INSTITUTE OF PHYSICS PUBLISHING
JOURNAL OF PHYSICS B: ATOMIC, MOLECULAR AND OPTICAL PHYSICS
J. Phys. B: At. Mol. Opt. Phys. 35 (2002) 2693–2701
PII: S0953-4075(02)33786-6
Hyperfine structure and isotope shift of transitions in
Yb I using UV and deep-UV cw laser light and the
angular distribution of fluorescence radiation
R Zinkstok, E J van Duijn, S Witte and W Hogervorst
Laser Centre Vrije Universiteit, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
E-mail: rzinkstk@nat.vu.nl
Received 7 February 2002, in final form 2 May 2002
Published 6 June 2002
Online at stacks.iop.org/JPhysB/35/2693
Abstract
Using the third harmonic of a cw titanium:sapphire laser, the hyperfine
structure (HFS) and isotope shift (IS) of three deep-UV transitions of neutral Yb
have been measured for the first time. By exploiting the angular distribution
of fluorescence radiation, accurate and complete results are obtained for the
HFS and IS of the 398.8 nm transition of Yb. From the measured data, normal
and specific mass shift as well as field shift values for all transitions considered
have been derived.
1. Introduction
Ytterbium (Yb) is a lanthanide with atomic number 70, and has closed 4f and 6s subshells in
the 4f14 6s2 1 S0 ground state. The natural isotopic composition shows five even isotopes, 168 Yb
(0.14%), 170 Yb (3.03%), 172 Yb (21.82%), 174 Yb (31.84%) and 176 Yb (12.73%), and two odd
isotopes, 171 Yb (14.31%) and 173 Yb (16.13%) with nuclear spin I = 1/2 and 5/2, respectively. Yb has been studied extensively in various contexts. Apart from a general analysis of
the emission spectrum [1] and of highly excited levels [2], data have been collected on Rydberg
and auto-ionizing states of Yb and Yb+ [3, 4], and on Stark shifts [5, 6]. Furthermore, Yb was
studied in the context of laser isotope separation [7–10] and magneto-optical trapping [11, 12]
experiments. Finally, much research has been done on the hyperfine structure (HFS) and isotope shift (IS) of even-parity Yb levels, mostly in the 40 000–50 000 cm−1 region using two-step
excitation processes (e.g. [13–15]). The odd-parity energy levels around 38 000 cm−1 , however, have never been investigated in detail, probably due to the high photon energy needed for
direct excitation. In this paper, we present data on the HFS and IS in three deep-UV transitions,
which are—to our knowledge—studied for the first time. The measurements are performed
using the third harmonic of a cw titanium:sapphire (Ti:S) laser, with a linewidth of ≈3 MHz.
In addition to a study of these lines, we performed measurements on one of the most
extensively studied lines of Yb, i.e. the 398.8 nm first resonance line, corresponding to the
0953-4075/02/122693+09$30.00
© 2002 IOP Publishing Ltd
Printed in the UK
2693
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R Zinkstok et al
transition from the 4f14 6s2 1 S0 ground state to the 4f14 6s6p 1 P1 state. This transition is used in
laser cooling experiments [11,12]. Due to several overlapping peaks in the spectrum, resolving
the HFS and IS in this transition has proven to be a challenge. Increasingly complex methods
have been applied to this issue: interferometric experiments [16], level crossing and anti-level
crossing spectroscopy [17–19], high-resolution laser spectroscopy [20, 21], laser sideband
techniques combined with photon burst spectroscopy [22] and cooled-atom spectroscopy [23],
giving increasingly accurate results. In this paper, we present a simple alternative to obtain
accurate results. Using the second harmonic of a Ti:S laser with a linewidth of ≈2 MHz
and exploiting the angular distribution of the fluorescence radiation emitted, we have in an
elegant way determined the HFS and IS of this transition with an accuracy exceeding that of
all previous experiments.
2. Angular distribution of fluorescence radiation
It is well known that the dipole radiation emitted by an atom can be non-isotropic. The angular
distribution F (θ, φ) depends on the value of m of the transition considered: for m = 0,
F (θ, φ) = sin2 (θ ), while for m = ±1, F (θ, φ) = 1 + cos2 (θ ) (see e.g. [24]). When more
magnetic sublevels are involved, the contribution of each mi → mf transition is calculated by
multiplying the appropriate angular distribution with the relevant (angular) part of the dipole
matrix element of that transition. The total angular distribution of the fluorescence radiation
is then obtained by summing over all contributions, taking into account the polarization (if
present) of the incident light.
These distributions of fluorescence radiation have been calculated for all components of
the 398.8 nm transition in Yb assuming excitation with linearly polarized light. Since this is
a J = 0 → 1 transition, it follows that the even isotopes (which have I = 0) can only decay
through m = 0 → 0, so these isotopes show the same anisotropic distribution. The distribution
for the odd isotopes, which have a non-zero nuclear spin, is much more isotropic because more
decay options are available, including both m = 0 and ±1. The distributions for all isotopes
are shown in figure 1. In the figure, the vertical z-axis is parallel to the polarization vector of
the incident light. Clearly, the spectrum that will be recorded depends highly on the position
of the detector. When the detector observes along the horizontal x-axis, the even isotopes
will dominate the signal, while they will be invisible when the detector is placed along the
vertical z-axis. Alternatively, the polarization of the incident light can be rotated over 90◦ , as
done in the present work. The two different spectra can be subtracted, resulting in a difference
spectrum featuring only the odd isotopes. This provides an easy and reliable means of fully
resolving the HFS in the 398.8 nm transition of Yb. It is to be noted that this discussion applies
only to closed atomic transitions, of which the 398.8 nm transition is an example. When other
decay channels are available, more magnetic transitions become possible, which may give
rise to a more isotropic angular distribution of the fluorescence radiation. Therefore, it is not
expected that this method is applicable to the other transitions presented in this paper.
3. Experimental method and set-up
3.1. Laser system
A schematic of the laser system is given in figure 2. The infra-red (IR) light from a cw Ti:S
laser (Coherent 899-21) pumped by a 10 W Spectra Physics Millennia X, is divided into two
beams by a 50% beamsplitter (BS). The first IR beam is frequency doubled in an external
enhancement cavity (EEC) using a LBO nonlinear crystal, Brewster cut for the fundamental
wavelength (θ = 90◦ and φ = 33.7◦ ). With 0.8 W of fundamental light, about 320 mW of
second harmonic (UV) light is produced, reaching 40% of useful conversion.
HFS and IS of several transitions in Yb I
2695
a
b
1
0.3
-1
-1
1
1
- 0.3
-1
c
d
0.4
0.4
-1
-1
1
1
- 0.4
- 0.4
Figure 1. Calculated angular distributions of fluorescence radiation in the 4f14 6s2 1 S0 –4f14 6s6p 1 P1
transition for (a) all even isotopes, (b) 171 YbF =1/2→1/2 , 173 YbF =5/2→3/2 and 173 YbF =5/2→5/2 ,
(c) 171 YbF =1/2→3/2 , (d) 173 YbF =5/2→7/2 . The vertical z-axis is parallel to the polarization vector
of the incident light.
PD
PD
Servo
PB
M
λ/4
M4
L 25 cm
BBO M5
HR deep-UV
HRIR
HRUV
M8
M7
M
ML 40 cm
HRUV
HRIR
HRIR
LBO
M1
M2
BS
λ/2 L 25 cm CL 15 cm CL 4 cm
HRIR
PB
M
HRUV
M4
M3
λ/2
ML 40 cm
HRUV
λ/4
M
PMT
PD
Servo
HR deep-UV
AB
PD
Vacuum chambers
BS
Ti:S laser
HRIR
Millennia X
Etalon
M
D
oven
Computer
Figure 2. Schematic of the experimental set-up. The beam of a cw Ti:S laser pumped by a 10 W
Millennia X is split into two beams by a 50% BS. One of these beams is frequency doubled inside
an EEC consisting of mirrors M1–M4 using an LBO crystal, while the other is enhanced in a second
EEC (mirrors M5–M8). The beam reflected off M3 is led into a Hänsch–Couillaud locking device
(M mirror, PB polarizing BS, PD photodiode). The second harmonic (UV) beam is imaged through
several lenses for beam-shaping (L lens, CL cylindrical lens) and coupled into the second EEC,
where the third harmonic is generated by sum-frequency mixing inside a BBO crystal. For both
EECs, mode matching is performed by a thin lens (ML). The resulting deep-UV light is collimated
by a lens and passes through the vacuum system, where it intersects an AB of Yb. Directly above
the point where the beams intersect, a PMT is placed. A small fraction of the fundamental Ti:S
beam is led through an etalon for frequency calibration. The etalon signal is measured with a
detector (D) and fed to a computer, together with the PMT signal.
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R Zinkstok et al
The second IR beam is also enhanced in an EEC, which contains a BBO crystal. The UV
beam generated in the first EEC is led single pass through this second enhancement cavity,
where it overlaps with the IR beam. Inside the BBO crystal, sum frequency mixing is then
realized, producing about 5 mW of third harmonic (deep-UV) light. Type I phase matching is
realized by rotating the polarization of the UV beam over 90◦ with a λ/2 plate. To keep the
cavities in resonance with the laser light, the Hänsch–Couillaud locking technique [25] is used.
In principle, the wavelength range of a Ti:S laser is about 690–1100 nm. In our case, phase
matching and mirror coating restrictions on the Ti:S laser and EECs yield in practice tunability
in the ranges 690–835, 370–415 and 255–278 nm for the fundamental, second harmonic and
third harmonic, respectively. Since the linewidth of the Ti:S laser is about 1 MHz, bandwidths
of the second and third harmonics are about 2 and 3 MHz respectively. The laser is continuously
tunable over about 10 GHz in the deep-UV. Frequency scans are calibrated by passing a small
fraction of the fundamental beam through an etalon with a free spectral range of 150±0.3 MHz,
while another part of the fundamental beam is led to an ATOS LM-007 lambda-meter as an
absolute wavelength reference.
3.2. Vacuum system and atomic beam
The atomic beam (AB) is produced by heating a sample of Yb inside a small tantalum oven.
This oven is heated to a temperature of about 950 K by electron bombardment using a nearby
tungsten wire heated by a large current (≈10 A at ≈17 V). At this temperature the vapour
pressure of Yb is high enough to produce an AB of sufficient intensity, emanating from the
oven through a small hole. About 30 cm downstream, the atoms pass through a diaphragm
3 mm in diameter, after which a highly collimated beam remains. This ensures that the Doppler
broadening of the measured spectral lines is limited to about 10 MHz for the second harmonic
measurements, and to about 16 MHz for the third harmonic.
The vacuum system consists of two compartments connected by a valve (figure 2). The first
compartment contains the oven where the AB is produced, while in the second compartment
the LIF measurements are performed. The laser beam passes through this second compartment,
where it intersects the AB under an angle of 90◦ to minimize Doppler broadening and shift.
Directly above the point where the beams intersect a photomultiplier tube (PMT) is mounted.
The fluorescence spot is imaged on the PMT with a lens system. In order to minimize detection
of stray light and radiation from the oven, spatial filtering in combination with filters for the
wavelength to be detected are employed. Also, the windows of the vacuum compartment are
anti-reflection coated for the laser wavelength to minimize stray reflections. The PMT signal
is then fed through a discriminator to a counter, which is connected to a computer for analysis.
By monitoring both etalon output and photomultiplier signal while scanning the laser, the
frequency difference between adjacent spectral components can be determined with a total
error smaller than 0.9 MHz, while the absolute wavelength can be measured by the ATOS
lambda-meter with a systematic error smaller than 100 MHz.
4. Results and discussion
4.1. Deep-UV transitions
Using the set-up described in the previous section, the spectra of several deep-UV transitions
in Yb from the 4f14 6s2 1 S0 ground state have been measured. The transitions involved
are to the 4f13 5d6s2 1 P1 state at 37 414.59 cm−1 (λ = 267.28 nm), the 4f14 1 S 6s7p 3 P1
state at 38 174.17 cm−1 (λ = 261.96 nm) and the 4f13 5d6s2 3 D1 state at 38 422.36 cm−1
(λ = 260.27 nm). Spectra of these transitions are shown in figure 3; they all show a good
signal to noise ratio, on the order of 100–1000.
HFS and IS of several transitions in Yb I
2697
174
6000
D1
171 − 1/2
173 − 7/2
176
171 − 3/2
173 − 3/2
Counts
4000
2000
3
172
(a)
0
0
1000
500
1500
174
4000
(b)
3
171 − 3/2
173 − 3/2
170
171 − 1/2
173 − 7/2
2000
173 − 5/2
Counts
172
P1
0
2000
4000
6000
174
0
1
(c)
P1
173 − 3/2
176
171 − 3/2
173 − 5/2
173 − 7/2
x100
170
5000
168
171 − 1/2
Counts
172
10000
8000
0
0
2000
4000
6000
Frequency [MHz]
Figure 3. Measured spectra of deep-UV transitions in Yb. Peaks are identified by mass number
and F -value of the upper state. Shown are spectra of the transitions from the ground state to (a) the
4f13 5d6s2 3 D1 state at 38 422.36 cm−1 , (b) the 4f14 1 S 6s7p 3 P1 state at 38 174.17 cm−1 and (c) the
4f13 5d6s2 1 P1 state at 37 414.59 cm−1 .
All isotopes can be identified in these spectra, except for 168 Yb, which is visible only in
the spectrum of the 5d6s2 1 P1 state, and for 170 Yb, which is buried under the 172 Yb peak in the
6s2 3 D1 state spectrum. The ISs are shown in table 1. The HFS of these transitions is solved
completely: table 2 shows the A and B constants deduced from the measurements (it is to be
noted that isotopes with I 1 do not have a B constant). Also shown are the ratios A173 /A171 .
These values are nearly equal for all transitions, in accordance with expectations. They agree
well with values for this ratio given by other authors, e.g. [13, 15].
4.2. The 398.8 nm line
We used a polarizing beam splitter and a half-wave plate to switch between horizontal and
vertical linearly polarized light while the PMT remained fixed in place, observing along the
vertical axis (thus defining ‘vertical’ and ‘horizontal’ directions). In this way, pairs of spectra
of the 398.8 nm line have been measured, each pair consisting of a horizontal polarization
spectrum and a vertical polarization spectrum. Because this transition is exceptionally strong,
the PMT current could be detected directly, resulting in a signal-to-noise ratio exceeding 1000.
168
171 − 1/2
170
168
171 − 1/2
3000
174
171 − 3/2
173 − 3/2
173 − 5/2
(b)
0.5
2000
173 − 7/2
1000
x100
176
0
173 − 5/2
1.0
(c)
2000
0.5
3000
171 − 1/2
1000
171 − 3/2
0
173 − 3/2
173 − 7/2
Intensity (a.u.)
x100
0
0
Intensity (a.u.)
171 − 3/2
173 − 5/2
176
(a)
0.5
173 − 7/2
174
1.0
172
R Zinkstok et al
Intensity (a.u.)
2698
0
0
1000
2000
Frequency (MHz)
Figure 4. Measured spectra of the 4f14 6s2 1 S0 –4f14 6s6p 1 P1 transition in Yb. Peaks are identified
as in figure 3. (a) Using horizontal polarization, (b) using vertical polarization and (c) the difference
spectrum showing only the odd isotopes.
Table 1. Measured ISs.
IS (MHz)
Final state
4f13 5d6s2 1 P
Energy level
4f14 6s7p 3 P1
4f13 5d6s2 3 D1
37 414.59
38 174.17
38 422.36
4f14 6s6p 1 P1
4f14 6s6p 3 P1 a
25 068.222
17 992.007
a
1
(cm−1 )
170–168
908(2)
172–170
842.6(0.6)
80.5(0.9)
−696.0(1.8) −659(4)
−1368.6(5) −1286.5(5)
174–172
176–174
601.2(1.6) 567(3)
32.3(1.8)
27.5(0.9)
−35.5(1.3) −36.2(1.6)
−529(2)
−1000.3(5)
−507.2(1.5)
−954.8(5)
Data taken from [26].
Examples of both spectra are shown in figure 4. It is to be noted that these spectra are in
fair agreement with the angular distribution plots of figure 1. However, there are still even
isotopes visible in the vertical polarization spectra, which is due to the finite opening angle of
the detector. Therefore, the spectra are subtracted pairwise after normalization, resulting in a
difference spectrum showing only the odd isotopes, also shown in figure 4. In this difference
spectrum, the HFS is fully resolved. Accurate values for the A and B constants now can
be derived directly. These values are included in table 2. From the horizontal polarization
spectrum, the IS can be deduced for the even isotopes, while the IS of the odd isotopes is
deduced from the difference spectra. All IS data are collected in table 1.
The IS data presented here for the 398.8 nm transition are in good agreement with those
measured in previous work [16, 20, 22, 23], while the present values have a higher accuracy.
For comparison, all values are displayed together in table 3. Our values for the HFS A and
B constants also agree well with those reported by others: for comparison, these are given in
table 4. Exceptions are those reported in [17], where the sign is not given for A171 , and in [22],
HFS and IS of several transitions in Yb I
2699
Table 2. HFS A and B constants of the excited states in MHz.
State
A171
4f13 5d6s2 1 P1
4f14 6s7p 3 P1
4f13 5d6s2 3 D1
2093(4)
4143(4)
−588(2)
4f14 6s6p 1 P1
−210.2(0.8)
A173
B173
A173 /A171
−577.6(0.5) 233(2)
−0.2760(5)
−1147.1(1.4) −12.1(1.1) −0.2769(4)
161.9(1.5) −177(6)
−0.275(3)
57.7(0.9)
602.1(1.1) −0.2746(8)
Table 3. Comparison of IS data of the 398.8 nm transition of Yb.
IS (MHz)
170–168
172–170
Present work −696.0(1.8) −659(4)
[16]
[20]
[22]
[23]
—
—
−698(2)
—
−627(30)
−665(10)
—
−648(8)
174–172
176–174
−529(2)
−507.2(1.5)
−531(30)
−530(4)
—
−528(3)
−470(27)
−509(4)
—
−507(3)
Table 4. Comparison of HFS data of the 398.8 nm transition of Yb.
A171
A173
B173
Present work −210.2(0.8)
57.7(0.9)
602.1(1.1)
[17]
[18]
[20]
[19]
[21]
[22]
[23]
59.7(1.3)
58.5(0.8)
603(17)
590(13)
605(20)
588(2)
216(4)
−213(3)
−211(1)
−213(10)
−201(3)
−212(3)
58.1(0.3)
where a fairly low A-value for 171 Yb is given, while the value for B173 reported by [19] seems to
be too low when compared with the others. The overall accuracy of our measurements is higher
than that obtained in all other experiments, while we applied a simple and elegant method.
4.3. Isotope shift analysis
The IS in a transition between two isotopes with mass numbers A and A can be decomposed into
several contributions. These are the normal mass shift (NMS), the specific mass shift (SMS)
and the field shift (FS):
A −A
δνiIS = δνiFS +
(MiNMS + MiSMS ).
(1)
AA
The M NMS and M SMS are constants for a given transition. The NMS can easily be calculated
using
νi
MiNMS =
(2)
1822.8
where νi is the transition frequency. Consequently, the NMS can be eliminated from
equation (1), yielding the reduced isotope shift (RIS). When the RIS of a transition is modified
by multiplying it with AA /(A − A), and then plotted against the modified IS of another
R Zinkstok et al
Modified IS of other transitions [MHz]
2700
1000
500
0
-500
-1400
-1600
-1200
14
-1000
3
Modified IS of the 4f 6s 6p P1 transition [MHz]
Figure 5. King lines of the measured transitions from the ground state to:
, 4f14 6s7p 3 P1 ; ♦, 4f13 5d6s2 3 D1 and , 4f14 6s6p 1 P1 .
◦, 4f13 5d6s2 1 P1 ;
Table 5. Contributions to the IS between 176 Yb and 174 Yb in the measured transitions in MHz.
Upper state
4f13 5d6s2 1 P
δνNMS
1
4f14 6s7p 3 P1
4f13 5d6s2 3 D1
4f14 6s6p 1 P1
40.2
41.0
41.3
26.9
δνSMS
δνFS
−307(13) 854(13)
−181(10) 168(10)
−184(10) 107(10)
−103(10) −431(10)
transition, a straight line results (King plot). The slope and intercept of such a line relate the
FS and SMS of the transitions involved (see [27]).
Using the measured IS data a King plot analysis has been made. As reference transition
we took the 555.6 nm 6s2 1 S0 → 6s6p 3 P1 transition in Yb, for which [26] gives very accurate
data, shown in table 1. Since this is known to be a pure s2 →sp transition [14,27], we can adopt
the estimate from [28], δν SMS = (0 ± 0.5)δν NMS , and assume the SMS of this transition to be
about zero (the NMS between 174 Yb and 176 Yb is calculated to be 20 MHz using equation (2)).
The King lines for the four measured transitions are shown in figure 5. From these King lines,
the values for the SMS and the FS have been derived, using the values for the known reference
transition at 555.6 nm. These are shown in table 5 for the 174–176 isotope pair.
The transition to the 4f13 5d6s2 1 P1 state shows a large negative SMS. This is due to the
change in the number of 4f electrons; the momentum of the 4f electrons is strongly coupled to
that of the inner-shell d electrons (see e.g. [27]). The positive FS is believed to be a screening
effect. The 5d electron in the excited state does not screen the two s electrons as well as the
4f electron in the ground state. This leads to a higher electron density at the nucleus for the
excited state, which results in a positive FS (see e.g. [28]).
The transition to the 4f14 6s6p 1 P1 state at 398.8 nm shows a negative FS, caused by the
decrease of electron density in the s → p transition. The negative SMS in this transition
HFS and IS of several transitions in Yb I
2701
is probably due to mixing with a 4f13 5d6s2 state, which exhibits a negative SMS as in the
4f13 5d6s2 1 P1 state [27].
The 4f14 6s7p 3 P1 and 4f13 5d6s2 3 D1 states are mutually perturbing according to [1], which
is confirmed by their very similar King lines. The negative SMS in the transitions to these states
can be attributed to the change in the number of 4f electrons in the 4f14 6s2 1 S0 → 4f13 5d6s2 3 D1
transition, as before. The positive FS is unexpected for an s2 →sp transition, but it can be due
to a screening effect in the 4f14 6s2 1 S0 → 4f13 5d6s2 3 D1 transition, similar to the screening
effect discussed above. The SMS and FS values for these two transitions seem to indicate that
the 4f13 5d6s2 configuration dominates the IS behaviour of this perturbing pair.
5. Conclusions
HFS and IS data have been measured for the first time for three deep-UV transitions in neutral
Yb using the third harmonic of a cw Ti:S laser. In addition, accurate measurements have
been performed on the 398.8 nm line in neutral Yb. Although a simple technique has been
used, exploiting the angular distribution of the fluorescence radiation, the accuracy of our
measurements exceeds that of previous experiments, where far more complicated techniques
were employed. From a King plot analysis of the data, values for the normal and SMS as well
as the FS have been obtained for all measured transitions.
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