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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 7 — Apr. 7, 2014
  • pp: 7898–7905
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Frequency ratio measurement of 171Yb and 87Sr optical lattice clocks

Daisuke Akamatsu, Masami Yasuda, Hajime Inaba, Kazumoto Hosaka, Takehiko Tanabe, Atsushi Onae, and Feng-Lei Hong  »View Author Affiliations


Optics Express, Vol. 22, Issue 7, pp. 7898-7905 (2014)
http://dx.doi.org/10.1364/OE.22.007898


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Abstract

The frequency ratio of the 1S0(F = 1/2)-3P0(F = 1/2) clock transition in 171Yb and the 1S0(F = 9/2)-3P0(F = 9/2) clock transition in 87Sr is measured by an optical-optical direct frequency link between two optical lattice clocks. We determined the ratio (νYb/νSr) to be 1.207 507 039 343 340 4(18) with a fractional standard uncertainty of 1.5 × 10−15. The measurement uncertainty of the frequency ratio is smaller than that obtained from absolute frequency measurements using the International Atomic Time (TAI) link. The measured ratio agrees well with that derived from the absolute frequency measurement results obtained at NIST and JILA, Boulder, CO using their Cs-fountain clock. Our measurement enables the first international comparison of the frequency ratios of optical clocks. The measured frequency ratio will be reported to the International Committee for Weights and Measures for a discussion related to the redefinition of the second.

© 2014 Optical Society of America

1. Introduction

Recent developments in ultra precise laser technology have provided the possibility for time keeping at the 10−18 level [1

1. C. W. Chou, D. B. Hume, J. C. J. Koelemeij, D. J. Wineland, and T. Rosenband, “Frequency comparison of two high-accuracy Al+ optical clocks,” Phys. Rev. Lett. 104(7), 070802 (2010). [CrossRef] [PubMed]

3

3. B. J. Bloom, T. L. Nicholson, J. R. Williams, S. L. Campbell, M. Bishof, X. Zhang, W. Zhang, S. L. Bromley, and J. Ye, “An optical lattice clock with accuracy and stability at the 10-18 level,” Nature 506(7486), 71–75 (2014). [CrossRef] [PubMed]

]. Single ion clocks have exhibited a systematic uncertainty of 8.6 × 10−18 [1

1. C. W. Chou, D. B. Hume, J. C. J. Koelemeij, D. J. Wineland, and T. Rosenband, “Frequency comparison of two high-accuracy Al+ optical clocks,” Phys. Rev. Lett. 104(7), 070802 (2010). [CrossRef] [PubMed]

], and enabled a tabletop demonstration of a relativistic gravitational effect [4

4. C. W. Chou, D. B. Hume, T. Rosenband, and D. J. Wineland, “Optical clocks and relativity,” Science 329(5999), 1630–1633 (2010). [CrossRef] [PubMed]

]. While the ion clock uses a single quantum absorber for an atomic reference, an optical lattice clock uses thousands of atoms [5

5. M. Takamoto, F.-L. Hong, R. Higashi, and H. Katori, “An optical lattice clock,” Nature 435(7040), 321–324 (2005). [CrossRef] [PubMed]

]. Thanks to the small quantum projection noise of an optical lattice clock, its stability can surpass that of an ion clock. Very recently a stability of 1.6 × 10−18 has been achieved with an Yb optical lattice clock [2

2. N. Hinkley, J. A. Sherman, N. B. Phillips, M. Schioppo, N. D. Lemke, K. Beloy, M. Pizzocaro, C. W. Oates, and A. D. Ludlow, “An atomic clock with 10-18 instability,” Science 341(6151), 1215–1218 (2013). [CrossRef] [PubMed]

] and an accuracy of 6.4 × 10−18 has been demonstrated with a Sr optical lattice clock [3

3. B. J. Bloom, T. L. Nicholson, J. R. Williams, S. L. Campbell, M. Bishof, X. Zhang, W. Zhang, S. L. Bromley, and J. Ye, “An optical lattice clock with accuracy and stability at the 10-18 level,” Nature 506(7486), 71–75 (2014). [CrossRef] [PubMed]

]. Together with ion clocks, optical lattice clocks are now promising candidates of a new definition of the second.

2. Experimental setup

The experimental setup is shown schematically in Fig. 1
Fig. 1 Schematic diagram of experimental setup. The two optical lattice clocks (OLCs) have different lattice geometries: Sr OLC uses a vertical optical lattice and Yb OLC uses a horizontal optical lattice. ECLD, extended cavity laser diode; PPLN-WG, periodically poled lithium niobate waveguide; ULE cavity, ultra-low-expansion cavity; PDH lock, Pound-Drever-Hall lock; EOM, electro-optic modulator; AOM, acousto-optic modulator. Local oscillators (LOs) are microwave sources.
. An Nd:YAG laser operating at 1064 nm (master laser) was used to prepare the clock lasers for an 87Sr optical lattice clock (Sr OLC) and a 171Yb optical lattice clock (Yb OLC) by the linewidth transfer method. The master laser was stabilized to a high-finesse ULE cavity by the Pound-Drever-Hall technique. The instantaneous linewidth of the master laser was less than 3.5 Hz. The linewidth including frequency jitter at an averaging time of several seconds was 10 Hz.

In this experiment, we employed fiber-type optical frequency combs (fiber combs) with a broad servo bandwidth for linewidth transfer [comb #1 and comb #2 in Fig. 1]. The oscillator cavity of the combs includes an electro-optic modulator (EOM) for a broad servo bandwidth (approximately 1.3 MHz). The fiber combs are described in detail in [18

18. H. Inaba, K. Hosaka, M. Yasuda, Y. Nakajima, K. Iwakuni, D. Akamatsu, S. Okubo, T. Kohno, A. Onae, and F.-L. Hong, “Spectroscopy of 171Yb in an optical lattice based on laser linewidth transfer using a narrow linewidth frequency comb,” Opt. Express 21(7), 7891–7896 (2013). [CrossRef] [PubMed]

, 20

20. Y. Nakajima, H. Inaba, K. Hosaka, K. Minoshima, A. Onae, M. Yasuda, T. Kohno, S. Kawato, T. Kobayashi, T. Katsuyama, and F.-L. Hong, “A multi-branch, fiber-based frequency comb with millihertz-level relative linewidths using an intra-cavity electro-optic modulator,” Opt. Express 18(2), 1667–1676 (2010). [CrossRef] [PubMed]

, 21

21. K. Iwakuni, H. Inaba, Y. Nakajima, T. Kobayashi, K. Hosaka, A. Onae, and F.-L. Hong, “Narrow linewidth comb realized with a mode-locked fiber laser using an intra-cavity waveguide electro-optic modulator for high-speed control,” Opt. Express 20(13), 13769–13776 (2012). [CrossRef] [PubMed]

]. A heterodyne beat was detected between the master laser and the frequency component of comb #1(#2) fbeat#1(#2) and then stabilized so that fbeat#1(-fbeat#2) = 30 MHz using the intracavity EOM1(EOM2).The carrier-envelope offset frequency was detected using a common-path f-2f interferometer and stabilized so that fceo#1 = -fceo#2 = 30 MHz. As a result, the repetition rates of the combs were stabilized so that frep#1 = frep#2 = 43.4 MHz. The linewidth of the comb components was reduced to Hz level (narrow-linewidth fiber combs). The observed beat linewidth between these two combs was 30.1 mHz, which was the measurement limit of the spectrum analyzer, and the frequency stability of the beat was 3 × 10−16 at a 1-s averaging time [21

21. K. Iwakuni, H. Inaba, Y. Nakajima, T. Kobayashi, K. Hosaka, A. Onae, and F.-L. Hong, “Narrow linewidth comb realized with a mode-locked fiber laser using an intra-cavity waveguide electro-optic modulator for high-speed control,” Opt. Express 20(13), 13769–13776 (2012). [CrossRef] [PubMed]

].

The clock laser for the Sr (Yb) OLC was prepared by transferring the linewidth of the master laser to the lasers at 698 nm (578 nm) through the narrow-linewidth fiber combs. A 698 nm light was generated by an extended cavity diode laser. Second-harmonic comb components around 698 nm were generated by passing the fundamental comb through a periodically poled lithium niobate (PPLN) crystal. The laser was phase-locked to the fiber comb by stabilizing a heterodyne beat note between the second-harmonic comb component and the clock laser using the current control of the diode laser. The tight phase-locking of the fiber comb to the master laser and the clock laser to the fiber comb allowed the linewidth of the master laser to be transferred to the clock laser. We note that comb #1 was also used to narrow the linewidth of a 689 nm laser for the 2nd stage laser cooling of the Sr OLC [22

22. D. Akamatsu, Y. Nakajima, H. Inaba, K. Hosaka, M. Yasuda, A. Onae, and F.-L. Hong, “Narrow linewidth laser system realized by linewidth transfer using a fiber-based frequency comb for the magneto-optical trapping of strontium,” Opt. Express 20(14), 16010–16016 (2012). [CrossRef] [PubMed]

]. A 578 nm light source was generated by the sum-frequency generation of a Nd:YAG laser at 1319 nm and an Yb:YAG laser at 1030 nm by using a PPLN waveguide (PPLN-WG) [23

23. F.-L. Hong, H. Inaba, K. Hosaka, M. Yasuda, and A. Onae, “Doppler-free spectroscopy of molecular iodine using a frequency-stable light source at 578 nm,” Opt. Express 17(3), 1652–1659 (2009). [CrossRef] [PubMed]

]. The clock laser for the Yb OLC was stabilized to fiber comb #2 using an AOM [not shown in Fig. 1].

The Sr OLC at the National Metrology Institute of Japan (NMIJ) is operated with spin-polarized 87Sr atoms. 87Sr atoms were slowed and magneto-optically trapped on a 1S0-1P1 transition at 461 nm [24

24. D. Akamatsu, M. Yasuda, T. Kohno, A. Onae, and F.-L. Hong, “A compact light source at 461 nm using a periodically poled LiNbO3 waveguide for strontium magneto-optical trapping,” Opt. Express 19(3), 2046–2051 (2011). [CrossRef] [PubMed]

]. Then the atoms were further cooled to a few μK by using the inter-combination transition 1S0-3P1 [22

22. D. Akamatsu, Y. Nakajima, H. Inaba, K. Hosaka, M. Yasuda, A. Onae, and F.-L. Hong, “Narrow linewidth laser system realized by linewidth transfer using a fiber-based frequency comb for the magneto-optical trapping of strontium,” Opt. Express 20(14), 16010–16016 (2012). [CrossRef] [PubMed]

]. The cooled atoms were loaded into a vertically one-dimensional optical lattice operating at fmagic = 368.5545 THz. The lattice laser frequency was monitored during the measurement with a calibrated wavelength meter and its fluctuation was kept within 300 MHz. The trap depth of the lattice laser was 28 Er (the lattice photon recoil energy Er/kB = 165 nK). The atoms were optically pumped to the Zeeman sublevel mF = ± 9/2 by using a weak light resonant with 1S0-3P1. The typical spectrum of a Zeeman component is shown in Fig. 2(a)
Fig. 2 Typical stretched state spectrum of the clock transition of (a) the Sr OLC and (b) the Yb OLC. The interrogation pulse durations were 40 ms in both cases.
for an interrogation time of 40 ms. A Fourier limited linewidth of 22 Hz was observed with a large excitation probability resulting a good signal-to-noise ratio for the spectrum.

The Yb OLC at the NMIJ is operated with non spin-polarized 171Yb atoms. The Yb OLC has been described previously [12

12. M. Yasuda, H. Inaba, T. Kohno, T. Tanabe, Y. Nakajima, K. Hosaka, D. Akamatsu, A. Onae, T. Suzuyama, M. Amemiya, and F.-L. Hong, “Improved absolute frequency measurement of the 171Yb optical lattice clock towards a candidate for the redefinition of the second,” Appl. Phys. Express 5(10), 102401 (2012). [CrossRef]

]. After 1st stage cooling by a laser at 399 nm, the atoms were further cooled to a few tens of μK by using the inter-combination transition 1S0-3P1 [25

25. M. Yasuda, T. Kohno, H. Inaba, Y. Nakajima, K. Hosaka, A. Onae, and F.-L. Hong, “Fiber-comb-stabilized light source at 556 nm for magneto-optical trapping of ytterbium,” J. Opt. Soc. Am. B 27(7), 1388–1393 (2010). [CrossRef]

]. The cooled atoms were loaded into a horizontally oriented one-dimensional optical lattice operating at fmagic = 394 798. 337 GHz. The lattice laser frequency was stabilized to a third optical frequency comb [not shown in Fig. 1] using a delay line lock technique with an uncertainty of 10 MHz. The trap depth of the lattice laser was 500 Er (the lattice photon recoil energy Er/kB = 97 nK). The typical spectrum of the Yb clock transition is shown in Fig. 2(b) for a 40 ms interrogation pulse. The observed linewidth was broader than the Fourier limited linewidth because of the saturation broadening. Both OLCs were located in the same laboratory room.

For the clock operation, the clock laser was frequency-stabilized to both stretched states (mF = ± 9/2 for Sr OLC; mF = ± 1/2 for Yb OLC) using an acousto-optic modulator (AOM1 for Sr OLC; AOM2 for Yb OLC) to eliminate the first-order Zeeman shift. The clock laser alternately probed the high- and low-frequency points at the full width of half maximum of the stretched state spectrum. A single probe cycle was 2 s for the Sr OLC and 1 s for the Yb OLC. The RF frequency driving the AOMs was controlled to equalize the excitation probabilities such that p+FWHM(±mF)=pFWHM(±mF). The average RF frequency (fAOMSr(Yb)) determined the center frequency of the clock transition without the first-order Zeeman shift. We simultaneously operated the Sr and Yb OLCs for the frequency ratio measurement.

3. Experimental results

The absolute frequency of the Sr (Yb) can be calculated by
νSr=nSrfrep#1+fCEO#1+fbeat#1+fAOMSr
(1)
νYb=nYbfrep#2+fCEO#2+fbeat#2+fAOMYb.
(2)
As we described in the experimental setup section,
frep#1=frep#2=frep
(3)
fCEO#1=fCEO#2=fCEO.
(4)
Therefore, the frequency ratio measurement of the clock transitions can be derived as
νYbνSr=r(1+r)fCEOfbeat#2fAOMYb+r(fbeat#1+fAOMSr)νSr,
(5)
where r=nYb/nSr1.2. Since the radio frequencies are divided by the optical frequency in the second term, the term is of the order of 10−6. Therefore the measurement uncertainty of the frequency ratio would be at the 1016 level even with the 10−10 measurement uncertainties for the radio frequencies [17

17. K. Matsubara, H. Hachisu, Y. Li, S. Nagano, C. Locke, A. Nogami, M. Kajita, K. Hayasaka, T. Ido, and M. Hosokawa, “Direct comparison of a Ca+ single-ion clock against a Sr lattice clock to verify the absolute frequency measurement,” Opt. Express 20(20), 22034–22041 (2012). [CrossRef] [PubMed]

].

Figure 3(a)
Fig. 3 (a) Frequency ratio measurements of Sr and Yb optical lattice clocks. The error bars are statistical. Data shown in this figure include the systematic corrections. (b) Allan standard deviation of the frequency ratio measurement for the measurement number 3 in Fig. 3(a).
shows 4 frequency ratio measurement results, where the corrections are included. Figure 3(b) shows a typical Allan standard deviation of the measured frequency ratio [# 3 in Fig. 3(a)]. The Allan standard deviation was 9.9 × 10−15 for an 8 s averaging time. The short-term stability is determined by that of the master laser. We note that if we used the clock lasers own ULE cavities, the short-term stability would become worse by a factor of the square root of two assuming the cavities have the same specifications as the cavity for the master laser. The Allan standard deviation is improved to 2.0 × 10−15 after an 840 s averaging time. Since the experiment was a direct comparison of the optical frequencies, the obtained Allan deviation was much smaller than that of the microwave reference used in the absolute frequency measurement. The error bars were determined by the Allan standard deviation at the longest averaging time for each measurement [e.g. the uncertainty for measurement # 3 in Fig. 3(a) was calculated by using the Allan standard deviation in Fig. 3(b)].

The corrections and uncertainties for the frequency ratio measurement were calculated from those for the Sr and Yb OLCs (Table 1

Table 1. The fractional uncertainties and corrections of the Sr OLC, Yb OLC, and the frequency ratio measurement. The asterisks represent the value depending on the measurements.

table-icon
View This Table
). The largest corrections for both the Sr and Yb OLCs were due to the blackbody radiation (BBR) shifts. The BBR corrections for the Sr OLC (Yb OLC) was estimated to be 55.3(2.3) × 10−16 (25.2(2.0) × 10−16) for the measured temperature of the vacuum chamber T = 303(3) K (T = 302(3)K). The evaluated ac Stark shift including the hyperpolarizability for the Sr OLC (Yb OLC) by the lattice laser was 0.0(3.6) × 10−16 (2.1(2.4) × 10−16). The light shifts induced by the clock laser for the Sr OLC and Yb OLC were conservatively estimated to be −0.2(2) × 10−16 and 0.8(2) × 10−16, respectively, using the measured clock laser intensities (0.3 mW/cm2 for Sr; 2.3 mW/cm2 for Yb). For evaluations of the second-order Zeeman and collision shifts for Sr OLC, we interleaved two independent stabilization sequences with switching the parameter of interest between two values and determined the shifts due to the different physical conditions (interleaved method). The second-order Zeeman shift caused by a bias magnetic field of 91 μT was evaluated to be −4.3 (1.1) × 10−16 for the Sr OLC. The collision shifts for the Sr OLC was estimated to be 0.0(2.1) × 10−16. The second-order Zeeman shift for Yb OLC caused by a bias magnetic field of 170 μT was evaluated to be −3.8(4) × 10−16 using the coefficient in ref [13

13. N. D. Lemke, A. D. Ludlow, Z. W. Barber, T. M. Fortier, S. A. Diddams, Y. Jiang, S. R. Jefferts, T. P. Heavner, T. E. Parker, and C. W. Oates, “Spin-1/2 optical lattice clock,” Phys. Rev. Lett. 103(6), 063001 (2009). [CrossRef] [PubMed]

]. The collisional shift was estimated to be −0.3(2.6) × 10−16 using the data in ref [13

13. N. D. Lemke, A. D. Ludlow, Z. W. Barber, T. M. Fortier, S. A. Diddams, Y. Jiang, S. R. Jefferts, T. P. Heavner, T. E. Parker, and C. W. Oates, “Spin-1/2 optical lattice clock,” Phys. Rev. Lett. 103(6), 063001 (2009). [CrossRef] [PubMed]

], the estimated similar trap volume and our number of atoms (n0 ≈103; we conservatively supposed its uncertainty of 10 × n0). We neglected the gravitational shift between the two clocks due to the height difference of 56(5) mm.

In the experiment, we found a relatively large servo error for the Sr OLC. In the clock laser frequency stabilization to the clock transition, the excitation probabilities for high- and low-frequency points p+FWHM(mF=±9/2),pFWHM(mF=±9/2) were not the same value because of the clock laser linear drift and the weak feedback servo gain, which results in a residual frequency offset for the Sr OLC. We determined the frequency offset for each measurement from the difference between the averaged excitation probabilities using the lineshape shown in Fig. 2(a). Since the correction of the servo error depends on the measurement number, we express the corrections in Table 1 using asterisks. The uncertainty was determined from the statistical deviation of the mean of the excitation probability difference.

The frequency ratio of Yb/Sr was determined from the weighted mean of the four measurements shown in Fig. 3(a) to be 1.207 507 039 343 340 4(18). The fractional standard uncertainty of the frequency ratio 1.5 × 10−15 was determined by combining the systematic uncertainty (8.1 × 10−16) with the statistical uncertainty of the measurements (1.3 × 10−15).

4. Discussion and conclusion

The uncertainty of the measured frequency ratio is limited by the statistical uncertainty in the experiment. With a longer averaging time, the statistical uncertainty could be reduced and the measurement uncertainty would eventually be limited by the systematic uncertainties of the OLCs. Uncertainty evaluations at the 10−17-10−18 level for Sr optical lattice clocks have been demonstrated recently at several laboratories [3

3. B. J. Bloom, T. L. Nicholson, J. R. Williams, S. L. Campbell, M. Bishof, X. Zhang, W. Zhang, S. L. Bromley, and J. Ye, “An optical lattice clock with accuracy and stability at the 10-18 level,” Nature 506(7486), 71–75 (2014). [CrossRef] [PubMed]

, 7

7. R. Le Targat, L. Lorini, Y. Le Coq, M. Zawada, J. Guéna, M. Abgrall, M. Gurov, P. Rosenbusch, D. G. Rovera, B. Nagórny, R. Gartman, P. G. Westergaard, M. E. Tobar, M. Lours, G. Santarelli, A. Clairon, S. Bize, P. Laurent, P. Lemonde, and J. Lodewyck, “Experimental realization of an optical second with strontium lattice clocks,” Nat. Commun. 4, 2109 (2013). [PubMed]

, 9

9. S. Falke, H. Schnatz, J. S. R. V. Winfred, T. Middelmann, S. Vogt, S. Weyers, B. Lipphardt, G. Grosche, F. Riehle, U. Sterr, and C. Lisdat, “The 87Sr optical frequency standard at PTB,” Metrologia 48(5), 399–407 (2011). [CrossRef]

]. Therefore, the uncertainty of the frequency ratio measurement is expected to reach the 10−17-10−18 level. For such an experiment, synchronized interrogation [19

19. M. Takamoto, T. Takano, and H. Katori, “Frequency comparison of optical lattice clocks beyond the Dick limit,” Nat. Photonics 5(5), 288–292 (2011). [CrossRef]

] would be a powerful tool for improving the short-term stability and hence reduce the total measurement time.

Acknowledgments

This research receives support from the JSPS through its FIRST Program and JSPS KAKENHI Grant Numbers 13222778 and 23540472.

References and links

1.

C. W. Chou, D. B. Hume, J. C. J. Koelemeij, D. J. Wineland, and T. Rosenband, “Frequency comparison of two high-accuracy Al+ optical clocks,” Phys. Rev. Lett. 104(7), 070802 (2010). [CrossRef] [PubMed]

2.

N. Hinkley, J. A. Sherman, N. B. Phillips, M. Schioppo, N. D. Lemke, K. Beloy, M. Pizzocaro, C. W. Oates, and A. D. Ludlow, “An atomic clock with 10-18 instability,” Science 341(6151), 1215–1218 (2013). [CrossRef] [PubMed]

3.

B. J. Bloom, T. L. Nicholson, J. R. Williams, S. L. Campbell, M. Bishof, X. Zhang, W. Zhang, S. L. Bromley, and J. Ye, “An optical lattice clock with accuracy and stability at the 10-18 level,” Nature 506(7486), 71–75 (2014). [CrossRef] [PubMed]

4.

C. W. Chou, D. B. Hume, T. Rosenband, and D. J. Wineland, “Optical clocks and relativity,” Science 329(5999), 1630–1633 (2010). [CrossRef] [PubMed]

5.

M. Takamoto, F.-L. Hong, R. Higashi, and H. Katori, “An optical lattice clock,” Nature 435(7040), 321–324 (2005). [CrossRef] [PubMed]

6.

G. K. Campbell, A. D. Ludlow, S. Blatt, J. W. Thomsen, M. J. Martin, M. H. G. de Miranda, T. Zelevinsky, M. M. Boyd, J. Ye, S. A. Diddams, T. P. Heavner, T. E. Parker, and S. R. Jefferts, “The absolute frequency of the 87Sr optical clock transition,” Metrologia 45(5), 539–548 (2008). [CrossRef]

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D. Akamatsu, H. Inaba, K. Hosaka, M. Yasuda, A. Onae, T. Suzuyama, M. Amemiya, and F.-L. Hong, “Spectroscopy and frequency measurement of the 87Sr clock transition by laser linewidth transfer using an optical frequency comb,” Appl. Phys. Express 7(1), 012401 (2014). [CrossRef]

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13.

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K. Matsubara, H. Hachisu, Y. Li, S. Nagano, C. Locke, A. Nogami, M. Kajita, K. Hayasaka, T. Ido, and M. Hosokawa, “Direct comparison of a Ca+ single-ion clock against a Sr lattice clock to verify the absolute frequency measurement,” Opt. Express 20(20), 22034–22041 (2012). [CrossRef] [PubMed]

18.

H. Inaba, K. Hosaka, M. Yasuda, Y. Nakajima, K. Iwakuni, D. Akamatsu, S. Okubo, T. Kohno, A. Onae, and F.-L. Hong, “Spectroscopy of 171Yb in an optical lattice based on laser linewidth transfer using a narrow linewidth frequency comb,” Opt. Express 21(7), 7891–7896 (2013). [CrossRef] [PubMed]

19.

M. Takamoto, T. Takano, and H. Katori, “Frequency comparison of optical lattice clocks beyond the Dick limit,” Nat. Photonics 5(5), 288–292 (2011). [CrossRef]

20.

Y. Nakajima, H. Inaba, K. Hosaka, K. Minoshima, A. Onae, M. Yasuda, T. Kohno, S. Kawato, T. Kobayashi, T. Katsuyama, and F.-L. Hong, “A multi-branch, fiber-based frequency comb with millihertz-level relative linewidths using an intra-cavity electro-optic modulator,” Opt. Express 18(2), 1667–1676 (2010). [CrossRef] [PubMed]

21.

K. Iwakuni, H. Inaba, Y. Nakajima, T. Kobayashi, K. Hosaka, A. Onae, and F.-L. Hong, “Narrow linewidth comb realized with a mode-locked fiber laser using an intra-cavity waveguide electro-optic modulator for high-speed control,” Opt. Express 20(13), 13769–13776 (2012). [CrossRef] [PubMed]

22.

D. Akamatsu, Y. Nakajima, H. Inaba, K. Hosaka, M. Yasuda, A. Onae, and F.-L. Hong, “Narrow linewidth laser system realized by linewidth transfer using a fiber-based frequency comb for the magneto-optical trapping of strontium,” Opt. Express 20(14), 16010–16016 (2012). [CrossRef] [PubMed]

23.

F.-L. Hong, H. Inaba, K. Hosaka, M. Yasuda, and A. Onae, “Doppler-free spectroscopy of molecular iodine using a frequency-stable light source at 578 nm,” Opt. Express 17(3), 1652–1659 (2009). [CrossRef] [PubMed]

24.

D. Akamatsu, M. Yasuda, T. Kohno, A. Onae, and F.-L. Hong, “A compact light source at 461 nm using a periodically poled LiNbO3 waveguide for strontium magneto-optical trapping,” Opt. Express 19(3), 2046–2051 (2011). [CrossRef] [PubMed]

25.

M. Yasuda, T. Kohno, H. Inaba, Y. Nakajima, K. Hosaka, A. Onae, and F.-L. Hong, “Fiber-comb-stabilized light source at 556 nm for magneto-optical trapping of ytterbium,” J. Opt. Soc. Am. B 27(7), 1388–1393 (2010). [CrossRef]

OCIS Codes
(120.3940) Instrumentation, measurement, and metrology : Metrology
(140.4050) Lasers and laser optics : Mode-locked lasers
(140.3425) Lasers and laser optics : Laser stabilization
(020.3320) Atomic and molecular physics : Laser cooling

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: February 10, 2014
Revised Manuscript: March 19, 2014
Manuscript Accepted: March 20, 2014
Published: March 27, 2014

Citation
Daisuke Akamatsu, Masami Yasuda, Hajime Inaba, Kazumoto Hosaka, Takehiko Tanabe, Atsushi Onae, and Feng-Lei Hong, "Frequency ratio measurement of 171Yb and 87Sr optical lattice clocks," Opt. Express 22, 7898-7905 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-7-7898


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References

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  19. M. Takamoto, T. Takano, H. Katori, “Frequency comparison of optical lattice clocks beyond the Dick limit,” Nat. Photonics 5(5), 288–292 (2011). [CrossRef]
  20. Y. Nakajima, H. Inaba, K. Hosaka, K. Minoshima, A. Onae, M. Yasuda, T. Kohno, S. Kawato, T. Kobayashi, T. Katsuyama, F.-L. Hong, “A multi-branch, fiber-based frequency comb with millihertz-level relative linewidths using an intra-cavity electro-optic modulator,” Opt. Express 18(2), 1667–1676 (2010). [CrossRef] [PubMed]
  21. K. Iwakuni, H. Inaba, Y. Nakajima, T. Kobayashi, K. Hosaka, A. Onae, F.-L. Hong, “Narrow linewidth comb realized with a mode-locked fiber laser using an intra-cavity waveguide electro-optic modulator for high-speed control,” Opt. Express 20(13), 13769–13776 (2012). [CrossRef] [PubMed]
  22. D. Akamatsu, Y. Nakajima, H. Inaba, K. Hosaka, M. Yasuda, A. Onae, F.-L. Hong, “Narrow linewidth laser system realized by linewidth transfer using a fiber-based frequency comb for the magneto-optical trapping of strontium,” Opt. Express 20(14), 16010–16016 (2012). [CrossRef] [PubMed]
  23. F.-L. Hong, H. Inaba, K. Hosaka, M. Yasuda, A. Onae, “Doppler-free spectroscopy of molecular iodine using a frequency-stable light source at 578 nm,” Opt. Express 17(3), 1652–1659 (2009). [CrossRef] [PubMed]
  24. D. Akamatsu, M. Yasuda, T. Kohno, A. Onae, F.-L. Hong, “A compact light source at 461 nm using a periodically poled LiNbO3 waveguide for strontium magneto-optical trapping,” Opt. Express 19(3), 2046–2051 (2011). [CrossRef] [PubMed]
  25. M. Yasuda, T. Kohno, H. Inaba, Y. Nakajima, K. Hosaka, A. Onae, F.-L. Hong, “Fiber-comb-stabilized light source at 556 nm for magneto-optical trapping of ytterbium,” J. Opt. Soc. Am. B 27(7), 1388–1393 (2010). [CrossRef]

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