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We develop a method of modified hyper-Ramsey spectroscopy in optical clocks, achieving complete immunity to the frequency shifts induced by the probing fields themselves. Using particular pulse sequences with tailored phases, frequencies, and durations, we can derive an error signal centered exactly at the unperturbed atomic resonance with a steep discriminant which is robust against variations in the probe shift. We experimentally investigate the scheme using the magneticallyinduced 1 S0− 3 P0 transition in 88 Sr, demonstrating automatic suppression of a sizeable 2 × 10 −13probe Stark shift to below 1 × 10 −16 even with very large errors in shift compensation.PACS numbers: 32.70. Jz,06.30.Ft,32.60.+i,42.62.Fi High-Q interrogation of narrow, forbidden optical transitions has formed the basis of a new generation of atomic clocks with exceptional accuracy and stability at the 10 −18 level [1,2]. As well as potentially supporting a redefinition of the SI second [3], such clocks underpin empirical investigations into areas of fundamental physics including relativity [4], the search for dark matter [5,6], and potential time-variation of fundamental constants [7,8]. However, several promising atomic species suffer from a clock transition which is too forbidden, requiring a high laser intensity − and therefore a large light shift − in order to drive the atoms into the excited state. Important examples include clocks based on high-order multipole [9, 10], two-photon [11,12], or magnetically-induced [13][14][15] transitions. Before these species can be used for precision frequency measurements, probe-induced shifts must be dealt with.A conceptually straightforward approach to the light shift is exemplified by recent realizations of the electricoctupole 2 S 1/2 → 2 F 7/2 171 Yb + clock, where the unperturbed atomic resonance is extrapolated from interleaved Rabi-spectroscopy sequences of high and low probe intensity [7,9]. Although careful extrapolation can be quite effective, achieving frequency uncertainty nearly 4 orders of magnitude smaller than the shift itself [7], the stability of the clock is deteriorated by the extrapolation process and the ultimate accuracy is limited by the precision with which the probe intensity ratio can be calibrated.In order to reduce the burden of probe intensity control, tailored spectroscopy pulses have been proposed which provide a central feature whose frequency is unchanged by the light shift [16][17][18][19]. The great potential of this approach has recently been illustrated using Yb + , where "hyper-Ramsey" spectroscopy was utilized to suppress the shift by more than four orders of magnitude below the 10 −17 level [20]. In this Letter, we propose a modified form of hyper-Ramsey spectroscopy which provides complete immunity to variations in the probe shift, considerably relaxing the experimental constraints on intensity control and potentially facilitating light shift uncertainties well below 10 −18 in Yb + . As indicated by the experimental results of this Letter, sub-10 −18 shi...

An absolute frequency measurement has been made of the 2 S 1/2 -2 F 7/2 electric octupole transition in a single ion of 171 Yb + . The implementation of a diode-based probe laser stabilized to this highly forbidden transition has resulted in an improvement of more than one order of magnitude upon the lowest published uncertainty. After correcting for systematic shifts, the frequency was determined to be 642 121 496 772 646.22 (67) Hz. This corresponds to a fractional uncertainty of 1.0 × 10 −15 .

Article (Published Version) http://sro.sussex.ac.uk Meyer, V, Boshier, M G and et al, (2000) Measurement of the 1s-2s energy interval in muonium.

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We have observed the narrow 1S-2S transition in hydrogen and deuterium with high resolution using Doppler-free two-photon absorption of continuous-wave 243-nm light. The transition frequencies were measured by direct comparison with accurately calibrated lines in the spectrum of the "Te2 molecule. We find the 1S-2S interval to be 2466061414.1(8) MHz in hydrogen and 2466732408.5(7) MHz in deuterium. By combining these results with recent measurements of the Rydberg constant we obtain the values 8172.6(7) and 8183.7(6) MHz for the 1S Lamb shifts in hydrogen and deuterium, respectively. These are the most precise measurements of the 1S Lamb shifts in these atoms and they are in excellent agreement with the theoretical values of 8173.03(9) and 8184.08(12) MHz. Alternatively, if the 1S Lamb shift is supposed known from theory, our measurements determine the Rydberg constant as R = 109 737.315 73 (3) cm Recently, the 1S-2S transition in hydrogen was observed using this source and its frequency was measured. ' By using an accurate value of the Rydberg constant it was possible to extract the Lamb shift. This calibration procedure is essentially the same comparison of hydrogen transitions used in the early experiments, but with several intermediate steps linking the two transitions. Our work at Oxford University" has concentrated on the development of frequency doubling as a means of generating cw 243-nm light because it offers the longterm prospect of a direct comparison of the 1S-2S and Balmer-P transitions. In this paper we describe the first experiment on hydrogen 1S-2S using cw 243-nm light generated by frequency doubling. ' ' We have measured the 1S-2S transition frequency f (1S-2S) in both hydrogen and deuterium. As in Ref. 9 our determination of the Lamb shift uses an indirect calibration via the Rydberg constant; however, the use of frequency doubling reduces the number of intermediate steps and by employing two lasers it was possible to calibrate the measurement using accurate heterodyne techniques.These improvements lead to a value of the hydrogen 1S Lamb shift which is a factor of 3 more precise than the previous value, and to the first cw measurement of the 1S Lamb shift in deuterium, improving the precision in this case by a factor of 50. An alternative interpretation of our measurements is pos-40 6169

The field isotope shift constant Cunif for a uniform nuclear charge distribution has been re-evaluated for s-electrons for elements with 10_< Z_< 95. A table is given which permits Cunif to be found for any isotope pair.Measurements of optical isotope shifts are usually undertaken in order to study the differences in the nuclear charge distributions of the isotopes of an element [1]. The observed shift consists of two contributions, a mass shift and a field shift, the latter containing the dependence on the nuclear charge distributions. In the interpretation of the results, it is usual to compare the field shift with that expected on the basis of a simple nuclear model, a uniformly charged sphere of radius 1.2A 1/3 fm where A is the mass number. This procedure is used to set the scale of the nuclear data which are extracted. It is thus necessary to have available results calculated on the basis of this model and several tabulations are given in the literature. They are expressed as values of the isotope shift constant Cunif, where the field isotope shift for a valence s-electron according to the model is given in wavenumbers by [2] (~ O'unif = I O (0)12 X ~za3 x Cunif. Z The quantity I t)(0)l 2 is the non-relativistic probability density of the s-electron at the origin. The calculation of values of Cun~f involves solving the Dirac equation for the valence s-electron in the vicinity of the nucleus. Different authors have made slightly different physical approximations, but, more seriously, the most frequently quoted [3, 4, 5] make mathematical approximations (in particular, truncations of series expansions) which lead to inac-* Dedicated to Prof. Dr. A. Steudel on the occasion of his 60th birthday curacy in the results for heavy elements. In consequence, experimentalists consulting the literature cannot rely on the published data to better than 10% in this region of the periodic table. Such a situation is very unsatisfactory since the measurements are often much more precise than this. An improved calculation of 6au,if following the method of approach of previous authors and removing the imperfections in published work will appear in a separate paper [6]. Our intention here is to give a definitive table of values of Cunif. We make certain physical approximations (as in [5]) in order to allow the form of the wave function of the valence selectron to be completely specified in the region of interest. They are:(i) The screening of the nuclear potential by core electrons in the vicinity of the nucleus is negligible.(ii) The form of the electron wave function in the vicinity of the nucleus differs negligibly from that appropriate to zero binding energy.It has been shown [7] that when the value of 10(0)12 is derived from hyperfine structure measurements these two approximations lead to very small errors, the largest being around 1% (in heavy elements). The normalization of the relativistic electron wavefunction in our calculations has been expressed in terms of I~p(0)l 2 in the same way as has been used in hyperfine str...