spectra shown pointing downwards are the
individual hyperfine lines as predicted using the ground state parameters of
[66] and the excited state parameters of [70]. The simulated line positions
and the experimental spectra are in good agreement. The fitted FWHM of the
lines is larger by about a factor 1.7 for the continuous beam, from which we
deduce a forward velocity of
$200\text{\,}\mathrm{m}\text{\,}{\mathrm{s}}^{-1}$. By comparison of the
relative fluorescence signals, we find that the continuous beam produces the
same number of molecules in the $J=1/2$ level in a
$5\text{\,}\mathrm{m}\mathrm{s}$ time interval as a single desorption pulse. A
spectrum for the R${}_{1}/$Q${}_{12}(3/2)$ line using the continuous source is
also shown in Figure 10d. The probe laser power is equal for both spectra,
showing that the $J=3/2$ level has greater population under these conditions.
The experiments with NO suggest that a similar effect occurs for the fluorine
donor gas during the production of metal fluoride molecules. The density of
the reactant gas increases around the time of ablation by vaporisation of ice
inside the cell. This may explain how reactant gas sources can be efficient
despite the high activation energy of the reaction.

Figure 10: Experiments with nitric oxide (NO) flowed into the buffer gas cell
through the fluorine donor gas inlet. (a): Scheme of the relevant energy
levels (hyperfine structure omitted). (b): Firing the ablation laser generates
a pulse of rotationally cold, slow NO molecules. (c): a spectrum of the
R1(1/2) and Q12(1/2) lines taken using the pulsed desorption method with the
buffer gas cell at 2.5 K, and a spectrum using a continuous beam with the
buffer gas cell at 70 K. (d): A spectrum of the R1(3/2) and Q12(3/2) lines
taken using the continuous source shown on the same vertical scale as (c).

##  4 Results: Molecular Beams

In this section, we determine the brightness of molecular beams of AlF, 40CaF,
24MgF and 174YbF and discuss the influence of experimental parameters on the
molecular beam. For CaF, MgF and YbF, we probe using the Q1(0) line of the
A${}^{2}\Pi_{1/2},v^{\prime}=0\leftarrow$X${}^{2}\Sigma^{+},v=0$ band. For
these molecules the vibrational branching is negligible for short interaction
times and we expect that at high laser intensities each molecule scatters on
average $\mathcal{N}=3$ photons before being optically pumped to $N=2$ in the
vibronic ground state. The total emission pattern for the Q${}_{1}(0)$ lines
is isotropic. To probe the AlF beam, we use the
A${}^{1}\Pi,v^{\prime}=0\leftarrow$X${}^{1}\Sigma^{+},v=0$ R($J$) lines, which
optically pumps molecules from rotational state $J$ to $J+2$ in the vibronic
ground state. For the R$(0)$ line, we also expect $\mathcal{N}=3$ photons per
molecule in saturated fluorescence. The emission pattern has been measured to
be slightly anisotropic by $\sim 20\%$, so we use light which is linearly
polarised parallel to the detector direction. In this configuration, the
relative number of photons scattered on P($J$) and R($J$) lines has been
experimentally found to be in agreement with the Hönl-London factors [46].

###  4.1 Comparison of Molecular Beams

The left panels of Figure 11 show the absorption spectra recorded directly
after the buffer gas cell orifice for all four molecular species. The peak
absorption of the AlF beam, presented in Figure 11a, is an order of magnitude
higher than for the other monofluoride species. The absorption measured
$20\text{\,}\mathrm{mm}$ downstream is shown magnified in Figure 11a. This
measurement reveals a broadening of the transverse velocity spread and is
comparable to the atomic beams. We extract the transverse velocity widths by
fitting the absorption spectra to Doppler-broadened line shapes, and use these
to predict the brightness of each molecular beam.

The right panels in Figure 11 show saturation of the fluorescence. The insets
show the results of pump-probe measurements for AlF, CaF, and MgF
demonstrating that the molecules are indeed optically pumped to $N=2$. For
AlF, the large transition linewidth and small hyperfine structure in the $N=0$
ground state permits efficient saturation of the fluorescence at
$I/I_{\textrm{sat}}<1$ and we observe a pumping efficiency of 97%. For CaF,
MgF and YbF a relatively high laser intensity of $I/I_{\textrm{sat}}>40$ is
required to power-broaden the transition enough to cover the ground state
spin-rotation and hyperfine structure. We verify this by fluorescence spectra
at high power and pump-probe measurements. In the case of YbF, the background
due to rotational lines of other molecular isotopologues leads to an increase
in the fluorescence above $I/I_{\textrm{sat}}=100$ and we assume our
conversion of fluorescence signal to molecule number is uncertain to within a
factor two.

Figure 11: Left column: absorption spectra recorded directly outside the cell
orifice. The solid red curves are fits based on the known energy structure of
the molecules and using a Gaussian lineshape. The enlarged spectrum shown for
AlF is measured $20\text{\,}\mathrm{mm}$ downstream. Right column: saturation
curves on the rotationally open transitions. For AlF, CaF and MgF, the insets
show the fluorescence signal without (blue) and with (red) optical pumping
applied in LIF-1, demonstrating that the molecules are indeed pumped away from
the addressed transition. In the case of YbF, high rotational lines from other
isotopologues prevent saturation.

Figure 12a shows a comparison of the maximum fluorescence signals obtained —
under identical experimental conditions — for all four molecules. The MgF, CaF
and YbF signals are magnified by a factor 5. From these signals and the
absorption measurements shown in Figure 12b, we calculated the respective
brightness in absorption and fluorescence. In Table 1, we summarise our
estimates of the brightness of each atomic and molecular beam source. For the
molecules, the given values correspond to the number of molecules in the
ground rotational state. In both absorption and fluorescence, AlF is the
brightest molecular species by about a factor 10, while the brightnesses of
the atomic beams are similar to within a factor two. This shows that the
source output of the ${}^{2}\Sigma^{+}$ molecules is likely to be limited by
the production of reaction by-products such as XF2 [73], for
$\textrm{X}=\textrm{Mg}$, Ca and Yb.

For AlF, we also recorded the relative rotational state populations by
saturated fluorescence of successive R($J$) lines up to $J=3$. The resulting
state distribution is presented in Figure 13a. It is poorly described by a
thermal Boltzmann distribution, we show expected distributions for $T=1.15$ K
and $2.5$ K as solid lines in the figure. The combined beam brightness for
$0\leq J\leq 3$ is $3\times 10^{12}$ $\text{\,}{\mathrm{sr}}^{-1}$ per pulse,
and consistent with the atomic aluminium beam measurement. This supports the
idea that NF3 reacts highly efficiently with aluminium atoms to produce AlF.
Assuming a similar rotational distribution for CaF, we estimate a beam
brightness which is $3\%$ of the atomic Ca beam. The helium flow has a
significant effect on the rotational thermalisation in the beam, as
illustrated in Figure 13b and c. The $J=0$ population is maximised at a He
flow rate of about $1\text{\,}\mathrm{s}\mathrm{c}\mathrm{c}\mathrm{m}$, but
it appears population is redistributed to higher rotational states as the flow
rate increases.

New simulation approaches for the in-cell dynamics will improve our
understanding of the various influences on the velocity and internal state
distributions of buffer gas molecular beams [74, 75, 76, 77, 78]. It has
already been shown that the extraction efficiency can be enhanced for high
buffer gas flow rates by choosing a specific cell geometry and by shaping the
exit aperture [79, 80].

The order of magnitude difference in molecule yield between AlF and the other
monofluorides can be explained by the electronic structures of the atoms and
molecules. Calcium and magnesium are group-II metals with a fully occupied $s$
orbital, ytterbium is a lanthanoid with fully occupied $f$ and $s$ orbitals,
but aluminium is a group-III metal with an unpaired $p$ electron, making it a
reactive radical. The gas-phase aluminium atoms react very strongly and
efficiently with the fluorine donor gas, whereas for the other metal species,
only a small percentage of the atoms reacts, as demonstrated in Figure 9.
While all studied monofluorides are stable molecules in the gas phase, only
AlF possesses no unpaired electrons, making it much less reactive than the
radicals CaF, MgF and YbF. The latter three are prone to the formation of
difluorides. Theoretical calculations for CaF predict that a considerable
amount of CaF2, comparable to or more than the amount of CaF, is formed in the
reaction of ablated calcium and a fluorine donor gas, while the difluoride
production is suppressed for Al [73].

Figure 12: (a): Comparison of the molecule count rates in the ground rotational state for all species, obtained in saturated fluorescence, as a function of arrival time in the detector. We plot the count rate as the number of molecules entering the detector, limited by the $2\times 2$ mm2 square aperture. (b): Comparison of the optical depth of the molecular beams, recorded at the buffer gas cell orifice. In both cases, the signal for MgF, CaF and YbF is magnified by a factor five. Table 1: Properties of the atomic and molecular beams, as determined from fluorescence and absorption experiments. For the molecular species, we quote the brightness as observed in the ground rotational state. The transverse velocities $v_{t}$ are derived from the absorption spectra taken directly outside the cell exit aperture; where possible we state the transverse spread downstream of the cell in brackets. The combined uncertainties of the detection efficiencies lead to error bars for the LIF brightnesses of around 30%. In the case of Yb and YbF, the given values are expected to be accurate within a factor 2 because we cannot use open transitions saturated by optical pumping. Species |  $v_{t}$($\text{\,}\mathrm{m}\text{\,}{\mathrm{s}}^{-1}$) |  $\mathcal{B}_{\mathrm{f}}$ (sr-1 per pulse) |  $\mathcal{B}_{\mathrm{abs}}$ (sr-1 per pulse)
---|---|---|---
Al |  90 (150) |  $3.0\text{\times}{10}^{12}\text{\,}$ |  $4.1\text{\times}{10}^{12}\text{\,}$
40Ca |  75 (120) |  $9.2\text{\times}{10}^{12}\text{\,}$ |  $7.4\text{\times}{10}^{12}\text{\,}$
174Yb |  40 (60) |  $5.0\text{\times}{10}^{12}\text{\,}$ |  $1.2\text{\times}{10}^{13}\text{\,}$
AlF |  74 (160) |  $1.6\text{\times}{10}^{12}\text{\,}$ |  $2.1\text{\times}{10}^{12}\text{\,}$
40CaF |  53 (125) |  $1.4\text{\times}{10}^{11}\text{\,}$ |  $1.1\text{\times}{10}^{11}\text{\,}$
24MgF |  112 |  $1.1\text{\times}{10}^{11}\text{\,}$ |  $1.1\text{\times}{10}^{11}\text{\,}$
174YbF |  50 |  $0.7\text{\times}{10}^{11}\text{\,}$ |  $2.1\text{\times}{10}^{11}\text{\,}$
Figure 13: (a): Distribution of the AlF population over the four lowest
rotational levels in the vibrational ground state of the X${}^{1}\Sigma^{+}$
state. The solid lines show Boltzmann distributions at $1.15$ K and $2.5$ K,
respectively. (b): Influence of the helium buffer gas flow rate
$f_{\mathrm{He}}$ on the fluorescence signal in LIF-2, detected on the R(0)
line (blue) and the R(1) line (red). (c): Q-branch scans at He buffer gas
flows of $1\text{\,}\mathrm{s}\mathrm{c}\mathrm{c}\mathrm{m}$ and
$8\text{\,}\mathrm{s}\mathrm{c}\mathrm{c}\mathrm{m}$.

###  4.2 Velocity Distribution of the Molecular Beam

#### Pump-Probe Method

We determined the forward velocity distributions of the Al and AlF beams,
using the pump-probe method described in [46]. Briefly, applying optical
pumping light in LIF-1 removes the signal in LIF-2; a short
($\sim$10\text{\,}\mathrm{\SIUnitSymbolMicro s}$$) removal of the pump light
results in an appearance of signal in LIF-2, in such a way that time of
arrival in LIF-2 correlates with velocity. Repeatedly switching off the pump
light at appropriate intervals as the molecules transit through LIF-1 then
allows estimating the forward velocity distribution, $f(v)$, using a single
molecular pulse with a high signal to noise ratio. We show the results of
these experiments in Figure 14 for Al and AlF, where the velocity
distributions for AlF are shown for $J=0-3$, and normalised such that the
integral $\int f(v)dv=1$ for each $J$. The finite transit time through the
laser beams corresponds to a velocity uncertainty of below $5\%$. Overall the
velocity of the molecular and atomic beams are similar, and in the case of
AlF, the ground rotational state contains the slowest molecules.

Figure 14: Velocity distributions, determined using a pump-probe method, of
(a) the Al atomic beam and (b) the AlF molecular beams, for the four lowest
rotational states in the X${}^{1}\Sigma^{+}$ , $v=0$ ground electronic state.
(c): Phase space distribution of the AlF molecular beam, measured by velocity
guiding $J=1$ molecules in a Stark Decelerator. The white curve shows the
relation $v_{z}=z_{0}/t_{i}$ with $z_{0}=$300\text{\,}\mathrm{m}\mathrm{m}$$.
The molecules which are well thermalised arrive with low velocities, and
delayed by about $0.7\text{\,}\mathrm{m}\mathrm{s}$ relative to this ballistic
trajectory. The inset shows the velocity distribution calculated by summing
over all $t_{i}$ for $100<v_{z}<300$.

#### Stark Decelerator

To gain additional insight into the molecular buffer gas source, we replaced
the LIF detection zones with a Stark decelerator to map out the longitudinal
phase space distribution $(z,v_{z})$ for AlF [81]. The decelerator [82]
consists of 132 electrode pairs spaced at $5.5\text{\,}\mathrm{mm}$ along the
$z$-axis, whose orientation alternates between $\pm 45^{\circ}$ to the $x$\-
and $y$-axes in the $x-y$ plane. We operate the decelerator in the S=1 guiding
mode (i.e. at a phase angle of zero), where the electrode configuration is
switched synchronously with a molecule travelling at velocity $v_{z}$, which
reaches the position of the decelerator entrance $z_{0}$ at a variable in-
coupling time $t_{i}$. In this way, molecules in a small region of phase space
($z_{0}\pm\delta_{z},v_{z}\pm\delta_{v}$) at time $t_{i}$ are guided through
the machine and arrive at a defined time in the LIF detection zone, located at
a short distance from the final electrode pair. The acceptance region
$(\delta_{z},\delta_{v})$ is determined by the longitudinal electrode spacing,
the peak electric field between the electrodes, and the number of used
electrode stages. Along the $z$-axis, the peak electric field is about
$100\text{\,}\mathrm{k}\mathrm{V}\mathrm{/}\mathrm{c}\mathrm{m}$,
corresponding to a potential depth of $0.5\text{\,}\mathrm{K}$ for AlF
molecules in weak field seeking states of the $J=1$ level. This results in
$\delta_{v}=$13\text{\,}\mathrm{m}\text{\,}{\mathrm{s}}^{-1}$$.

Figure 14c shows a false colour plot of the LIF signal as a function of the
scanned parameters $t_{i}$ and $v_{z}$, for AlF molecules in the $J=1$ state.
The white line in the figure marks the relation $v_{z}=z_{0}/t_{i}$ with
$z_{0}=$30\text{\,}\mathrm{c}\mathrm{m}$$, representing ballistic motion from
the target at the time of the ablation to the decelerator entrance. The buffer
gas cooled pulse of molecules reaches the decelerator with an average velocity
of about $170\text{\,}\mathrm{m}\text{\,}{\mathrm{s}}^{-1}$,
$0.7\text{\,}\mathrm{m}\mathrm{s}$ later than the ballistic curve due to
collisions and thus thermalisation with the buffer gas in the cell. A faster
part of the beam arrives close to the ballistic trajectory curve near
$320\text{\,}\mathrm{m}\text{\,}{\mathrm{s}}^{-1}$, which presumably results
from molecules which leave the cell shortly after the ablation without
thermalising with the helium in the cell. This tends to occur over the course
of several thousand shots necessary for such a measurement. In the inset of
the figure, the velocity distribution is computed by integrating over all in-
coupling times for $100<v<300$
$\text{\,}\mathrm{m}\text{\,}{\mathrm{s}}^{-1}$. The distribution is narrower
than measured by the pump-probe method in panel (b), with its peak velocity
about $40\text{\,}\mathrm{m}\text{\,}{\mathrm{s}}^{-1}$ slower. The two
different measurements were taken months apart, with the decelerator
measurement using a freshly cleaned cell, and this can account for such a
difference.

###  4.3 Influence of the Ablation Laser Fluence

The influence of the energy of the Nd:YAG infrared ablation laser on the
number of atoms and molecules is shown in Figure 15. The signal measured in
LIF-2 is shown as a function of the ablation pulse energy and laser fluence
using the measured spot size of $0.7\text{\,}\mathrm{mm}$. We observe that the
threshold energy for observing Al and AlF is between 10 and
$15\text{\,}\mathrm{mJ}$, and the signal from both species increases up to the
maximum available pulse energy of $40\text{\,}\mathrm{mJ}$. In particular, the
AlF yield is proportional to the ablation energy, and both would appear to
benefit from increased pulse energy. For Ca and Yb, the threshold is
$5-$10\text{\,}\mathrm{mJ}$$, and we observe an optimum in respective
molecular production at about $25\text{\,}\mathrm{mJ}$. Above this pulse
energy, the atomic signal either plateaus or weakly increases, but the number
of molecules decreases. This may be due to incomplete thermalisation with the
buffer gas, or changing reaction dynamics at higher ablation energies.

The differences in the phase explosion threshold energy for the metals used in
our study likely arise from the difference in the latent heat of vaporisation
of the atomic species, where the value for Al is roughly a factor two larger
than for Ca, Mg and Yb. The reflectivity of the bulk metal surfaces at room
temperature — values for cryogenic temperatures are not reported — is around
93% for Al, Ca, and Mg, but 70% for Yb [83]. The latter is a possible
explanation for the large number of vaporised Yb atoms.

Figure 15: Fluorescence signals of all investigated species as a function of
the ablation laser pulse energy (upper $x$-axes) and laser fluence (lower
$x$-axes). We plot the relative LIF for the atomic beams and for the
rotational ground state of the molecules.

###  4.4 Influence of the Fluorine Donor Gas

While the inert gas SF6 is commonly used in experiments with monofluorides,
theory suggests that the use of the more reactive and corrosive molecule NF3
has advantages [73]. We find that both produce a similar number of molecules
when observed downstream of the source, within the range of day-to-day
fluctuations of source operation with one fluorine donor gas. Overall, the
response of molecule yield to the gas flow rates was not reliably reproducible
from day to day, and strongly dependent on the flow rate history during a
measurement sequence. We attribute this to probable freezing effect of the
reactant gas discussed previously, and to the ‘poisoning’ effect discussed
below. However, we typically find NF3 performs well with flow rates
$0.001\text{\,}\mathrm{s}\mathrm{c}\mathrm{c}\mathrm{m}$ or below, but that
SF6 requires about ten times more flow to give comparable signal. This is
illustrated in Figure 16 for the case of MgF. Operating the source with NF3 is
more reliable and results in a slower beam for a longer period of operation.
SF6 can produce a similar beam brightness with a freshly cleaned cell, but
after one day of operation, the TOF profile shifts to higher velocities. This
effect is particularly striking for AlF, where the forward velocity increases
steadily with the number of ablation shots when SF6 is used. We do not observe
this effect when only flowing SF6 or only ablating Al for a day. We assume
that this speed-up is caused by the buildup of ablation products and sulphur-
containing inorganic compounds on the internal buffer gas cell wall, thus
hindering efficient (re-)thermalisation of the helium buffer gas. This effect
is less pronounced for the other molecules. A larger internal volume of the
cell is likely to improve this, but typically results in long temporal pulses.
We find that extracting the molecular beam through the aperture into an
extension that has the same bore diameter but no aperture reduces the forward
velocity and significantly improves the long-term stability of the beam
without affecting the beam brightness. This indeed indicates that the helium
thermalisation is affected by ablation products in the main cell. An
additional mesh on the extension reduces the mean forward velocity of AlF by
up to $70\text{\,}\mathrm{m}\text{\,}{\mathrm{s}}^{-1}$, but reduces the beam
brightness [30, 46].

Figure 16: Influence of the fluorine donor gas flow rate on the MgF Q1(0)
fluorescence signal in LIF-2.

In Figure 17, we use the compact Q-branch of AlF as a convenient means to
probe the rotational distribution reaching LIF-2, and thereby gain insight
into the thermalisation dynamics in the cell. We plot a series of Q-branch
spectra, separated by the arrival time of the molecules in the detection
region, incremented in $0.5\text{\,}\mathrm{ms}$ steps. Thus, we can see the
time dependent rotational distribution of the molecular beam. The upper blue
set of spectra show typical behaviour when using NF3 gas. The middle (black)
set of spectra are measurements taken with a clean cell and an SF6 flow rate
of $0.0006\text{\,}\mathrm{s}\mathrm{c}\mathrm{c}\mathrm{m}$, and are similar
to the NF3 data. The red spectra are measurements with a flow rate of
$0.005\text{\,}\mathrm{s}\mathrm{c}\mathrm{c}\mathrm{m}$ after one day of
source operation without cleaning afterwards. These spectra show that at a
higher flow rate and in the used cell, the molecules arrive earlier at the
detector, and are distributed over many rotational states; we indeed observe
molecules in $J=13$ arriving $1\text{\,}\mathrm{ms}$ after the ablation pulse.
The inset of the figure shows TOF fluorescence traces when saturating the R(0)
line, demonstrating how the molecular pulse shifts towards higher velocities.
We find that the onset of this reduced thermalisation occurs more rapidly as
the flow rate increases, and that good thermalisation can only be recovered by
cleaning ablation products from the buffer gas cell. The rotational spectra
for different molecule arrival times also serve to show that translational and
rotational energy of the AlF molecules are correlated - fast molecules are
rotationally hotter than slow ones.

Figure 17: Q-branch spectra of the A${}^{1}\Pi\leftarrow$X${}^{1}\Sigma^{+}$
transition in AlF selected by arrival time at the detector, in
$0.5\text{\,}\mathrm{m}\mathrm{s}$ increments. The upper blue spectrum is
recorded with a clean buffer gas cell using NF3 gas (blue, top), whereas the
lower two spectra are recorded with a clean (black, middle) and contaminated
(red, bottom) cell using SF6. The ruler inside the figure marks the different
Q($J$)-lines. The inset shows the signal obtained for the $J=0$ population
using the R($0$) line, for the two SF6 examples.

Sulphur hexafluoride and nitrogen trifluoride are not the only possible
fluorine donors. We performed preliminary experiments using tetrafluoromethane
(CF4) as fluorine donor gas that lead to similar molecule yields as for NF3
and SF6, and we therefore did not further pursue this avenue. Solid xenon
difluoride (XeF2), theoretically predicted to be a good candidate fluorine
donor molecule [73], did not prove as a viable option. At room temperature,
the compound evaporates quickly into a hazardous gas. Nevertheless, we
connected a reservoir containing XeF2 crystals to the buffer gas cell and
adjusted the flow with a needle valve. We observed efficient molecule
production, but the relatively high flow rate resulted in a very fast
molecular beam.

##  5 Conclusion and Outlook

We have presented a series of experiments comparing buffer gas cooled beams of
Al, Yb, Ca, and their monofluorides AlF, CaF, MgF and YbF formed by reaction
of laser-ablated atoms with a fluorine donor gas inside a buffer gas cell. We
find that the molecular beam brightness of AlF is about one order of magnitude
larger than for the other monofluorides, and when multiple rotational states
are considered we observe a similar beam brightness to the atomic Al beam.
This is qualitatively consistent with the near complete loss of atomic signal
upon introducing the reactant gas into the cell. In contrast, the Ca and Yb
atomic beams are relatively unaffected by the fluorine reagents, and brighter
than the Al beam. The molecular yield of CaF, MgF and YbF suggests a reaction
efficiency on the few percent level. This difference in reactivity is
explained by the radical character of aluminium and the stability of the AlF
molecule, while the other molecules are radicals that are formed from less
reactive atoms.

We demonstrated high-flux pulsed and continuous molecular beams of buffer gas
cooled NO, and performed CW UV spectroscopy of low-$J$ lines of the
A${}^{2}\Sigma^{+},v^{\prime}=0\leftarrow$ X${}^{2}\Pi_{1/2},v=0$ transition.
The low forward velocity and rotational state purity of the pulsed beam
provide a useful starting point for low-energy collision experiments with NO.
Our observations also provide insight about the vaporisation of ice in the
cell, and the pulsed desorption method may be applicable to other diatomic
molecules (e.g. H2, O2).

We conclude with some guidance for others wishing to develop cryogenic buffer
gas beam sources. First, we find it useful to measure the molecular beam
brightness with both absorption and fluorescence methods, noting that
absorption directly outside the cell leads to an overestimate. A large
discrepancy between the two measurements indicates insufficient cryopumping or
deteriorating charcoal. Second, monitoring the atomic buffer gas beams,
especially in sources using reactant gases, provides a useful reference when
studying the molecular beam properties. Finally, thermalisation inside the
cell is influenced by both the choice of reactant gas, and the condition of
the internal cell surfaces. NF3 reacts more efficiently to form fluoride
molecules as a significantly lower flow rate is required to produce the same
molecular beam brightness. The lower freezing point also allows cooling the
capillary that feeds the fluorine donor gas, which reduces the thermal heat
load on the cell. We also find that the molecular beam parameters, especially
for AlF, are more consistent when using NF3.

## Acknowledgements

We thank Sebastian Kray and Klaus-Peter Vogelgesang as well as the mechanical
workshop of the Fritz Haber Institute for expert technical assistance. We are
grateful to Jesús Pérez Ríos for helpful and stimulating discussions which
prompted this study. This project received funding from the European Research
Council (ERC) under the European Union’s Horizon 2020 Research and Innovation
Programme (CoMoFun, Grant Agreement No. 949119).

## Data Availability

The data presented can be accessed from Zenodo
(https://doi.org/10.5281/zenodo.7063976) and may be used under the Creative
Commons Attribution 4.0 International license.

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