JOURNAL OF PHYSICS B: ATOMIC, MOLECULAR AND OPTICAL PHYSICS J. Phys. B: At. Mol. Opt. Phys. 35 (2002) PII: S (02)

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1 INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS B: ATOIC, OLECULAR AND OPTICAL PHYSICS J. Phys. B: At. ol. Opt. Phys. 35 (22) PII: S (2) 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,EJvanDuijn, S Witte and W Hogervorst Laser Centre Vrije Universiteit, De Boelelaan 181, 181 HV Amsterdam, The Netherlands rzinkstk@nat.vu.nl Received 7 February 22, in final form 2 ay 22 Published 6 June 22 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 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 7, and has closed 4f and 6s subshells in the 4f 14 6s 21 S ground state. The natural isotopic composition shows five even isotopes, 168 Yb (.14%), 17 Yb (3.3%), 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 1] 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 4 5 cm 1 region using two-step excitation processes (e.g. [13 15]). The odd-parity energy levels around 38 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 Hz. In addition to a study of these lines, we performed measurements on one of the most extensively studied lines of Yb, i.e. the nm first resonance line, corresponding to the /2/ $3. 22 IOP Publishing Ltd Printed in the UK 2693

2 2694 R Zinkstok et al transition from the 4f 14 6s 21 S ground state to the 4f 14 6s6p 1 P 1 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 [2, 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 Hz 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 =, F(θ,φ) = sin 2 (θ), while for m =±1, F(θ,φ) = 1 + cos 2 (θ) (see e.g. [24]). When more magnetic sublevels are involved, the contribution of each m i m f 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 nm transition in Yb assuming excitation with linearly polarized light. Since this is a J = 1 transition, it follows that the even isotopes (which have I = ) can only decay through m =, 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 = 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 9,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 nm transition of Yb. It is to be noted that this discussion applies only to closed atomic transitions, of which the 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 ) pumped by a 1 W Spectra Physics illennia X, is divided into two beams by a 5% 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 = 9 and φ = 33.7 ). With.8 W of fundamental light, about 32 mw of second harmonic (UV) light is produced, reaching 4% of useful conversion.

3 HFS and IS of several transitions in Yb I 2695 a b c.4.4 d Figure 1. Calculated angular distributions of fluorescence radiation in the 4f 14 6s 21 S 4f 14 6s6p 1 P 1 transition for (a) all even isotopes, (b) 171 Yb F =1/2 1/2, 173 Yb F =5/2 3/2 and 173 Yb F =5/2 5/2, (c) 171 Yb F =1/2 3/2, (d) 173 Yb F =5/2 7/2. The vertical z-axis is parallel to the polarization vector of the incident light. PD PD PB Servo λ/4 4 BBO 5 L 25 cm HR deep-uv L 4 cm BS HRUV LBO 2 HRUV L 4 cm λ/2 L 25 cm CL 15 cm CL 4 cm HRUV HRUV 3 4 PT PB PD Servo HR deep-uv AB λ/2 λ/4 PD Vacuum chambers BS Ti:S laser illennia X oven Etalon D Computer Figure 2. Schematic of the experimental set-up. The beam of a cw Ti:S laser pumped by a 1 W illennia X is split into two beams by a 5% BS. One of these beams is frequency doubled inside an EEC consisting of mirrors 1 4 using an LBO crystal, while the other is enhanced in a second EEC (mirrors 5 8). The beam reflected off 3 is led into a Hänsch Couillaud locking device ( 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 (L). 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 PT 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 PT signal.

4 2696 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 9 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 nm. In our case, phase matching and mirror coating restrictions on the Ti:S laser and EECs yield in practice tunability in the ranges , and nm for the fundamental, second harmonic and third harmonic, respectively. Since the linewidth of the Ti:S laser is about 1 Hz, bandwidths of the second and third harmonics are about 2 and 3 Hz respectively. The laser is continuously tunable over about 1 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 15±.3 Hz, while another part of the fundamental beam is led to an ATOS L-7 lambda-meter as an absolute wavelength reference 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 95 K by electron bombardment using a nearby tungsten wire heated by a large current ( 1 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 3 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 1 Hz for the second harmonic measurements, and to about 16 Hz 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 9 to minimize Doppler broadening and shift. Directly above the point where the beams intersect a photomultiplier tube (PT) is mounted. The fluorescence spot is imaged on the PT 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 PT 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.9 Hz, while the absolute wavelength can be measured by the ATOS lambda-meter with a systematic error smaller than 1 Hz. 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 4f 14 6s 2 1 S ground state have been measured. The transitions involved are to the 4f 13 5d6s 2 1 P 1 state at cm 1 (λ = nm), the 4f 14 1 S 6s7p 3 P 1 state at cm 1 (λ = nm) and the 4f 13 5d6s 2 3 D 1 state at cm 1 (λ = nm). Spectra of these transitions are shown in figure 3; they all show a good signal to noise ratio, on the order of 1 1.

5 HFS and IS of several transitions in Yb I 2697 Counts (a) D1 4 (b) P1 Counts (c) P1 Counts 5 x Frequency [Hz] Figure 3. easured 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 4f 13 5d6s 23 D 1 state at cm 1, (b) the 4f 14 1 S 6s7p 3 P 1 state at cm 1 and (c) the 4f 13 5d6s 21 P 1 state at cm 1. All isotopes can be identified in these spectra, except for 168 Yb, which is visible only in the spectrum of the 5d6s 21 P 1 state, and for 17 Yb, which is buried under the 172 Yb peak in the 6s 23 D 1 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 A 173 /A 171. 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] The nm line We used a polarizing beam splitter and a half-wave plate to switch between horizontal and vertical linearly polarized light while the PT remained fixed in place, observing along the vertical axis (thus defining vertical and horizontal directions). In this way, pairs of spectra of the 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 PT current could be detected directly, resulting in a signal-to-noise ratio exceeding 1.

6 2698 R Zinkstok et al Intensity (a.u.) 1..5 (a) x1 168 Intensity (a.u.) Intensity (a.u.) (b) (c) Frequency (Hz) x1 Figure 4. easured spectra of the 4f 14 6s 21 S 4f 14 6s6p 1 P 1 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. easured ISs. IS (Hz) Final state Energy level (cm 1 ) f 13 5d6s 21 P (2) 842.6(.6) 61.2(1.6) 567(3) 4f 14 6s7p 3 P (.9) 32.3(1.8) 27.5(.9) 4f 13 5d6s 23 D (1.3) 36.2(1.6) 4f 14 6s6p 1 P (1.8) 659(4) 529(2) 57.2(1.5) 4f 14 6s6p 3 P a (5) (5) 1.3(5) 954.8(5) a 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 nm transition are in good agreement with those measured in previous work [16, 2, 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 A 171, and in [22],

7 HFS and IS of several transitions in Yb I 2699 Table 2. HFS A and B constants of the excited states in Hz. State A 171 A 173 B 173 A 173 /A 171 4f 13 5d6s 21 P 1 293(4) 577.6(.5) 233(2).276(5) 4f 14 6s7p 3 P (4) (1.4) 12.1(1.1).2769(4) 4f 13 5d6s 23 D 1 588(2) 161.9(1.5) 177(6).275(3) 4f 14 6s6p 1 P (.8) 57.7(.9) 62.1(1.1).2746(8) Table 3. Comparison of IS data of the nm transition of Yb. IS (Hz) Present work 696.(1.8) 659(4) 529(2) 57.2(1.5) [16] 627(3) 531(3) 47(27) [2] 665(1) 53(4) 59(4) [22] 698(2) [23] 648(8) 528(3) 57(3) Table 4. Comparison of HFS data of the nm transition of Yb. A 171 A 173 B 173 Present work 21.2(.8) 57.7(.9) 62.1(1.1) [17] 216(4) 59.7(1.3) 63(17) [18] 58.5(.8) 59(13) [2] 213(3) 65(2) [19] 211(1) 58.1(.3) 588(2) [21] 213(1) [22] 21(3) [23] 212(3) where a fairly low A-value for 171 Yb is given, while the value for B 173 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 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 (NS), the specific mass shift (SS) and the field shift (FS): δν IS i = δν FS i + ( A A AA ) (i NS + i SS ). (1) The NS and SS are constants for a given transition. The NS can easily be calculated using i NS = ν i (2) where ν i is the transition frequency. Consequently, the NS 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

8 27 R Zinkstok et al odified IS of other transitions [Hz] odified IS of the 4f 14 6s 6p 3 P 1 transition [Hz] Figure 5. King lines of the measured transitions from the ground state to:, 4f 13 5d6s 2 1 P 1 ;, 4f 14 6s7p 3 P 1 ;, 4f 13 5d6s 23 D 1 and, 4f 14 6s6p 1 P 1. Table 5. Contributions to the IS between 176 Yb and 174 Yb in the measured transitions in Hz. Upper state δν NS δν SS δν FS 4f 13 5d6s 21 P (13) 854(13) 4f 14 6s7p 3 P (1) 168(1) 4f 13 5d6s 23 D (1) 17(1) 4f 14 6s6p 1 P (1) 431(1) transition, a straight line results (King plot). The slope and intercept of such a line relate the FS and SS of the transitions involved (see [27]). Using the measured IS data a King plot analysis has been made. As reference transition we took the 555.6nm6s 21 S 6s6p 3 P 1 transition in Yb, for which [26] gives very accurate data, shown in table 1. Since this is known to be a pure s 2 sp transition [14,27], we can adopt the estimate from [28], δν SS = ( ±.5)δν NS, and assume the SS of this transition to be about zero (the NS between 174 Yb and 176 Yb is calculated to be 2 Hz using equation (2)). The King lines for the four measured transitions are shown in figure 5. From these King lines, the values for the SS and the FS have been derived, using the values for the known reference transition at nm. These are shown in table 5 for the isotope pair. The transition to the 4f 13 5d6s 21 P 1 state shows a large negative SS. 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 4f 14 6s6p 1 P 1 state at nm shows a negative FS, caused by the decrease of electron density in the s p transition. The negative SS in this transition

9 HFS and IS of several transitions in Yb I 271 is probably due to mixing with a 4f 13 5d6s 2 state, which exhibits a negative SS as in the 4f 13 5d6s 21 P 1 state [27]. The 4f 14 6s7p 3 P 1 and 4f 13 5d6s 23 D 1 states are mutually perturbing according to [1], which is confirmed by their very similar King lines. The negative SS in the transitions to these states can be attributed to the change in the number of 4f electrons in the 4f 14 6s 21 S 4f 13 5d6s 23 D 1 transition, as before. The positive FS is unexpected for an s 2 sp transition, but it can be due to a screening effect in the 4f 14 6s 21 S 4f 13 5d6s 23 D 1 transition, similar to the screening effect discussed above. The SS and FS values for these two transitions seem to indicate that the 4f 13 5d6s 2 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 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 SS as well as the FS have been obtained for all measured transitions. References [1] Wyart J F and Camus P 1979 Phys. Scr [2] Camus P, Débarre A and orillon C 198 J. Phys. B: At. ol. Phys [3] Komarovskii V A and Verolainen Y F 1992 Opt. Spektrosk [4] Xu C B, Xu X Y, Huang W, Xue and Chen D Y 1994 J. Phys. B: At. ol. Opt. Phys [5] Dai C J, Zhang S, Shu X W, Fang D W and Li J 1995 J. Quant. Spectrosc. Radiat. Transfer [6] Li J and van Wijngaarden W A 1995 J. Phys. B: At. ol. Opt. Phys [7] Park H, Lee J, Lee J and Chang J 1996 Phys. Rev. A [8] Derzhiev V I, Kuznetsov V A, ikhal tsov L A, ushta V, Sapozhkov A Y, Tkachev A N, Chaushanskii S A and Yakovlenko S I 1996 Quantum Electron [9] Borisov S K, Kuz mina A and ishin V A 1996 J. Russ. Laser Res [1] Sankari and Suryanarayana V 1998 J. Phys. B: At. ol. Opt. Phys [11] Honda K, Takahashi Y, Kuwamoto T, Fujimoto, Toyoda K, Ishikawa K and Yabuzaki T 1999 Phys. Rev. A 59 R934 [12] Kuwamoto T, Honda K, Takahashi Y and Yabuzaki T 1999 Phys. Rev. A 6 R745 [13] aier J, Kischkel C S and Baumann 1991 Z. Phys. D [14] Jin W, Horiguchi T, Wakasugi, Hasegawa T and Yang W 1991 J. Phys. Soc. Japan [15] Kischkel C S, Baumann and Kümmel E 1991 J. Phys. B: At. ol. Opt. Phys Kischkel C S, Baumann and Kümmel E 1992 J. Phys. B: At. ol. Opt. Phys [16] Chaiko Y 1965 Opt. Spectrosc Chaiko Y 1966 Opt. Spectrosc [17] Budick B and Snir J 1969 Phys. Rev [18] Baumann, Liening H and Lindel H 1977 Phys. Lett. A [19] Liening H 1985 Z. Phys. A [2] Grundevik P, Gustavsson, Rosén A and Rydberg S 1979 Z. Phys. A [21] Berends R W and aleki L 1992 J. Opt. Soc. Am. B [22] Deilamian K, Gillaspy J D and Kelleher D E 1993 J. Opt. Soc. Am. B [23] Loftus T, Bochinski J R and ossberg T W 2 Phys. Rev. A [24] Davydov A S 1965 Quantum echanics (Oxford: Pergamon) p 39 [25] Hänsch T W and Couillaud B 198 Opt. Commun [26] Clark D L, Cage E, Lewis D A and Greenlees G W 1979 Phys. Rev. A [27] King W H 1984 Isotope Shifts in Atomic Spectra (New York: Plenum) pp 63, 142 [28] Heilig K and Steudel A 1974 At. Data Nucl. Data Tables