Comment on "Laser cooling of $^{173}$Yb for isotope separation and precision hyperfine spectroscopy"
Quinton McKnight Adam Dodson Tucker Sprenkle Tyler Bennett Scott Bergeson
physics.atom-ph











 scott.bergeson@byu.edu
Department of Physics and Astronomy, Brigham Young University, Provo, UT 84602, USA




We present measurements of the hyperfine splitting in the Yb-173 6s6p ^1P_1^ o (F^'=3/2,7/2) states that disagree significantly with those measured previously by Das and Natarajan [Phys. Rev. A 76, 062505 (2007)]. We point out inconsistencies in their measurements and suggest that their error is due to optical pumping and improper determination of the atomic line center. Our measurements are made using an optical frequency comb. We use an optical pumping scheme to improve the signal-to-background ratio for the F^'=3/2 component.


32.70.Jz, 32.10.Fn, 06.30.Ft, 42.62.Fi
                             

                              
Comment on “Laser cooling of ^173Yb
 for isotope separation and precision hyperfine spectroscopy”
    Scott Bergeson
    December 30, 2023
=================================================================================================





§ INTRODUCTION


Measurements of isotope shifts are important for benchmarking atomic structure calculations <cit.>. They can help address questions of nucleosynthesis in the early universe <cit.>, parity non-conservation <cit.>, measuring the charge distribution in the nucleus <cit.>, and constraining the search for new physics beyond the standard model <cit.>. It is critically important, therefore, that the quality of isotope shift measurements is verified, and that systematic errors are properly identified and controlled. In the case of Yb, calculations can be extremely difficult because of significant configuration interaction in the complicated level structure <cit.>.

Ten years ago, Das and Natarajan (DN) published what appeared to be definitive measurements of the hyperfine splitting in the Yb-173 6s6p ^1P_1^ o (F^'=3/2) and (F^'=7/2) levels <cit.>. They used laser spectroscopy on the 6s^2 ^1S_0^ - 6s6p ^1P_1^ o transition at 399 nm. In a standard laser-induced fluorescence experiment using an atomic beam, these measurements are challenging because the transition in Yb-173 to the (F^'=3/2) level is nearly coincident with the resonance transition in Yb-172. To overcome this problem, DN used a one-dimensional optical molasses to selectively deflect Yb-173 atoms into a spatially separated slow atomic beam. They performed standard laser-induced fluorescence spectroscopy on the now clearly-resolved Yb-173 transitions. They reported a frequency splitting of 72.093 ± 0.036 MHz between the F^'=3/2 and F^'=7/2 levels. This is an excellent method that appears to be plagued by spectroscopy and metrology errors. We have repeated their experiment and measure a frequency splitting at significant variance with their results.

In this comment, we will describe measurements made using two experimental systems. Both use laser-induced fluorescence on collimated atomic beams. In one experimental configuration, we use a fast atomic beam. It is generated by heating a solid Yb sample to 500 ^∘C. The beam passes through a microcapillary array <cit.> and is further collimated after passing through a 12 mm aperture farther downstream. This configuration is similar to an older measurement by the DN group <cit.> and similar to what we used in a publication last year <cit.>. In the other experimental configuration, we reproduce the optical molasses setup of DN to generate a slow (20 m/s) isotopically pure atomic beam. Our molasses laser beam has a power of 1.1 W and an intensity of 1.4 W/cm^2. Our probe laser beam is generated using an independent laser. We also use a fixed-frequency laser beam tuned to the F^'=5/2 transition to address the optical pumping problem, which we describe below.



§ THE OPTICAL PUMPING PROBLEM


We question the data shown in Fig. 2 of the DN paper. That figure shows fluorescence measurements from the Yb-173 F^'=3/2 and F^'=7/2 levels in an isotopically pure, slow Yb-173 beam. Their probe laser beam size is 8 mm. The intensity of that laser beam ranges from about 0.3 to 0.5 times the saturation intensity. Rate equations show that optical pumping populates the ground state m_F=± 5/2 level after only 1 μs. Because the atoms spent 80 μs interacting with the laser beam, the F^'=3/2 transition should have been completely dark.

We show this in our optical molasses measurements. In Fig. <ref> we show that in a nearly exact repeat of the DN measurement as they described it there is no peak from the F^'=3/2 level. The only peak that is visible is from the F^'=7/2 level.

In our experiment, We address the optical pumping problem by introducing another laser beam into the interaction region. This additional laser is tuned to the 6s^2 ^1S_0^(F=5/2) - 6s6p ^1P_1^ o (F^'=5/2) transition, approximately 840 MHz below the F^'=7/2 transition. This laser scrambles the population in the lower m_F levels. When this laser is present, fluorescence from the F^'=3/2 level can be readily measured, as shown in Fig. <ref>.



We also note that the fluorescence levels shown in Fig. 2c of the DN paper appear to be in error. That figure shows 100% deflection of Yb-172 in the fast atomic beam. However, their optical molasses only addresses atoms with velocities less than 25 m/s. Given that the thermal velocity of their atoms is v_ th = (k_ B T/m)^1/2 = 165 m/s, one would expect only (π/18)^1/2 (25/165)^3 = 0.15% of the Yb-172 atoms to be deflected.

Optical pumping should have made measurement of the F^'=3/2 level impossible in the experiment of DN. It is not clear how the DN data could have been obtained given the information in their paper.



§ METROLOGY AND SPECTROSCOPY PROBLEMS


The group of DN has published many atomic transition frequency measurements over the past several years. As we pointed out in an earlier publication, their absolute transition frequencies in Yb <cit.> and K <cit.> have been shown to be in error by ∼ 500 MHz in spite of  estimated error bars of tens of kHz. Measurements in Rb <cit.> and Li <cit.> deviate from frequency comb measurements in the MHz range again in spite of estimated error of tens of kHz. In all cases, issues such as quantum interference in hyperfine spectroscopy <cit.> have been neglected by them, leading to additional MHz-level errors.

Recently, the group of DN has acknowledged that their spectroscopy method has been the likely cause of errors in isotope shift and hyperfine splitting measurements <cit.>. In many of their papers they dithered their laser by 10 MHz while monitoring the fluorescence from their atomic samples. They demodulated the fluorescence signal at the third harmonic of the dither frequency to obtain a dispersion-shaped error signal. They locked their lasers to the zero-crossing of this error signal. Any DC-offset errors are mapped directly into a frequency error. In a recent paper, the group of DN showed that this effect was the cause of  a 4.5 MHz error in the Rb-87 5P_1/2 D1 hyperfine splitting <cit.>.

As for the 2007 DN paper, we point out an additional error in the metrology. The spectra published in Fig. 2b of DN shows that the F^'=3/2,7/2 splitting is over 80 MHz, disagreeing with their final result of 72.093 ± 0.036 MHz. This is readily verified by extracting their data using a program such as WebPlotDigitizer and fitting to a two-Lorentzian lineshape model. DN admit that this spectrum was not the one used to determine the splitting, because they used the method described in the previous paragraph. This was necessary because their AOMs did not have enough bandwidth to tune across the line profile. Interestingly, the data in Fig. 2b of the 2007 DN paper was obtained by scanning a separate laser over the line profile, the improved method used their correction of the Rb-87 5P_1/2 D1 hyperfine splitting <cit.>.

The laser metrology and atomic spectroscopy methods used by DN are problematic and have been shown in some cases to be in error. The Yb spectrum published by DN doesn't agree with their final result <cit.>. Their final result does, surprisingly, match previous measurements from their own group <cit.>. It is to these measurements that we now turn our attention.



§ PSEUDO-PEAKS FROM ERRONEOUS LINE FITTING 




In two earlier experiments, the group of DN measured laser-induced fluorescence from Yb atoms in a fast collimated atomic beam <cit.>. When the laser was scanned across the Yb-172/Yb-173 complex at 399 nm, they observed two peaks. The dominant one they correctly attributed to Yb-172. The smaller one they correctly attributed to Yb-173 (F^'=7/2). When they fit this signal to a two-Lorentzian line shape model, they noticed that the Yb-172 peak was 1.3 times the width of the Yb-173 (F^'=7/2) peak. They hypothesized that this was due to the presence of the Yb-173 (F^'=3/2) component at a somewhat lower frequency. They then analyzed their data using a line shape model with three Lorentzians, requiring the width of all three Lorentzians to be the same. Critically, they fixed the frequencies of the Yb-172 and Yb-173 (F^'=7/2) transitions and allowed the frequency of the lesser component to be a fit parameter. This artificially forces a peak to appear.

We show the unsuitability of this fitting procedure using a computer simulation. We simulate their data analysis by generating a Lorentzian peak at 531 MHz and a Lorentzian peak at 589 MHz, the approximate positions of the Yb-172 and Yb-173 (F^'=7/2) transitions (see Fig. <ref>). We add pseudo-random noise with an rms value of 1.5%. The simulated Yb-172 peak has a Lorentzian full-width of 39 MHz. The simulated Yb-173 (F^'=7/2) peak has a Lorentzian full-width of 30 MHz, similar to what was observed in Ref. <cit.>. We fit this simulated data to a three-Lorentzian line shape model, fixing the frequencies of the Yb-172 and Yb-173 (F^'=7/2) transitions, and requiring the widths of all three peaks to be the same.

To show the error in this fitting procedure, we vary the frequency of the Yb-172 peak in the model. This forces a third peak to appear. In Fig. <ref>(b) we show the frequency of the pseudo-peak as a function of the frequency of the Yb-172 peak in the model. As can be readily seen, a very good fit can be obtained with a shift that corresponds to the published data of Ref. <cit.> if one carefully chooses the “correct” frequency for Yb-172. This simulation shows that the analysis used in the paper of Ref. <cit.> (and also Refs. <cit.> and <cit.>) is completely unfounded. The fact that the results of DN agree with this earlier publication in spite of the many concerns listed above is remarkable and surprising.



§ FREQUENCY COMB MEASUREMENTS


We now present our measurements of the Yb-173 F^'=3/2 and F^'=7/2 levels. We have measured fluorescence from these levels in a fast thermal atom beam with the Yb isotopes in their natural abundances and also using an isotopically pure beam of slow Yb-173 atoms. In both cases, we used a pump laser beam tuned to the F^'=5/2 level to overcome the optical pumping problem discussed previously. The pump and probe beams are orthogonally polarized. They are combined on a polarizing beam splitter cube before traversing the atomic beam. The pump and probe beam intensities are less than 1.5 mW/cm^2. 

In our measurements, these weak probe laser beams cross a collimated Yb atomic beam at a right angle <cit.>. We collect scattered laser photons in a direction orthogonal to both the laser propagation direction and the atomic beam direction. We offset-lock our probe laser to an optical frequency comb <cit.>. We have shown that the absolute frequency error in our experiment is less than 40 kHz <cit.>. In the fast-beam measurements, the interaction region is enclosed in a single-layer mu-metal shield to minimize the influence of ambient magnetic fields on our measurements. In the slow beam measurements, the lasers are retroreflected. 

For convenience, we will define the fluorescence collection direction as the ẑ-axis and measure the laser polarization angle θ_L with respect to that axis, as in previous work  <cit.>. Because the pump and probe polarizations are orthogonal to each other, we will only refer to the polarization of the probe beam. A half-wave plate located before the vacuum chamber is used to rotate the polarization of both the pump and probe laser beams. This allows us to assess the influence of quantum interference on the apparent centers of the transitions <cit.>. For some measurements, we use a chopper wheel in the pump beam and phase-sensitive detection to eliminate background signal, for example, from the Yb-172 isotope.



Quantum interference in the excitation and decay pathways can shift the frequency of line centers measured in fluorescence spectroscopy <cit.>. Our measured frequencies of the F^'=7/2 level in Yb-173 are shown in Fig. <ref>. As we rotate the laser polarization angle, we see a 3 MHz shift in the transition frequency. We see a somewhat larger shift but with opposite sign in the F^'=3/2 transition. The measurements account for this shift by setting θ_L = cos^-1(3^-1/2) = 54.7^∘, where the quantum interference terms vanish.

Based on these frequency-comb measurements, we report the frequencies of the Yb-173 6s^2 ^1S_0^ - 6s6p ^1P_1^ o (F^'=3/2) and (F^'=7/2) transitions, relative to Yb-174, to be

    [ 6s^2 ^1S_0^ - 6s6p ^1P_1^ o (F^'=3/2)                         503.22 ± 0.70; 6s^2 ^1S_0^ - 6s6p ^1P_1^ o (F^'=7/2)                       589.51 ± 0.33 . ]

This value of F^'=7/2 is consistent with our previous measurement <cit.>, differing by less than 1 standard deviation. The frequency splitting between these two hyperfine levels is 86.29 ± 0.77 MHz.



§ COMPARISON WITH THE LITERATURE


We calculate the hyperfine constants for Yb-173 using the Hamiltonian in Ref. <cit.> and also the F^'=5/2 data from Ref. <cit.>. Our values are given in Table <ref> and compared with values from the literature.

Laser spectroscopy measurements for Yb-173 are reported in Refs. <cit.> and <cit.>. The group of DN published values with the smallest error estimates in Table <ref> <cit.>, and we question these publications in this comment. The analysis in Ref. <cit.> follows the unfortunate analysis of the DN group, which we have shown in Sec. <ref> to be prone to significant systematic error. None of the values in the literature address the quantum interference in the F^'=7/2 level. None of them address the influence of optical pumping for the F^'=3/2 fluorescence level. In the atomic beam data of Refs. <cit.>, the F^'=3/2 component is invisible.

The laser spectroscopy measurement of Ref. <cit.> used a different approach. They measured fluorescence from an atomic beam of Yb atoms with the laser polarized at θ_L=0 and θ_L=90^∘. In the θ_L=0 measurement, the fluorescence signal is dominated by fluorescence from the highly abundant even isotopes. In the θ_L=90^∘ measurement, fluorescence the even isotopes are strongly suppressed compared to the odd isotopes because of the dipole radiation pattern. The small residual fluorescence from the even isotopes can be subtracted out using an appropriate scaling of the θ_L=0 data. From the hyperfine constants in Ref. <cit.>, we calculate a hyperfine splitting between the Yb-173 F^'=7/2 and 3/2 levels to be 75.3 ± 4.0 MHz. This θ_L=0 measurement needs to be corrected for the quantum interference effect. Our measurements suggest this is approximately 5 MHz, making their measurement a little over 80 MHz with an uncertainty of 4 MHz. This interval differs from our measurement by just under two standard deviations.




We acknowledge support from the National Science Foundation under grant number PHY-1500376 and from the Air Force Office of Scientific Research under grant number AFOSR-FA9550-17-1-0302.









26
fxundefined [1]
 ifx#1

fnum [1]
 #1firstoftwo
 secondoftwo
 
fx [1]
 #1firstoftwo
 secondoftwo
 





noop [0]secondoftwo

ref[1]@startlink#1@href
href[1]#1@endlink
anitize@url [0]`
12`$12`&12`#12`1̂2`_12`%12
startlink[1]
endlink[0]

rl [1]href #1












@bib@innerbibempty

[Dzuba et al.(2005)Dzuba,
  Johnson, and Safronova]PhysRevA.72.022503
  author author V. A. Dzuba, author W. R. Johnson,
   and author M. S. Safronova,  10.1103/PhysRevA.72.022503 journal journal Phys. Rev. A volume 72, pages 022503 (year 2005)NoStop
[Cowan and Sneden(2006)]cowan2006
  author author J. J. Cowan and author C. Sneden,  10.1038/nature04807 journal journal Nature volume 440, pages
  1151  (year 2006)NoStop
[Ginges and Flambaum(2004)]GINGES200463
  author author J. Ginges and author V. Flambaum, https://doi.org/10.1016/j.physrep.2004.03.005
  journal journal Physics Reports volume 397, pages 63  (year
  2004)NoStop
[Antypas et al.(2017)Antypas, Fabricant, Bougas, Tsigutkin, and Budker]Antypas2017
  author author D. Antypas, author A. Fabricant,
  author L. Bougas, author K. Tsigutkin,  and author D. Budker, 10.1007/s10751-017-1396-8 journal journal
  Hyperfine Interactions volume 238 (year
  2017), 10.1007/s10751-017-1396-8NoStop
[Flambaum et al.(2017)Flambaum, Dzuba, and Harabati]Flambaum2017
  author author V.V. Flambaum, author V.A. Dzuba,   and author C. Harabati, 10.1103/PhysRevA.96.012516 journal journal Physical Review A volume 96 
  pages 012516 (year 2017), 10.1103/PhysRevA.96.012516NoStop
[Zheng et al.(2017)Zheng,
  Sun, Chen, Jiang,
  Pachucki, and Hu]PhysRevLett.118.063001
  author author X. Zheng, author Y. R. Sun,
  author J.-J. Chen, author W. Jiang, author
  K. Pachucki,  and author
  S.-M. Hu, 10.1103/PhysRevLett.118.063001 journal journal
  Phys. Rev. Lett. volume 118, pages
  063001 (year 2017)NoStop
[Frugiuele et al.(2017)Frugiuele, Fuchs, Perez, and  Schlaffer]PhysRevD.96.015011
  author author C. Frugiuele, author E. Fuchs,
  author G. Perez,  and author M. Schlaffer, 10.1103/PhysRevD.96.015011 journal journal Phys.
  Rev. D volume 96, pages 015011
  (year 2017)NoStop
[Porsev et al.(1999)Porsev,
  Rakhlina, and Kozlov]0953-4075-32-5-006
  author author S. G. Porsev, author Y. G. Rakhlina,  and author M. G. Kozlov, http://stacks.iop.org/0953-4075/32/i=5/a=006 journal journal Journal of Physics B: Atomic, Molecular and
  Optical Physics volume 32, pages 1113
  (year 1999)NoStop
[Das and Natarajan(2007)]PhysRevA.76.062505
  author author D. Das and author V. Natarajan, 10.1103/PhysRevA.76.062505 journal journal Phys. Rev. A volume
  76, pages 062505 (year 2007)NoStop
[Senaratne et al.(2015)Senaratne, Rajagopal, Geiger, Fujiwara, Lebedev, and Weld]senaratne2015
  author author R. Senaratne, author S. V. Rajagopal, author Z. A. Geiger, author K. M. Fujiwara, author V. Lebedev,   and author D. M. Weld, http://dx.doi.org/10.1063/1.4907401 journal
  journal Review of Scientific Instruments volume 86, eid 023105 (year 2015),  http://dx.doi.org/10.1063/1.4907401NoStop
[Das et al.(2005)Das,
  Barthwal, Banerjee, and Natarajan]PhysRevA.72.032506
  author author D. Das, author S. Barthwal,
  author A. Banerjee,  and  author V. Natarajan, 10.1103/PhysRevA.72.032506 journal journal Phys. Rev. A volume 72, pages 032506 (year 2005)NoStop
[Kleinert et al.(2016)Kleinert, Gold Dahl, and Bergeson]PhysRevA.94.052511
  author author M. Kleinert, author M. E. Gold Dahl,  and author S. Bergeson, 10.1103/PhysRevA.94.052511 journal journal Phys. Rev. A volume
  94, pages 052511 (year 2016)NoStop
[Falke et al.(2006)Falke,
  Tiemann, Lisdat, Schnatz,  and Grosche]falke2006
  author author S. Falke, author E. Tiemann,
  author C. Lisdat, author H. Schnatz,  and author G. Grosche, 10.1103/PhysRevA.74.032503 journal journal Phys.
  Rev. A volume 74, pages 032503
  (year 2006)NoStop
[Maric et al.(2008)Maric,
  McFerran, and Luiten]maric2008
  author author M. Maric, author J. J. McFerran,
   and author A. N. Luiten,  10.1103/PhysRevA.77.032502 journal journal Phys. Rev. A volume 77, pages 032502 (year 2008)NoStop
[Sansonetti et al.(2011)Sansonetti, Simien, Gillaspy, Tan, Brewer, Brown, Wu,  and Porto]sansonetti2011
  author author C. J. Sansonetti, author C. E. Simien, author J. D. Gillaspy, author J. N. Tan,
  author S. M. Brewer, author R. C. Brown, author
  S. Wu,  and author
  J. V. Porto, 10.1103/PhysRevLett.107.023001 journal journal
  Phys. Rev. Lett. volume 107, pages
  023001 (year 2011)NoStop
[Brown et al.(2013)Brown,
  Wu, Porto, Sansonetti,
  Simien, Brewer, Tan, and  Gillaspy]brown2013
  author author R. C. Brown, author S. Wu, author J. V. Porto, author
  C. J. Sansonetti, author
  C. E. Simien, author
  S. M. Brewer, author
  J. N. Tan,  and author
  J. D. Gillaspy, 10.1103/PhysRevA.87.032504 journal journal Phys.
  Rev. A volume 87, pages 032504
  (year 2013)NoStop
[Datar et al.(2016)Datar,
  Kotibhaskar, Ananthamurthy, and  Natarajan]1611.02406
  author author D. Datar, author N. Kotibhaskar,
  author S. Ananthamurthy,  and  author V. Natarajan, @noop
     (year 2016), http://arxiv.org/abs/arXiv:1611.02406 arXiv:1611.02406 NoStop
[Banerjee et al.(2003)Banerjee, Rapol, Das, Krishna, and Natarajan]banerjee2003
  author author A. Banerjee, author U. D. Rapol,
  author D. Das, author
  A. Krishna,  and author
  V. Natarajan, http://stacks.iop.org/0295-5075/63/i=3/a=340 journal
  journal EPL (Europhysics Letters) volume
  63, pages 340 (year 2003)NoStop
[Wen-Li and Xin-Ye(2010)]xinye2010
  author author W. Wen-Li and author X. Xin-Ye, http://stacks.iop.org/1674-1056/19/i=12/a=123202
  journal journal Chinese Physics B volume 19, pages 123202 (year
  2010)NoStop
[Fendel et al.(2007)Fendel,
  Bergeson, Udem, and Hänsch]Fendel:07
  author author P. Fendel, author S. D. Bergeson, author T. Udem,   and author T. W. Hänsch,  10.1364/OL.32.000701 journal journal Opt. Lett. volume 32, pages
  701 (year 2007)NoStop
[Lyon and Bergeson(2014)]Lyon:14
  author author M. Lyon and author S. D. Bergeson, 10.1364/AO.53.005163 journal
  journal Appl. Opt. volume 53,  pages 5163 (year 2014)NoStop
[Arimondo et al.(1977)Arimondo, Inguscio, and Violino]RevModPhys.49.31
  author author E. Arimondo, author M. Inguscio,
   and author P. Violino, 10.1103/RevModPhys.49.31 journal journal Rev. Mod. Phys. volume 49, pages 31 (year 1977)NoStop
[Zinkstok et al.(2002)Zinkstok, van Duijn, Witte, and  Hogervorst]hogervorst2002
  author author R. Zinkstok, author E. J. van
  Duijn, author S. Witte,  and  author W. Hogervorst, http://stacks.iop.org/0953-4075/35/i=12/a=305 journal
  journal Journal of Physics B: Atomic, Molecular and Optical
  Physics volume 35, pages 2693
  (year 2002)NoStop
[Liening(1985)]Liening1985
  author author H. Liening, 10.1007/BF01415711 journal
  journal Zeitschrift für Physik A Atoms and Nuclei  volume 320, pages 363 (year
  1985)NoStop
[Baumann et al.(1977)Baumann, Liening, and Lindel]BAUMANN1977433
  author author M. Baumann, author H. Liening,   and author H. Lindel, https://doi.org/10.1016/0375-9601(77)90647-8 journal
  journal Physics Letters A volume 59,  pages 433  (year 1977)NoStop
[Budick and Snir(1969)]PhysRev.178.18
  author author B. Budick and author J. Snir,  10.1103/PhysRev.178.18 journal journal Phys. Rev. volume 178, pages
  18 (year 1969)NoStop



