Franck-Condon Factors and Radiative Lifetime of the A21/2 - X 2+ Transition of
Ytterbium Monoflouride, YbF
Xiujuan Zhuanga, Anh Lea, Timothy C. Steimlea, N. E. Bulleidb, I. J. Smallmanb,
R. J. Hendricksb, S. M. Skoffb, J. J. Hudsonb, B E. Sauerb, E. A. Hindsb and M. R. Tarbuttb
aDepartment of Chemistry and Biochemistry, Arizona State University, Tempe, Arizona
bCentre for Cold Matter, Blackett Laboratory, Imperial College London, Prince Consort Road,
London SW7 2AZ, UK.
The fluorescence spectrum resulting from laser excitation of the A21/2 X 2+ (0,0) band of ytterbium
monofluoride, YbF, has been recorded and analyzed to determine the Franck-Condon factors. The measured values
are compared with those predicted from Rydberg-Klein-Rees (RKR) potential energy curves. From the fluorescence
decay curve the radiative lifetime of the A21/2 state is measured to be 28±2 ns, and the corresponding transition
dipole moment is 4.39±0.16 D. The implications for laser cooling YbF are discussed.
The recent demonstration of optical cycling and laser
cooling in strontium monofluoride [1,2] suggests that other
similar molecules may also be amenable to laser cooling
. YbF is a particularly interesting candidate because it is
being used to measure the electric dipole moment of the
electron [4,5]. The use of optical forces to produce slower
and colder beams of YbF molecules would enable longer
interaction times and hence an improved sensitivity in this
measurement . For laser cooling to be feasible, the state
excited by the laser should have a short lifetime so that the
scattering rate is high, and it should decay to only a small
number of ro-vibronic levels to minimize the number of
laser frequencies required . The A21/2 X 2+ (0,0)
transition of ytterbium monofluoride, YbF, is expected to
meet these criteria. The transition is intense because, to a
first approximation, it is a promotion of an electron from a
non-bonding 6s/6p/5d -orbital to the non-bonding
6p±1/5d±1 -orbital both located on Yb+. The associated
minimal change in the intermolecular potential assures that
the emission will be predominately back to the X 2+ (v=0)
The A21/2 X 2+ (0,0) band system of YbF has been
extensively studied both at Doppler limited (1.4 GHz)
resolution  and at sub-Doppler resolution using
molecular beam techniques [8-14]. The Fourier transform
N=1 N=0, X 2+ (v=0 and 1) pure rotational microwave
spectrum of the 174YbF isotopologue has also been recorded
and analyzed . An optimized set of field-free
spectroscopic parameters for
(170Yb(3.5%), 171Yb(14.3%), 172Yb(21.9%), 173Yb(16.1%),
174Yb (31.8%) and 176Yb (12.7%)) can be found in Ref. 13.
The electric dipole moment, e(= 3.49 D), for the X 2+ (v
=0) state was determined from the analysis of the Stark
effect on the radio frequency transition between the F=1
and F=0 hyperfine levels of the N=0 rotational state .
The optical Stark effect in the Q(0) line of the A21/2
X2+ (0,0) band was analyzed to determine e(= 2.48D) for
the A21/2(v =0) state . The optical Zeeman spectra of
the A21/2 X2+(0,0) band of 171YbF, 172YbF and 174YbF
isotopologues have recently been recorded and analyzed
all six isotopologues
Here we report on the fluorescence spectrum resulting
from excitation of the R1(2)(=18109.454 cm-1) branch
feature of the A21/2 X 2+ (0,0) band. Franck-Condon
factors, fv’-v’’, are determined from the relative intensities
under the assumption that the transition moment does not
have a strong internuclear separation dependence in the
region of the equilibrium bond distances. The spectroscopic
parameters are used to predict the Franck-Condon factors
and these are compared to the experimental values. The
radiative lifetime is determined from the decay of
fluorescence following pulsed excitation of lines in the
P1+Q12 band head (=18106 cm-1).
The Franck-Condon factors were independently
determined at both Imperial College (IC) and Arizona State
University (ASU) using wavelength-resolved fluorescence
The experimental setup used at IC, shown
schematically in Figure 1, employs a pulsed supersonic
beam of YbF seeded in helium carrier gas which is cooled
to cryogenic temperatures. The new source is inspired by
recent work on the formation of YbF in a cold buffer gas
cell [16, 17]. The molecules are created by laser ablation of
a Yb/AlF3 target located inside an open-ended copper tube
mounted on the low temperature cold plate of a closed-
circuit cryocooler. A solenoid valve, thermally connected
to the cold plate, is used to create a pulse of cold helium gas
that passes through a thin tube into the region just below the
target. The timing of the laser ablation pulse is such that
YbF molecules are formed just as the gas pulse passes near
the target. Collisions between the YbF molecules and the
cold helium lead to cooling of the translational, rotational
and vibrational modes of the molecules to approximately
4 K. The molecules entrained in the gas pulse form a well-
directed beam that travels at about 300 m/s into the
detection region. Although similar speeds and temperatures
are obtained using room temperature xenon as the carrier
gas , the present source provides far higher beam
The molecules are illuminated with light from a cw
single-mode ring dye laser, tuned to the
R1(2)(=18109.454 cm-1) line of the A21/2 X 2+ (0,0)
band. The resulting fluorescence is collected by an imaging
system consisting of a spherical mirror and an aspheric lens
placed on either side of the molecular beam. The collimated
fluorescence is directed onto a plate beamsplitter which
divides the fluorescence into “reference” and “signal”
components. Each component is focused, spatially filtered
and passed through an infrared blocking filter to eliminate
1064 nm light from the ablation laser, and is then detected
with a photomultiplier tube (PMT). A 40 nm full-width
half-maximum (FWHM) band pass filter centred on 550 nm
is used to reduce ambient background light in the reference
channel. Various bandpass and longpass filters are placed
in the signal arm to study different spectral components of
the fluorescence light. Bandpass filters centred at 550 nm,
570 nm, and 580 nm, each with ±10 nm FWHM, are used to
measure the A21/2 (v’=0) X 2+ (v” =0, 1 and 2)
fluorescence intensities. A longpass filter with nominal cut-
off at 590 nm permits the measurement of any additional
light due to transitions to higher vibrational states. The
absolute transmissions of the beamsplitter, windows and
filters are all separately measured at the 0-0, 0-1 and 0-2
wavelengths by measuring the laser power they each
transmit. This, combined with the PMT's specified
wavelength-dependent response, determines the relative
sensitivity of the detection system at each wavelength.
Each filter was used multiple times in a varying order and
rotated at various angles about the normal, so as to
randomise effects due to filter placement and to average
away a small observed polarization dependence. The probe
laser was modulated on and off on alternate ablation pulses
to distinguish between the LIF and any background light.
By using the ratio of the signal in the signal arm to that in
the reference arm, the measurement is insensitive to
variations in the probe laser power and the intensity of the
The apparatus used at ASU for molecular beam
production and detection of YbF has been previously
described [14,15]. A molecular beam of YbF was generated
by ablating a solid, rotating, ytterbium rod near a
supersonically expanding mixture of 5% SF6 and 95%
argon. Excitation spectra were recorded using both a cw
single-mode dye laser ( < 1 MHz) and a pulsed dye laser
( 3 GHz) that provides 10 ns long pulses. In the high-
resolution scans absolute frequencies were determined to an
accuracy of 3 MHz by simultaneously recording the sub-
Figure 1: The apparatus used to create and detect cold YbF
pulses at Imperial College.
Doppler I2 spectrum. Between I2 lines, frequency shifts
could be measured to approximately 50 MHz by
simultaneously recording the transmission of an actively
stabilized étalon. Dispersed laser-induced fluorescence
(DLIF) spectra were obtained by recording the LIF signal
with a 2/3 meter scanning monochromator. The slits of the
monochromator were adjusted to give a spectral resolution
of 1.5 nm. The digital delay controller set the relative
timing of the laser ablation, pulse valve and gated photon
counter. The wavelength dependence of the spectrometer
sensitivity was determined by recording the emission of a
calibrated tungsten filament. The fluorescence decay curves
were recorded by replacing the single-mode ring dye laser
with a pulsed dye laser and the gated photon counting
system with a digital storage oscilloscope.
Figure 2 shows two typical traces obtained from the IC
experiment, one with the probe laser on and the other with it
off, each an average of 100 molecular pulses measured by
the reference PMT. Both traces show a small decaying
signal at early times due to light from the ablation plume
and any ablation laser light that passes through the infrared
filter. When the probe laser is on, the YbF LIF signal is
observed as an 80 s wide peak centred some 250 s after
the ablation pulse. For each trace, any constant background
light is subtracted and then the trace obtained with the probe
laser off is subtracted from the one with the probe laser on.
The resulting background-free photon rates for both the
signal and reference are integrated over the time window
between 120 s and 600 s. The ratio yields a relative LIF
signal that is independent of the molecular flux. The signals
for each filter, together with the wavelength-dependent
response of the detection system, determine the Franck-
Condon factors which are presented in Table I. The quoted
uncertainties are dominated by a 5% uncertainty in the
relative PMT efficiency at different wavelengths, and to a
lesser extent by residual variations in the measured signals
due to the polarisation dependence of the filters.
A DLIF spectrum obtained at ASU from excitation of
the 174YbF R1(2) branch feature is shown in Figure 3. The
spectrum was obtained using a 0.1 nm step size for the
scanning monochromator and averaging 40 ablation pulses
per step. Spectra recorded under the same conditions but
with the ablation laser blocked and separately with the
excitation laser blocked were subtracted to remove very
small chemiluminescence and background light from the
excitation laser. DLIF spectra resulting from single-mode
dye laser excitation of both the R1(2) branch feature and
near the P1+Q12 band head (N”4) were recorded multiple
times. The integrated areas of the spectral features were
used to determine the relative DLIF intensities from which
the fv’-v’’ of Table I were extracted. The quoted errors
represent the 1 statistical uncertainties determined from
multiple measurements. Systematic errors are estimated to
be 1%. The values for fv’-v’’ obtained at the two excitation
frequencies and in the two setups (IC and ASU) are
consistent with one another, and we take their weighted
means to obtain the final experimental values.
Figure 2: Signal from the reference PMT, with probe laser on
(solid line) and off (dashed line), averaged over 100 shots. The
initial decaying signal is light from the ablation process. The
peak at approximately 250 s is the LIF signal resulting from
excitation of the R1(2)(=18109.454 cm-1) branch feature of the
A21/2 X 2+ (0,0) transition of 174YbF.
Figure 3: The DLIF spectrum resulting from excitation of the
R1(2)(=18109.454 cm-1) branch feature of the A21/2 X 2+
(0,0) transition of 174YbF and viewed through a 2/3 m scanning
The decay curve resulting from pulsed dye laser
excitation of the P1+Q12 band head (N”4) is shown in
Figure 4. The fit to a single exponential curve, with the
10 ns pulse width of the laser excluded, gives a
characteristic decay time of 28 2 ns. The YbF molecules
spend approximately 5 s in the LIF collection zone, and
since this is far longer than the measured decay time there is
no distortion of the decay profile due to molecules exiting
the detection region.
The suite of programs developed by Prof. Robert
LeRoy (Waterloo University)  was used to predict the
Franck-Condon factors. The potential energy curves were
calculated using the first-order
(RKR1) procedure. The rotational parameters for the A21/2
and X 2+ state were taken from Ref. 14 and the vibrational
parameters from Ref. 7. The ro-vibronic wavefunctions
were numerically evaluated to predict the Franck-Condon
factors. The results are compared with experimental values
in Table I. The measured value for f0-0 is slightly larger than
we calculate, and correspondingly the measured f0-1 is
slightly smaller than calculated.
The radiative lifetime of the A(v’=0) state, , is given
10 137. 3
transition dipole moment, A-Xis in Debye (D), and the
transition wavenumbers v’’are in cm-1. From our
measured and f0-v’’ we obtain A-X = 4.39 0.16 D, where
the uncertainty is dominated by the uncertainty in the
lifetime. The lifetime and transition moment are similar to
those of CaF  and SrF .
' ' , 0' '
, where the
fluoresce to a minimal number of ro-vibronic levels so that
only a small number of laser frequencies are needed to keep
it in the cooling cycle. Let us first consider the rotational
branching. Neglecting small hyperfine splittings due to
nuclear-spin interactions, each state of A21/2 (v=0, J, p),
specified by the total angular momentum J and the parity p,
decays to three levels within each vibrational state of X 2+
(J=0, 1). The lowest two levels of A21/2 are exceptions,
because they have J=1/2 and so have only two decay routes
(J=0, +1) to each vibrational state of X.
Efficient laser cooling requires the molecule to
For the A21/2 (v=0, J=1/2) component of positive parity
the decay channels are the P1(1) and
features, which are separated only by the spin-rotation
splitting of order 10 MHz. This is easily spanned by adding
radio-frequency (rf) sidebands to the laser light. Each line is
further split into two hyperfine components due to the
fluorine nuclear spin, but these are also easily spanned using
rf sidebands. The SrF laser cooling experiment [1,2] utilized
these branch features. Unlike SrF, and most other
molecules, the equilibrium bond distance for YbF is smaller
in the A 21/2 state than in the X 2+ state. Consequently,
low-N band heads form in the P1 and PQ12 branches in YbF
and so the P1(1) and
congested part of the spectrum. This is illustrated in Figure
5 where the observed pulsed-dye laser excitation spectrum
of the A21/2 X 2+ (0,0) band of a supersonic YbF beam
is compared with the predicted spectrum. Only the OP12
branch is free from overlap. The high density of
overlapping lines does not pose any serious problem for
laser cooling, but does makes it a little more difficult to
locate the correct transitions.
PQ12(1) lines lie in a severely
For the component of A21/2 (v=0, J=1/2) with negative
parity the decay channels are the Q1(0) and OP12(2) branch
features. These features lie in less congested parts of the
spectrum, particularly the OP12(2) line where there is no
overlap with any other lines. However, these two branch
features are separated by 6B (43 GHz) which is a
Figure 4: The fluorescence decay curve resulting from
excitation of the P1+Q12 band head (=18106 cm-1).
Table I. Measured and predicted Franck-Condon factors, fv’-v’’, for the A21/2(v’=0) X 2+(v”) transition of YbF.
fv’-v’’ ICa ASUb
a Imperial College with R(2) excitation. b Arizona State University with R(2) excitation. c Arizona State University with P1+Q12 band
head excitation. d Weighted mean of measurements. e R(2) transition predicted using an RKR1 potential with the parameters (cm-1):
Be” = 0.241294, Be’=0.247629, De” = 2.38810-7, De’=1.99910-7, e”= 506.674, exe”= 2.245,e’=537.0, exe’=3.0.
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considerably less convenient frequency separation to span.
With the use of three lasers it is possible to drive transitions
from v’’=0, 1 and 2 so that molecules remain in the cooling
cycle until they decay from v’=0 to v’’>2. Our
measurements place an upper bound of 510-4 on the
probability of this unwanted decay, indicating that a YbF
molecule can scatter at least 2000 photons on average
before it decouples from the cooling light. This will allow
substantial cooling of the translational motion of a
supersonic or buffer-gas-cooled beam. Laser deceleration
of the beam requires more photons to be scattered and may
not be feasible, but the laser-cooled beam can be
decelerated using conservative forces, e.g using a travelling-
trap Stark decelerator [20, 21]. Together, Stark deceleration
and laser cooling of a buffer-gas-cooled beam of YbF will
allow ultra-cold slow-moving YbF pulses to be produced,
with enormous potential for improving the measurement of
the electron’s electric dipole moment.
The research at Arizona State University has been
supported by the National Science Foundation (Grant
No.0646473). The research at Imperial College has been
supported by the EPSRC, the STFC and the Royal Society.
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Figure 5: The observed(bottom) and predicted (top) broad-band
LIF spectrum of the A21/2 X 2+ (0,0) band system of YbF. The
observed spectrum was recorded using pulsed dye laser excitation
with a 0.05 cm-1 spectral resolution. The predicted spectrum was
calculated using the spectroscopic parameters of Ref.13, a line
width of 20 MHz and a rotational temperature of 20 K.