Abstract

We report the measurement of the absolute frequencies of the 6s21S06s6p 3P1 transition (253.7 nm) and the relevant isotope shifts in five mercury isotopes  198Hg,  199Hg,  200Hg,  202Hg, and  204Hg. The Doppler-free saturated absorption measurements were performed in an atomic vapour cell at room temperature with a four-harmonic generated (FHG) continuous-wave (cw) laser digitally locked to the atomic transition. It was referenced with a femtosecond optical frequency comb synchronized to the frequency of local representation of the International Atomic Time to provide traceability to the SI second by the 330 km-long stabilized fibre optical link. The transition frequencies and isotope shifts have been determined with an accuracy of a few hundred kHz, at least one order of magnitude better than any previous measurement. By making a King plot with the isotope shifts of 6s6p 3P26s7s 3S1 transition (546 nm) we determined the accurate value of the ratio of the electronic field-shift parameters E546/E254 and estimated the electronic field-shift term E254.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

The study of spectral lines of mercury has been a subject of interest for more than a century. It dates back to 1891 when Kaiser and Runge published a collection of over 90 different spectroscopic lines [1]. Further spectroscopic studies on mercury were carried out by Moore [2] and Reader [3] and extended by Sansonetti and Martin [4]. The hyperfine-structure intervals of the stable fermions  199Hg and  201Hg were measured with a double-resonance technique by Kohler [5] and Stager [6]. Schweitzer presented isotopic shifts for  1S03P1 transition using interferometric techniques on the absorption spectrum of the atomic beam [7]. A well detailed compilation of wavelengths and energy levels for the spectrum of  198Hg and for the natural isotope mixture of neutral mercury was reported by Saloman [8]. He presented the most accurate values to date for a wavelength range from 200 to 2000 nm. A major revision of  198Hg spectral lines was performed by Kramida [9] who examined experimental results in the context of possible systematic shifts also due to different reference standards that have changed over the years.

With the advent of high power diode lasers and a non-linear frequency conversion, precise spectroscopic measurements became available for several elements whose wavelengths were not reachable with commercially available laser diodes. Among those elements mercury is of particular importance due to its special advantages. Large mass makes mercury suitable for “new physics” experiments [10] like parity-violation studies [11], search for electron electric dipole moment [12–14], and measurements of the time-variability of the fine-structure constant [15]. Furthermore, mercury is regarded as a very good candidate for an optical frequency standard, mainly due to its very low blackbody radiation shift [16, 17]. Also, relatively strong intercombination transition  1S03P1, favourable for laser cooling with a Doppler limit at 31 μK, and a variety of isotopes make mercury a very interesting element from an experimental point of view.

Neutral mercury has seven stable isotopes, including five bosons:  196Hg (0.15%),  198Hg (9.97%),  200Hg (23.1%),  202Hg (29.86%),  204Hg (6.87%) and two fermions:  199Hg (16.87%),  201Hg (13.18%) [18]. Except for the  196Hg, the natural abundances allow for trapping each of the isotopes. In fact, several groups succeeded in cooling and trapping of different mercury isotopes in a magneto-optical trap taking advantage of  1S03P1 transition [16, 17, 19–22].

In this work we present an absolute frequency determination of the intercombination transition  1S03P1 for four bosons ( 198Hg,  200Hg,  202Hg,  204Hg) and for one of the hyperfine transitions (F=1/2F=1/2) in fermionic  199Hg. The Doppler-free saturated spectroscopy measurements were performed with the FHG cw laser light digitally locked to an atomic transition in Hg atomic vapour cell and referenced with an optical frequency comb synchronized to the frequency of the local representation of the UTC.

We determined also the isotope shifts values referenced to  198Hg and compared with previously reported data. By making the King plot [23] with the corresponding data for  3P2 3S1 (546 nm) transition [24] we determined the ratio of electronic field-shift factors of 254 nm and 546 nm lines. The King plot analysis has been shown to be a very promising tool for fundamental physics research and for search for “new physics” beyond the Standard Model [25–27].

2. Experimental setup and procedure

The scheme of the experimental setup is presented in Fig. 1. The core of the laser system is based on the FHG (1014.8→253.7 nm) setup described in detail elsewhere [22, 28], so only its most important features are presented below. The source of the fundamental laser light consists of a home-made external-cavity laser diode (ECDL) operating at 1014.8 nm and a tapered amplifier (Sacher Lasertechnic) which amplifies the power of the laser beam up to 1.2 W. For a frequency quadrupling two bow-tie build-up cavities (Leos Company) are used with lithium triborate and beta barium borate crystals for the first (1014.8→ 507.4 nm) and the second (507.4→253.7 nm) doubling stage, respectively.

 

Fig. 1 A simplified scheme of the laser setup. A fourth harmonic generation laser system delivers up to 30 mW of the 253.7 nm laser light which is frequency shifted by a double-pass transition in the acousto-optical modulator AOM1 and then directed to a mercury cell. A Doppler-free saturation absorption signal is used to monitor a deviation of the UV laser frequency from an atomic transition of a given Hg isotope. A part of the 1014.8 nm laser light is transferred through an AOM2 to a transfer cavity. The cavity length is stabilized to the wavelength of a 689 nm laser while the 1014.8 nm laser wavelength is locked to one of the cavity modes. The frequency of the 1014.8 nm laser is compared via the optical frequency comb to the frequencies of UTC(AOS) and UTC(PL) [29, 30] via the stabilized fibre optic link [31] of the OPTIME network [32, 33]. DDS stands for a direct digital synthesizer, PC – a desktop computer, μ-c – a microcontroller, PD – a photodiode, and PDH – Pound-Drever-Hall locking technique.

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The FHG system delivers up to 30 mW of the UV 253.7 nm laser light. A part of the light is frequency shifted by an acousto-optical modulator AOM1 and sent to a 1 mm thick cylindrical shape fused silica absorption cell containing Hg vapours. We take advantage of the Doppler-free saturation spectroscopy signal to monitor a deviation of the UV laser frequency from an atomic resonance of a given Hg isotope. The deviation is tracked by a digital locking technique [31, 34] which provides a feedback correction signal sent to the AOM1.

 

Fig. 2 Schematic illustration of the background-induced frequency shift of the typical saturated absorption spectral line. a) a symmetrical profile; the red solid curve shows the slope-dependent SNR in the digital locking technique. b) a profile with a linear background. c) a profile with a linear (grey) and a non-linear (black) background. The red (panel b) and green (panel c) circles correspond to the probed range 2δf in the linear and the non-linear background case, respectively. The inflection points of the profile are marked with the blue circles. f0 (blue arrow) is a non-shifted frequency, fSNR (red arrow) and fSNR+NL (green arrow) are the frequencies obtained with f+ and f calculated from maximal SNR of fUV signal with the linear and the non-linear background, respectively.

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The AOM1 is driven by a direct digital synthesizer (DDS), and square-wave modulates the light frequency with the step 2δf (see Fig. 2(a)). The AOM1 carrier frequency fAOM1 is chosen such that the AOM1 efficiency for f+=fAOM1+δf and f=fAOM1δf is the same. The microcontroller (μC - STM32F ARM) records the absorption signals detected by a photodiode (PD). The error signal for the laser lock is calculated from the difference of the signals corresponding to the absorption for f+ and f. The software PI regulator in the μC calculates and sends the correction signal to a direct digital synthesizer (DDS) which controls the frequency of the AOM1.

The frequency fAOM1 recorded by a PC, is used later together with the frequency measured with the optical frequency comb to determine the transition frequency fUV. The optimal difference between frequencies 2δf=f+f was found by maximizing signal-to-noise (SNR) of the measured fUV signal. We typically probed a few thousand samples for each measured frequency which resulted in the accuracy allowing for sub-natural linewidth measurements. This scheme enables keeping the frequency of the UV laser light on the atomic resonance with the response time limited by an acquisition time (typically a few tens of ms). A sample saturated absorption line used in digital locking is shown in zoomed part of Fig. 3. The line is power broadened and averaged about ten times for better visibility.

 

Fig. 3 Top: structure of the 254 nm line in the natural isotopic composition of mercury based on the data published by Schweitzer [35] and Zadnik [36]. Red and blue colour corresponds to bosons and fermions, respectively. The letters indicate the following hyperfine components: F = 1/2 (a), F = 3/2 (b), and F = 5/2 (c). The line strengths are normalized to the most abundant isotope, i.e. 202Hg. Bottom: a typical saturated absorption spectroscopy signal recorded in our measurements, averaged about ten times and power broadened for better visibility.

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For the saturation spectroscopy setup, we used a typical technique overlapping a pump and a probe beam in a retroreflected configuration. To ensure the proper overlapping of the beams, a pair of pinholes were set before and after the cell. Both beams were linearly polarized with the polarization planes perpendicular to each other. To exclude the residual Doppler shift, the beams are not focused. The typical power of the pump beam is about 1 mW and its diameter is about 2 mm. To provide more stable conditions, the cell was enclosed in a box. The temperature inside the box was continuously recorded during measurements to verify the thermal stability.

To stabilize the frequency of the 1014.8 nm laser, and consequently the frequency of the UV laser beam, the following scheme has been implemented. A part of the 1014.8 nm laser beam double-passes the AOM2 which shifts the frequency of the beam in the range between 80 and 240 MHz either into the red or the blue side depending on the Hg isotope. Afterwards, the laser beam is sent through a single-mode polarization maintaining fibre to the transfer cavity. The length of the transfer cavity is stabilized to the wavelength of a 689 nm laser. The 689 nm laser is itself frequency stabilized to a high-Q ultra-stable ultra-low expansion glass cavity and disciplined to a narrow 7.5 kHz  1S03P1 transition in Sr, leading to sub-kHz stability [37].

The transfer cavity transfers the stability of the 689 nm laser to the 1014.8 nm laser. To stabilize the length of the transfer cavity one of its mirrors is mounted on a piezo-ceramic tube. The Pound-Drever-Hall (PDH) locking scheme [38] generates the error signal which is fed into a high-speed servo controller (LB1005, New Focus) that controls the piezoelectric transducer in the cavity. A similar method is used for the frequency stabilization of the 1014.8 nm ECDL. A fast analog PID controller (FALC, Toptica) converts a PDH error signal into a voltage control signal which is fed back to the ECDL. By tuning the temperature of the transfer cavity we are able to simultaneously match different frequency modes with the frequencies of 689 and 1014.8 nm light. Combination of a broad tuning range of the 1014.8 nm ECDL and the thermal tuning of the transfer cavity makes all Hg isotopes attainable.

 

Fig. 4 A scheme of the relevant frequencies, both radio (denoted by f) and optical (denoted by ν), used in the experimental setup. The coloured arrows indicate schematic paths of the laser beams while the black arrows correspond to the RF signalssent to a PC-based data acquisition system.

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To facilitate the absolute frequency measurements, a part of the 1014.8 nm laser beam sent to an optical frequency comb (FC1500, MenloSystems). To provide traceability to the SI second, the optical frequency comb is referenced to the frequencies of UTC(AOS) and UTC(PL) [29, 30] via the 330 km-long stabilized fibre optic link [31] of the OPTIME network [32, 33]. The frequency fB of the beat between a comb mode and the 1014.8 nm laser beam is detected with two photodiodes, one providing the beat note signal and the other gating signal to increase the SNR in the beat note. The gating is achieved by mixing bothsignals in a double-balanced mixer according to the method described in [39]. The absolute frequency fUV of the 253.7 nm laser beam is given as

fUV=4(fo+nfR±fB2fAOM2)+2fAOM1,
where fo is a carrier-envelope offset frequency, n is optical frequency comb mode number, fR is a repetition rate of the comb, fAOM1 and fAOM2 are the AOMs’ driving frequencies. A simplified scheme of all frequencies essential for the absolute measurements is shown in Fig. 4. All mentioned frequencies are monitored continuously and recorded by a desktop computer, as seen in Fig. 4, and monitored continuously. Our data acquisition software synchronizes the Hg saturation spectroscopy measurement and the frequency of the beat note between the 1014.8 nm laser beam and the comb mode.

3. Results and discussion

The experimental data were acquired over seven days according to a timeline shown in Fig. 5. To determine the absolute values of the intercombination transition for Hg isotopes, several effects, such as AC-Stark shift, pressure shift, Zeeman shift and the locking scheme factor, should be taken into account. In the following, we discuss the influence of these effects on the results. The results of the systematic shifts and their uncertainties are listed in Table 1.

 

Fig. 5 Results of the absolute frequency measurements for 1S03P1 transition in Hg isotopes. Both sample standard deviation (red error bars) and mean standard deviation (black error bars) for a given measurement are shown. The red dotted lines and the blue dashed lines are statistical and total (including statistical and systematic) uncertainties, respectively, as listed in Table 2.

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3.1. Digital lock and line pulling

As shown in Table 3 and in Fig. 3, the isotopic shifts for Hg isotopes are roughly 2.5 GHz per amu. The positions of the fermionic lines are randomly scattered because of hyperfine splitting of their energy levels. The only Hg isotopes with completely separated Doppler background profiles at room temperature are the most abundant ones, i.e.  202Hg and  200Hg. All others measured isotopes share Doppler backgrounds which implies that the subdoppler line is shifted according to the centre of the background profile as shown in the sample Fig. 3. In that case, the biased background could affect the measurements based on the digital locking scheme as shown in Fig. 2.

If we assume that the measured line has a linear background (Fig. 2(b)), the measured frequency fSNR is shifted with respect to f0. This shift depends on the line shape and the slope of the background. A more general situation with the non-linear background is presented in Fig. 2(c). The frequency fSNR+NL, which includes the additional shift due to the nonlinearity of the background, is denoted by the green arrow and the probed frequencies are marked with the green circles.

In our measurements the frequency probing range corresponds to the maximal steepness of the profile (and consequently the maximal signal-to-noise of the measured signal fUV). To determine the frequency shift due to the linear background we performed a numerical analysis comparing the measured frequency with the frequency f0 that would result from probing the inflection points of the line slopes (blue circles in Fig. 2) while the background slope was assumed to be linear. This shift depends on the position of the line with respect to thebottom part of the Doppler-broadened background and is less than 90 kHz in our typical experimental conditions.

The higher-order frequency shift due to the background nonlinearity was determined by comparison of f+ and f calculated from maximal SNR of fUV signal for profiles with linear and gaussian backgrounds. It yields the value of a few kHz, typically one order of magnitude lower than the shift induced by the linear background. The effect of nonlinearity is small thanks to a large Doppler linewidth of Hg at room temperature (about 1 GHz) in contrast to the linewidth of the measured lines (typically less than 3 MHz). To determine the uncertainty related to the measurements of the slope-lying lines, we estimated the shift due to the non-optimal (out of the maximal SNR) probing range. The results are summarized in Table 1.

3.2. AC-Stark shift

The atomic energy levels are altered by AC-Stark effect while the atoms cross the UV laser beam. To correct for this effect, the measurements were performed at different UV light powers. A variance-weighted linear regression of the dependence of the transition frequency on the power of the UV laser beam (Fig. 6) yields the corrected value of the frequency. The uncertainty of the light shift effect has been deduced using the statistical analysis based on an external variance estimation.

 

Fig. 6 Results of a sample AC-Stark shift measurement in the 1S0-3P1 transition of 204Hg. f204Hg is the absolute frequency of the transition. Each point represents the average of measurements for a given power of the UV light. Black and red error bars correspond to the mean and the sample standard deviation, respectively. The dashed blue lines indicate linear regression bands. The black solid line is the linear regression fit to the data weighted by the mean standard deviations.

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3.3. Pressure effects

Another effect which affects the absolute frequency measurements is a pressure-dependent shift of the atomic resonance due to Hg–Hg collisions as well as due to residual gases impact. The temperature of the Hg cell, monitored with a thermoresistor (PT100), was between 299.15 and 306.15 K, which corresponds to Hg vapour pressure ranging from 0.284 to 0.499 Pa [40].

To estimate the frequency shift due to Hg-Hg collisions [41] we used the expression for pressure shift based on impact limit approximation [42, 43] and approximated the Hg-Hg interaction by van der Waals potential in the way proposed by Unsöld [44]. We used the value of Hg polarizability 33.9 a03 published by Koperski [45]. The estimated coefficient of the Hg-Hg collision-induced frequency shift is equal to -33(11) kHz/Pa. The uncertainty of the frequency shift represents possible discrepancy between our approach and more sophisticated treatments where proper interactions at short range and orientation of colliding atoms are incorporated [46, 47]. To calculate the shift of the Hg lines due to collisions with other gases, we assumed that hydrogen is a dominant component of the residual gas with the pressure less than 0.13 Pa at room temperature which is consistent with measurements of the residual gas inside the fused silica cell made by Palosz [48]. The estimated frequency shift due to collisions between Hg and H 2 is equal to -52(17) kHz/Pa.

In the case of the Doppler-free experiment, the actual frequency shifts are presumably lower as the velocity changing collisions can reduce the shifts at the same time significantly increasing collisional width. This effect was indicated for example in Sr [47]. In view of the above, we extended the uncertainties such that the coefficients of the frequency shifts are estimated to be -22(22) kHz/Pa and -35(35) kHz/Pa due to Hg-Hg and Hg-H 2 collisions, respectively. Our conservative estimation of the uncertainty is motivated also by the lack of knowledge of the exact composition of the residual gases as well as no available values of the collisional shift due to water vapour.

3.4. Zeeman shift

Among the measured Hg isotopes only the fermionic one ( 199Hg) has nonzero nuclear spin number (I=1/2) which leads to the hyperfine splitting of the  3P1 state into two states (F=1/2 and F=3/2). We probed a transition to the excited hyperfine F=1/2 state which splits into two Zeeman sublevels (mF=±1/2). In a weak magnetic field both sublevels shift in the opposite direction by the same value. It results in no effective Zeeman shift of the measured frequency but broaden the absorptionline. For the typical magnetic field in our measurements of 4105 T, measured by a magnetometer (Teslameter FM302 Elektronik Projekt GmbH), the broadening of the  199Hg line is on the level of 1 MHz. Similar broadening effect is observed for the bosonic isotopes (I = 0) with three Zeeman sublevels (mJ = 0, mJ=±1) in the excited state and one (mJ = 0) in the ground state. All bosons share the same value of the Landé factor (gJ=3/2) which gives an isotope-independent broadening of the absorption line of 1.6 MHz.

Additional magnetic effect is induced by splitting the ground  1S0 state in the presence of the magnetic field. However, since the nuclear Landé factor is much smaller than the orbital and the electron factors (by the electron-to-proton mass ratio)the induced splitting of the ground state is negligible.

 

Fig. 7 Comparison of present work results to the previous determinations of the 1S03P1 frequency for different Hg isotopes. The experimental results are referenced to the following lines: 198Hg 546 nm (green circle), 86Kr 606 nm (red square) and 198Hg 185 nm (blue triangle). (1), (2) Burns and Adams [49, 50], (3) Gerstenkorn et al. eGerstenkorn1977, (4) Meggers and Kessler [52], (5) Barger and Kessler [53], (6) Barger and Kessler result corrected according to the Bruce and Hill data [54], (7) correction of the Barger result [53] made by Kramida [9] based on the measurement of 313.2749895 nm 198Hg [55] as a reference, (8) Kaufman [56], (9) Schweitzer [35], (10) Schweitzer’s result [35] corrected according to the Bruce and Hill data [54]. Black points are our results while the orange ones (cross) correspond to the corrected measurements.

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Fig. 8 A comparison of isotope shift results referenced to 198Hg. Our results (black) are compared with the data shown by Schweitzer [35] (blue circle), Crane [57] (red cross) and Gerstenkorn [51] (brown square). For better visibility, the results are separated horizontally and shifted by an isotope shift value measured in the present work for a given isotope.

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Fig. 9 King plot of normalised isotope shifts in the 6s6p 3P2-6s7s 3S1 (546 nm) transition (taken from [24]) versus normalised isotope shifts in the 5d10 6s2 1S0-5d10 6s6p 3P1 (254 nm) transition (our results). The isotope shifts of 199Hg were shifted to the centre of gravity of the hyperfine manifold according to the data published by Rayman [24], Sansonetti [58] (546 nm), and Stager [59] (254 nm). The red solid line is the linear fit weighted by uncertainties of isotope shifts. The common reference isotope is 198Hg.

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Tables Icon

Table 1. Systematic shifts and their uncertainties for typical experimental conditions, i.e. the UV laser beam intensity of 400 W/m2 and the temperature of the Hg-vapour cell of 26.1°C. All results are in MHz. Remote frequency reference characterisation, i.e. gravitational red shift between AOS laboratory and our laboratory as well as uncertainty between UTC(AOS) and TT (the SI second on the geoid) are taken from [31].

3.5. Transition frequencies and isotope shift

In Table 2, we summarize our measured absolute frequencies of the  1S03P1 transition with the appropriate uncertainties. In Fig. 7 we compare our results (black points) with the data reported by other authors. The comparison is colour-coded with colours indicate the spectroscopic lines the measurements were referenced to:  198Hg 546 nm (green),  86Kr 606 nm (red) and  198Hg 185 nm (blue). In addition, a few corrections to the previous measurements were shown (orange).

Tables Icon

Table 2. Measured absolute frequencies of the 1S0-3P1 transition.

Table 3 contains our results of the isotope shifts measurements compared with the data previously published. The same data are visualized in Fig. 8.

The isotope shift for i-th transition between isotopes with mass numbers A and A can be expressed as

ISiAA=AAAAMSi+Eiδr2AA,
where MSi stands for the mass shift term, Ei is the electronic field-shift term, and δr2AA is the difference between the nuclear charge mean-square radii of isotopes A and A.

Figure 9 shows the King plot of the normalised isotope shifts ζ546198,A in 6s6p 3P26s7s 3S1 (546 nm) transition [24] plotted against the normalised isotope shifts ζ254198,A in the 5d106s2 1S05d106s6p 3P1 (254 nm) transition (our results). The isotope shifts are normalised by a mass factor AA/(AA), i.e. ζiAA=ISiAAAA/(AA). The isotope shifts for  199Hg in Fig. 9 were shifted to the centre of gravity of the hyperfine manifold according to the hyperfine splitting parameters shown by Rayman [24], Sansonetti [58] (546 nm), and Stager [59] (254 nm).

The linear relationship between normalised isotope shifts in two different transitions allows eliminating the δr2AA from their dependence:

ζ546AA=ζ254AAE546E254+MS546E546E254MS254.

The weighted least squares fit of Eq. (3) to the data (solid red line in Fig. 9) provides the ratio of electronic field-shift parameters E546/E254=0.17047(11) which is consistent with the less accurate value 0.1707(12) published by Ulm [60].

The y-intercept of the King plot provides the relation of mass shift parameters for both 254 nm and 546 nm transitions MS546E546/E254MS254=0.0536(11) MHz amu.

With the value of MS546=682(203) GHz amu taken from [24] we determined the mass shift term MS254=4.0(1.2) GHz amu which leads to the electronic field-shift term E254 of -51.277(46) GHz/fm 2. On the other hand, our IS254 measurements and the experimental values of δr2198,A published by Ulm [60], on the basis of the empirical relation between two components of the mass shift term, namely the normal (M254NMS) and the specific (M254SMS) mass shifts M254SMS=(0±0.5)M254NMS, which is assumed to be valid for ns2nsnp transitions [61], lead to the limit of the electronic field-shift term E254 equal to -51.63(17) GHz/fm 2. Comparison of both results reveals some inconsistency between these two approaches.

Independently of the above empirically-based results, we calculated the electronic field-shift term Ei as

Ei=Ze26ϵ0Δρel(0),
where Δρel(0) is the change of electronic density at nucleus upon the electronic transition [62]. To determine the value of ρel(0) we used the ADF package [63]. The program is based on Slater-type orbitals which are particularly good for representing the wavefunction near the nucleus. We used density functional theory with zeroth-order relativistic approach (ZORA) with specially tailored basis set for the nuclear properties [64]. Recently, such calculations for a similar problem (the Mössbauer spectroscopy of mercury atom compounds) were performed and basis sets and DFT functionals were scrutinized [65]. For 3P state we used the spin-unrestricted DFT calculations. We used PBE functional in the actual calculations but comparisons of Δρel(0) with KT2 and PBE0 functionals agree with PBE to within 0.3%. The absolute density at nucleus for the ground state Hg atom was found to be 2359836.4 a03 while for the 3P to be 2359702.4 a03 (these values agree very well with literature data listed in [65]). The difference of electron density upon the electron excitation to 6s5p state is -134 a03. This value translates into the electronic field-shift term E254 of -52.7 GHz/fm 2.

To assess the values of electron densities at nucleus and estimate the systematic error burdened by the electronic structure calculation we obtained the hyperfine coupling constants for the the  199Hg  3P state which with PBE functional was 17.919 GHz compared to the experimental 14.7570(60) GHz [35]. Since the isotropic coupling constant depends essentially on the same property as the field shift, namely on the behaviour of the electronic wavefunction near the nucleus, we can treat the difference between calculated hyperfine constant and the experimental one as the systematic error (subject to a factor of 1/3). Hence, the final systematic error of theory is 10% which results in the electronic field-shift term of -52.7(5.3) GHz/fm 2. This result is consistent with our empirically-based estimations as well as the experimental [66, 67] and ab initio calculations [68].

Tables Icon

Table 3. Isotope shifts for the 1S0-3P1 transition in Hg referenced to 198Hg. The measured values are compared with the results presented by Schweitzer [35], Crane [57] and Gerstenkorn [51].

4. Conclusions

In summary, we measured the absolute frequency of the  1S0 3P1 transition in four bosons ( 198Hg,  200Hg,  202Hg,  204Hg) and one of the hyperfine transitions (F=1/2F=1/2) in fermion ( 199Hg). These are the first reported values of the cooling transition in Hg measured with the aid of the optical frequency comb. We presented isotope shifts for all measured isotopes referenced to the relevant transition in  198Hg. By comparing our results with previously reported indirect determinations we showed an improvement in accuracy of at least one order of magnitude.

By plotting our isotope shifts results against the data for the 6s6p 3P26s7s 3S1 transition (546 nm line) measured by Rayman [24] we determined the accurate value of the ratio of the electronic field-shift parameters E546/E254 and then we used this value to estimate the electronic field-shift term E254. We calculated E254 independently taking advantage of the density functional theory with zeroth-order relativistic approach. The result agrees within its uncertainty with our estimation as well as the previous experimental results and theoretical calculations [66–68].

Funding

Foundation for Polish Science Team Programme (Project TEAM/2017-4/42); European Regional Development Fund; the Polish Ministry of Science and Higher Education; National Science Centre, Poland, (NCN) (2012/07/B/ST2/00235, 2013/11/N/ST2/00846, 2016/21/N/ST2/00334, 2017/24/T/ST2/00242).

Acknowledgments

The measurements were performed as a part of research done at the National Laboratory FAMO (KL FAMO) in Toruń, Poland.

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13. M. D. Swallows, T. H. Loftus, W. C. Griffith, B. R. Heckel, E. N. Fortson, and M. V. Romalis, “Techniques used to search for a permanent electric dipole moment of the  199Hg atom and the implications for CP violation,” Phys. Rev. A 87, 012102 (2013). [CrossRef]  

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15. E. J. Angstmann, V. A. Dzuba, and V. V. Flambaum, “Relativistic effects in two valence-electron atoms and ions and the search for variation of the fine-structure constant,” Phys. Rev. A 70, 014102 (2004). [CrossRef]  

16. H. Hachisu, K. Miyagishi, S. G. Porsev, A. Derevianko, V. D. Ovsiannikov, V. G. Pal’chikov, M. Takamoto, and H. Katori, “Trapping of neutral mercury atoms and prospects for optical lattice clocks,” Phys. Rev. Lett. 100,053001 (2008). [CrossRef]   [PubMed]  

17. L. Yi, S. Mejri, J. J. McFerran, Y. Le Coq, and S. Bize, “Optical lattice trapping of  199Hg and determination of the magic wavelength for the ultraviolet  1S03P0 clock transition,” Phys. Rev. Lett. 106, 073005 (2011). [CrossRef]  

18. J. K. Böhlke, J. R. De Laeter, P. De Bièvre, H. Hidaka, H. S. Peiser, K. J. R. Rosman, and P. D. P. Taylor, “Isotopic compositions of the elements, 2001,” J. Phys. Chem. Ref. Data 34(1), 57–67 (2005). [CrossRef]  

19. P. Villwock, S. Siol, and T. Walther, “Magneto-optical trapping of neutral mercury,” The Eur. Phys. J. D 65(1), 251–255 (2011). [CrossRef]  

20. L. Hong-Li, Y. Shi-Qi, L. Kang-Kang, Q. Jun, X. Zhen, H. Tao, and W. Yu-Zhu, “Magneto-optical trap for neutral mercury atoms,” Chin. Phys. B 22(4), 043701 (2013). [CrossRef]  

21. J. R. Paul, “Construction and characterization of a neutral Hg magneto-optical trap and precision spectroscopy of the 61P0 – 63P0 Hg199 clock transition,” Ph.D. thesis, The University of Arizona (2015).

22. M. Witkowski, B. Nagórny, R. Munoz-Rodriguez, R. Ciuryło, P. S. Żuchowski, S. Bilicki, M. Piotrowski, P. Morzyński, and M. Zawada, “Dual Hg-Rb magneto-optical trap,” Opt. Express 25(4), 3165–3179 (2017). [CrossRef]   [PubMed]  

23. W. H. King, Isotope Shifts in Atomic Spectra (Springer, 1984). [CrossRef]  

24. M. D. Rayman, C. G. Aminoff, and J. L. Hall, “Precise laser frequency scanning using frequency-synthesized optical frequency sidebands: application to isotope shifts and hyperfine structure of mercury,” J. Opt. Soc. Am. B 6(4), 539–549 (1989). [CrossRef]  

25. C. Delaunay, R. Ozeri, G. Perez, and Y. Soreq, “Probing atomic Higgs-like forces at the precision frontier,” Phys. Rev. D 96, 093001 (2017). [CrossRef]  

26. V. V. Flambaum, A. J. Geddes, and A. V. Viatkina, “Isotope shift, nonlinearity of King plots, and the search for new particles,” Phys. Rev. A 97, 032510 (2018). [CrossRef]  

27. J. C. Berengut, D. Budker, C. Delaunay, V. V. Flambaum, C. Frugiuele, E. Fuchs, C. Grojean, R. Harnik, R. Ozeri, G. Perez, and Y. Soreq, “Probing new long-range interactions by isotope shift spectroscopy,” Phys. Rev. Lett. 120, 091801 (2018). [CrossRef]   [PubMed]  

28. M. Witkowski, R. Munoz-Rodriguez, A. Raczyński, J. Zaremba, B. Nagórny, P. S. Żuchowski, R. Ciuryło, and M. Zawada, “Photoionization cross section of the  5S 1/2 and  5P 3/2 states of Rb in simultaneous magneto-optical trapping of Rb and Hg,” Phys. Rev. A 98, 053444 (2018). [CrossRef]  

29. J. Azoubib, J. Nawrocki, and W. Lewandowski, “Independent atomic timescale in Poland-organization and results,” Metrologia 40(3), S245–S248 (2003). [CrossRef]  

30. Z. Jiang, A. Czubla, J. Nawrocki, W. Lewandowski, and E. F. Arias, “Comparing a GPS time link calibration with an optical fibre self-calibration with 200 ps accuracy,” Metrologia 52(2), 384–391 (2015). [CrossRef]  

31. P. Morzyński, M. Bober, D. Bartoszek-Bober, J. Nawrocki, P. Krehlik, L. Śliwczyński, M. Lipiński, P. Masłowski, A. Cygan, P. Dunst, M. Garus, D. Lisak, J. Zachorowski, W. Gawlik, C. Radzewicz, R. Ciuryło, and M. Zawada, “Absolute measurement of the  1S 0 -  3P 0 clock transition in neutral  88Sr over the 330 km-long stabilized fibre optic link,” Sci. Rep. 5, 17495 (2015). [CrossRef]  

32. L. Śliwczyński, P. Krehlik, A. Czubla, L. Buczek, and M. Lipiński, “Dissemination of time and RF frequency via a stabilized fibre optic link over a distance of 420 km,” Metrologia 50(2), 133–145 (2013). [CrossRef]  

33. P. Krehlik, L. Śliwczyński, L. Buczek, J. Kołodziej, and M. Lipiński, “Ultrastable long-distance fibre-optic time transfer: active compensation over a wide range of delays,” Metrologia 52(1), 82–88 (2015). [CrossRef]  

34. P. Morzyński, P. Wcisło, P. Ablewski, R. Gartman, W. Gawlik, P. Masłowski, B. Nagórny, F. Ozimek, C. Radzewicz, M. Witkowski, R. Ciuryło, and M. Zawada, “Absolute frequency measurement of rubidium 5S - 7S two-photon transitions,” Opt. Lett. 38(22), 4581–4584 (2013). [CrossRef]  

35. W. G. Schweitzer, “Hyperfine structure and isotope shifts in the 2537-Å line of mercury by a new interferometric method,” J. Opt. Soc. Am. 53(9), 1055–1072 (1963). [CrossRef]  

36. M. Zadnik, S. Specht, and F. Begemann, “Revised isotopic composition of terrestrial mercury,” Int. J. Mass Spectrome. Ion Process. 89, 103 – 110 (1989). [CrossRef]  

37. A. Cygan, D. Lisak, P. Morzyński, M. Bober, M. Zawada, E. Pazderski, and R. Ciuryło, “Cavity mode-width spectroscopy with widely tunable ultra narrow laser,” Opt. Express 21(24), 29744–29754 (2013). [CrossRef]  

38. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B Photophysics Laser Chem. 31(2), 97–105 (1983). [CrossRef]  

39. J. D. Deschênes and J. Genest, “Heterodyne beats between a continuous-wave laser and a frequency comb beyond the shot-noise limit of a single comb mode,” Phys. Rev. A 87, 023802 (2013). [CrossRef]  

40. M. L. Huber, A. Laesecke, and D. G. Friend, “Correlation for the vapor pressure of mercury,” Ind. Eng. Chem. Res. 45(21), 7351–7361 (2006). [CrossRef]  

41. N. Allard and J. Kielkopf, “The effect of neutral nonresonant collisions on atomic spectral lines,” Rev. Mod. Phys. 54(4), 1103–1182 (1982). [CrossRef]  

42. J. Szudy and W. Baylis, “Asymmetry in pressure-broadened spectral lines,” J. Quant. Spectrosc. Radiat. Transf. 17(5), 681 – 684 (1977). [CrossRef]  

43. S. Brym, R. Ciurylo, E. Lisicki, and R. S. Trawinski, “Pressure broadening and shift of the 326.1 nm Cd line perturbed by argon,” Phys. Scripta 53(5), 541–544 (1996). [CrossRef]  

44. A. Unsöld, Physik der Sternatmosphären (Springer, 1955). [CrossRef]  

45. J. Koperski, “Study of diatomic van der Waals complexes in supersonic beams,” Phys. Rep. 369(3), 177–326 (2002). [CrossRef]  

46. R. Trawiński, “On argon-induced pressure shifts of  198Hg spectral lines associated with quasi-Rydberg transitions,” Acta Phys. Pol. A 110(1), 51–56 (2006). [CrossRef]  

47. N. Shiga, Y. Li, H. Ito, S. Nagano, T. Ido, K. Bielska, R. S. Trawiński, and R. Ciuryło, “Buffer-gas-induced collision shift for the  88Sr 1S 03P 1 clock transition,” Phys. Rev. A 80, 030501 (2009). [CrossRef]  

48. W. Palosz, “Residual gas in closed systems-I: development of gas in fused silica ampoules,” J. Cryst. Growth 267(3), 475 – 483 (2004). [CrossRef]  

49. K. Burns and K. B. Adams, “Energy levels and wavelengths of the isotopes of mercury-198 and -202,” J. Opt. Soc. Am. 42(1), 56–59 (1952). [CrossRef]  

50. K. Burns and K. B. Adams, “Energy levels and wavelengths of the isotopes of mercury-199 and -200,” J. Opt. Soc. Am. 42(10), 716–721 (1952). [CrossRef]  

51. S. Gerstenkorn, J. J. Labarthe, and J. Vergès, “Fine and hyperfine structures and isotope shifts in the arc spectrum of mercury. Part I. Experimental study of the infrared spectrum by Fourier transform spectroscopy,” Phys. Scripta 15(3), 167–172 (1977). [CrossRef]  

52. W. F. Meggers and K. G. Kessler, “Wave-lengths of mercury 198,” J. Opt. Soc. Am. 40(11), 737–741 (1950). [CrossRef]  

53. R. L. Barger and K. G. Kessler, “Kr 86 and atomic-beam-emitted Hg 198 wavelengths,” J. Opt. Soc. Am. 51(8), 827–829 (1961). [CrossRef]  

54. C. F. Bruce and R. M. Hill, “Wavelengths of krypton 86, mercury 198, and cadmium 114,” Aust. J. Phys. 14(1), 64–88 (1961). [CrossRef]  

55. D. Veza, M. L. Salit, C. J. Sansonetti, and J. C. Travis, “Wave numbers and Ar pressure-induced shifts of  198Hg atomic lines measured by Fourier transform spectroscopy,” J. Phys. B: At. Mol. Opt. Phys. 38(20), 3739–3753 (2005). [CrossRef]  

56. V. Kaufman, “Wavelengths, energy levels, and pressure shifts in mercury 198,” J. Opt. Soc. Am. 52(8), 866–870 (1962). [CrossRef]  

57. J. K. Crane, G. V. Erbert, S. D. Mostek, R. C. Kerlin, and J. A. Paisner, “High-resolution absorption spectrum of the 6 1S 06 3P 1 transition in mercury with a CW dye laser,” in AIP Conference Proceedings, (American Institute of Physics, 1986), pp. 411–412.

58. C. J. Sansonetti and D. Veza, “Doppler-free measurement of the 546 nm line of mercury,” J. Phys. B: At. Mol. Opt. Phys. 43, 205003 (2010). [CrossRef]  

59. C. V. Stager, “Hyperfine Structure of  197Hg and  199Hg,” Phys. Rev. 132(1), 275–279 (1963). [CrossRef]  

60. G. Ulm, S. K. Bhattacherjee, P. Dabkiewicz, G. Huber, H. J. Kluge, T. Kühl, H. Lochmann, E. W. Otten, K. Wendt, S. A. Ahmad, W. Klempt, R. Neugart, and ISOLDE Collaboration, “Isotope shift of  182Hg and an update of nuclear moments and charge radii in the isotope range  181Hg- 206Hg,” Zeitschrift für Physik A Atomic Nuclei 325(3), 247–259 (1986). [CrossRef]  

61. K. Heilig and A. Steudel, “Changes in mean-square nuclear charge radii from optical isotope shifts,” At. Data Nucl. Data Tables 14(5–6), 613–638 (1974). [CrossRef]  

62. J. Schlembach and E. Tiemann, “Isotopic field shift of the rotational energy of the Pb-chalcogenides and Tl-halides,” Chem. Phys. 68(1–2), 21–28 (1982). [CrossRef]  

63. E. J. Baerends, T. Ziegler, A. J. Atkins, J. Autschbach, D. Bashford, O. Baseggio, A. Bérces, F. M. Bickelhaupt, C. Bo, P. M. Boerritger, L. Cavallo, C. Daul, D. P. Chong, D. V. Chulhai, L. Deng, R. M. Dickson, J. M. Dieterich, D. E. Ellis, M. van Faassen, A. Ghysels, A. Giammona, S. J. A. van Gisbergen, A. Goez, A. W. Götz, S. Gusarov, F. E. Harris, P. van den Hoek, Z. Hu, C. R. Jacob, H. Jacobsen, L. Jensen, L. Joubert, J. W. Kaminski, G. van Kessel, C. König, F. Kootstra, A. Kovalenko, M. Krykunov, E. van Lenthe, D. A. McCormack, A. Michalak, M. Mitoraj, S. M. Morton, J. Neugebauer, V. P. Nicu, L. Noodleman, V. P. Osinga, S. Patchkovskii, M. Pavanello, C. A. Peeples, P. H. T. Philipsen, D. Post, C. C. Pye, H. Ramanantoanina, P. Ramos, W. Ravenek, J. I. Rodríguez, P. Ros, R. Rüger, P. R. T. Schipper, D. Schlüns, H. van Schoot, G. Schreckenbach, J. S. Seldenthuis, M. Seth, J. G. Snijders, M. Solà, M. Stener, M. Swart, D. Swerhone, G. te Velde, V. Tognetti, P. Vernooijs, L. Versluis, L. Visscher, O. Visser, F. Wang, T. A. Wesolowski, E. M. van Wezenbeek, G. Wiesenekker, S. K. Wolff, T. K. Woo, and A. L. Yakovlev, “ADF2017, SCM, Theoretical Chemistry, Vrije Universiteit, Amsterdam, The Netherlands,” (2017).

64. E. van Lenthe, J. G. Snijders, and E. J. Baerends, “The zero-order regular approximation for relativistic effects: the effect of spin-orbit coupling in closed shell molecules,” J. Chem. Phys. 105(15), 6505–6516 (1996). [CrossRef]  

65. S. Knecht, S. Fux, R. Van Meer, L. Visscher, M. Reiher, and T. Saue, “Mössbauer spectroscopy for heavy elements: a relativistic benchmark study of mercury,” Theor. Chem. Accounts 129(3–5), 631–650 (2011). [CrossRef]  

66. A. A. Hahn, J. P. Miller, R. J. Powers, A. Zehnder, A. M. Rushton, R. E. Welsh, A. R. Kunselman, P. Roberson, and H. K. Walter, “An experimental study of muonic x-ray transitions in mercury isotopes,” Nucl. Phys. A 314(2–3), 361–386 (1979). [CrossRef]  

67. P. L. Lee, F. Boehm, and A. A. Hahn, “Variations of nuclear charge radii in mercury isotopes with A=198, 199, 200, 201, 202, and 204 from x-ray isotope shifts,” Phys. Rev. C 17(5), 1859–1861 (1978). [CrossRef]  

68. G. Torbohm, B. Fricke, and A. Rosén, “State-dependent volume isotope shifts of low-lying states of group-IIa and -IIb elements,” Phys. Rev. A 31(4), 2038–2053 (1985). [CrossRef]  

References

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    [Crossref]
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    [Crossref]
  30. Z. Jiang, A. Czubla, J. Nawrocki, W. Lewandowski, and E. F. Arias, “Comparing a GPS time link calibration with an optical fibre self-calibration with 200 ps accuracy,” Metrologia 52(2), 384–391 (2015).
    [Crossref]
  31. P. Morzyński, M. Bober, D. Bartoszek-Bober, J. Nawrocki, P. Krehlik, L. Śliwczyński, M. Lipiński, P. Masłowski, A. Cygan, P. Dunst, M. Garus, D. Lisak, J. Zachorowski, W. Gawlik, C. Radzewicz, R. Ciuryło, and M. Zawada, “Absolute measurement of the  1S 0 -  3P 0 clock transition in neutral  88Sr over the 330 km-long stabilized fibre optic link,” Sci. Rep. 5, 17495 (2015).
    [Crossref]
  32. L. Śliwczyński, P. Krehlik, A. Czubla, L. Buczek, and M. Lipiński, “Dissemination of time and RF frequency via a stabilized fibre optic link over a distance of 420 km,” Metrologia 50(2), 133–145 (2013).
    [Crossref]
  33. P. Krehlik, L. Śliwczyński, L. Buczek, J. Kołodziej, and M. Lipiński, “Ultrastable long-distance fibre-optic time transfer: active compensation over a wide range of delays,” Metrologia 52(1), 82–88 (2015).
    [Crossref]
  34. P. Morzyński, P. Wcisło, P. Ablewski, R. Gartman, W. Gawlik, P. Masłowski, B. Nagórny, F. Ozimek, C. Radzewicz, M. Witkowski, R. Ciuryło, and M. Zawada, “Absolute frequency measurement of rubidium 5S - 7S two-photon transitions,” Opt. Lett. 38(22), 4581–4584 (2013).
    [Crossref]
  35. W. G. Schweitzer, “Hyperfine structure and isotope shifts in the 2537-Å line of mercury by a new interferometric method,” J. Opt. Soc. Am. 53(9), 1055–1072 (1963).
    [Crossref]
  36. M. Zadnik, S. Specht, and F. Begemann, “Revised isotopic composition of terrestrial mercury,” Int. J. Mass Spectrome. Ion Process. 89, 103 – 110 (1989).
    [Crossref]
  37. A. Cygan, D. Lisak, P. Morzyński, M. Bober, M. Zawada, E. Pazderski, and R. Ciuryło, “Cavity mode-width spectroscopy with widely tunable ultra narrow laser,” Opt. Express 21(24), 29744–29754 (2013).
    [Crossref]
  38. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B Photophysics Laser Chem. 31(2), 97–105 (1983).
    [Crossref]
  39. J. D. Deschênes and J. Genest, “Heterodyne beats between a continuous-wave laser and a frequency comb beyond the shot-noise limit of a single comb mode,” Phys. Rev. A 87, 023802 (2013).
    [Crossref]
  40. M. L. Huber, A. Laesecke, and D. G. Friend, “Correlation for the vapor pressure of mercury,” Ind. Eng. Chem. Res. 45(21), 7351–7361 (2006).
    [Crossref]
  41. N. Allard and J. Kielkopf, “The effect of neutral nonresonant collisions on atomic spectral lines,” Rev. Mod. Phys. 54(4), 1103–1182 (1982).
    [Crossref]
  42. J. Szudy and W. Baylis, “Asymmetry in pressure-broadened spectral lines,” J. Quant. Spectrosc. Radiat. Transf. 17(5), 681 – 684 (1977).
    [Crossref]
  43. S. Brym, R. Ciurylo, E. Lisicki, and R. S. Trawinski, “Pressure broadening and shift of the 326.1 nm Cd line perturbed by argon,” Phys. Scripta 53(5), 541–544 (1996).
    [Crossref]
  44. A. Unsöld, Physik der Sternatmosphären (Springer, 1955).
    [Crossref]
  45. J. Koperski, “Study of diatomic van der Waals complexes in supersonic beams,” Phys. Rep. 369(3), 177–326 (2002).
    [Crossref]
  46. R. Trawiński, “On argon-induced pressure shifts of  198Hg spectral lines associated with quasi-Rydberg transitions,” Acta Phys. Pol. A 110(1), 51–56 (2006).
    [Crossref]
  47. N. Shiga, Y. Li, H. Ito, S. Nagano, T. Ido, K. Bielska, R. S. Trawiński, and R. Ciuryło, “Buffer-gas-induced collision shift for the  88Sr 1S 0−3P 1 clock transition,” Phys. Rev. A 80, 030501 (2009).
    [Crossref]
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2018 (4)

M. S. Safronova, D. Budker, D. DeMille, D. F. J. Kimball, A. Derevianko, and C. W. Clark, “Search for new physics with atoms and molecules,” Rev. Mod. Phys. 90, 025008 (2018).
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V. V. Flambaum, A. J. Geddes, and A. V. Viatkina, “Isotope shift, nonlinearity of King plots, and the search for new particles,” Phys. Rev. A 97, 032510 (2018).
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J. C. Berengut, D. Budker, C. Delaunay, V. V. Flambaum, C. Frugiuele, E. Fuchs, C. Grojean, R. Harnik, R. Ozeri, G. Perez, and Y. Soreq, “Probing new long-range interactions by isotope shift spectroscopy,” Phys. Rev. Lett. 120, 091801 (2018).
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M. Witkowski, R. Munoz-Rodriguez, A. Raczyński, J. Zaremba, B. Nagórny, P. S. Żuchowski, R. Ciuryło, and M. Zawada, “Photoionization cross section of the  5S 1/2 and  5P 3/2 states of Rb in simultaneous magneto-optical trapping of Rb and Hg,” Phys. Rev. A 98, 053444 (2018).
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2017 (2)

2016 (1)

B. Graner, Y. Chen, E. G. Lindahl, and B. R. Heckel, “Reduced limit on the permanent electric dipole moment of  199Hg,” Phys. Rev. Lett. 116, 161601 (2016).
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2015 (3)

Z. Jiang, A. Czubla, J. Nawrocki, W. Lewandowski, and E. F. Arias, “Comparing a GPS time link calibration with an optical fibre self-calibration with 200 ps accuracy,” Metrologia 52(2), 384–391 (2015).
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P. Morzyński, M. Bober, D. Bartoszek-Bober, J. Nawrocki, P. Krehlik, L. Śliwczyński, M. Lipiński, P. Masłowski, A. Cygan, P. Dunst, M. Garus, D. Lisak, J. Zachorowski, W. Gawlik, C. Radzewicz, R. Ciuryło, and M. Zawada, “Absolute measurement of the  1S 0 -  3P 0 clock transition in neutral  88Sr over the 330 km-long stabilized fibre optic link,” Sci. Rep. 5, 17495 (2015).
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P. Krehlik, L. Śliwczyński, L. Buczek, J. Kołodziej, and M. Lipiński, “Ultrastable long-distance fibre-optic time transfer: active compensation over a wide range of delays,” Metrologia 52(1), 82–88 (2015).
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2013 (6)

P. Morzyński, P. Wcisło, P. Ablewski, R. Gartman, W. Gawlik, P. Masłowski, B. Nagórny, F. Ozimek, C. Radzewicz, M. Witkowski, R. Ciuryło, and M. Zawada, “Absolute frequency measurement of rubidium 5S - 7S two-photon transitions,” Opt. Lett. 38(22), 4581–4584 (2013).
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L. Śliwczyński, P. Krehlik, A. Czubla, L. Buczek, and M. Lipiński, “Dissemination of time and RF frequency via a stabilized fibre optic link over a distance of 420 km,” Metrologia 50(2), 133–145 (2013).
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J. D. Deschênes and J. Genest, “Heterodyne beats between a continuous-wave laser and a frequency comb beyond the shot-noise limit of a single comb mode,” Phys. Rev. A 87, 023802 (2013).
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L. Hong-Li, Y. Shi-Qi, L. Kang-Kang, Q. Jun, X. Zhen, H. Tao, and W. Yu-Zhu, “Magneto-optical trap for neutral mercury atoms,” Chin. Phys. B 22(4), 043701 (2013).
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M. D. Swallows, T. H. Loftus, W. C. Griffith, B. R. Heckel, E. N. Fortson, and M. V. Romalis, “Techniques used to search for a permanent electric dipole moment of the  199Hg atom and the implications for CP violation,” Phys. Rev. A 87, 012102 (2013).
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A. Cygan, D. Lisak, P. Morzyński, M. Bober, M. Zawada, E. Pazderski, and R. Ciuryło, “Cavity mode-width spectroscopy with widely tunable ultra narrow laser,” Opt. Express 21(24), 29744–29754 (2013).
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2011 (4)

S. Knecht, S. Fux, R. Van Meer, L. Visscher, M. Reiher, and T. Saue, “Mössbauer spectroscopy for heavy elements: a relativistic benchmark study of mercury,” Theor. Chem. Accounts 129(3–5), 631–650 (2011).
[Crossref]

L. Yi, S. Mejri, J. J. McFerran, Y. Le Coq, and S. Bize, “Optical lattice trapping of  199Hg and determination of the magic wavelength for the ultraviolet  1S0↔3P0 clock transition,” Phys. Rev. Lett. 106, 073005 (2011).
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P. Villwock, S. Siol, and T. Walther, “Magneto-optical trapping of neutral mercury,” The Eur. Phys. J. D 65(1), 251–255 (2011).
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A. E. Kramida, “Re-optimized energy levels and Ritz wavelengths of (198)Hg I,” J. Res. Natl. Inst. Stand. Technol. 116(2), 599–619 (2011).
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2010 (1)

C. J. Sansonetti and D. Veza, “Doppler-free measurement of the 546 nm line of mercury,” J. Phys. B: At. Mol. Opt. Phys. 43, 205003 (2010).
[Crossref]

2009 (2)

N. Shiga, Y. Li, H. Ito, S. Nagano, T. Ido, K. Bielska, R. S. Trawiński, and R. Ciuryło, “Buffer-gas-induced collision shift for the  88Sr 1S 0−3P 1 clock transition,” Phys. Rev. A 80, 030501 (2009).
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K. V. P. Latha, D. Angom, B. P. Das, and D. Mukherjee, “Probing CP violation with the electric dipole moment of atomic mercury,” Phys. Rev. Lett. 103, 083001 (2009).
[Crossref] [PubMed]

2008 (1)

H. Hachisu, K. Miyagishi, S. G. Porsev, A. Derevianko, V. D. Ovsiannikov, V. G. Pal’chikov, M. Takamoto, and H. Katori, “Trapping of neutral mercury atoms and prospects for optical lattice clocks,” Phys. Rev. Lett. 100,053001 (2008).
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2006 (3)

E. B. Saloman, “Wavelengths, energy level classifications, and energy levels for the spectrum of neutral mercury,” J. Phys. Chem. Ref. Data 35(4), 1519–1548 (2006).
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M. L. Huber, A. Laesecke, and D. G. Friend, “Correlation for the vapor pressure of mercury,” Ind. Eng. Chem. Res. 45(21), 7351–7361 (2006).
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R. Trawiński, “On argon-induced pressure shifts of  198Hg spectral lines associated with quasi-Rydberg transitions,” Acta Phys. Pol. A 110(1), 51–56 (2006).
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2005 (3)

D. Veza, M. L. Salit, C. J. Sansonetti, and J. C. Travis, “Wave numbers and Ar pressure-induced shifts of  198Hg atomic lines measured by Fourier transform spectroscopy,” J. Phys. B: At. Mol. Opt. Phys. 38(20), 3739–3753 (2005).
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J. E. Sansonetti and W. C. Martin, “Handbook of basic atomic spectroscopic data,” J. Phys. Chem. Ref. Data 34(4), 1559–2259 (2005).
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J. K. Böhlke, J. R. De Laeter, P. De Bièvre, H. Hidaka, H. S. Peiser, K. J. R. Rosman, and P. D. P. Taylor, “Isotopic compositions of the elements, 2001,” J. Phys. Chem. Ref. Data 34(1), 57–67 (2005).
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2004 (2)

E. J. Angstmann, V. A. Dzuba, and V. V. Flambaum, “Relativistic effects in two valence-electron atoms and ions and the search for variation of the fine-structure constant,” Phys. Rev. A 70, 014102 (2004).
[Crossref]

W. Palosz, “Residual gas in closed systems-I: development of gas in fused silica ampoules,” J. Cryst. Growth 267(3), 475 – 483 (2004).
[Crossref]

2003 (1)

J. Azoubib, J. Nawrocki, and W. Lewandowski, “Independent atomic timescale in Poland-organization and results,” Metrologia 40(3), S245–S248 (2003).
[Crossref]

2002 (1)

J. Koperski, “Study of diatomic van der Waals complexes in supersonic beams,” Phys. Rep. 369(3), 177–326 (2002).
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1996 (2)

S. Brym, R. Ciurylo, E. Lisicki, and R. S. Trawinski, “Pressure broadening and shift of the 326.1 nm Cd line perturbed by argon,” Phys. Scripta 53(5), 541–544 (1996).
[Crossref]

E. van Lenthe, J. G. Snijders, and E. J. Baerends, “The zero-order regular approximation for relativistic effects: the effect of spin-orbit coupling in closed shell molecules,” J. Chem. Phys. 105(15), 6505–6516 (1996).
[Crossref]

1989 (2)

1986 (1)

G. Ulm, S. K. Bhattacherjee, P. Dabkiewicz, G. Huber, H. J. Kluge, T. Kühl, H. Lochmann, E. W. Otten, K. Wendt, S. A. Ahmad, W. Klempt, R. Neugart, and ISOLDE Collaboration, “Isotope shift of  182Hg and an update of nuclear moments and charge radii in the isotope range  181Hg- 206Hg,” Zeitschrift für Physik A Atomic Nuclei 325(3), 247–259 (1986).
[Crossref]

1985 (1)

G. Torbohm, B. Fricke, and A. Rosén, “State-dependent volume isotope shifts of low-lying states of group-IIa and -IIb elements,” Phys. Rev. A 31(4), 2038–2053 (1985).
[Crossref]

1983 (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B Photophysics Laser Chem. 31(2), 97–105 (1983).
[Crossref]

1982 (2)

J. Schlembach and E. Tiemann, “Isotopic field shift of the rotational energy of the Pb-chalcogenides and Tl-halides,” Chem. Phys. 68(1–2), 21–28 (1982).
[Crossref]

N. Allard and J. Kielkopf, “The effect of neutral nonresonant collisions on atomic spectral lines,” Rev. Mod. Phys. 54(4), 1103–1182 (1982).
[Crossref]

1979 (1)

A. A. Hahn, J. P. Miller, R. J. Powers, A. Zehnder, A. M. Rushton, R. E. Welsh, A. R. Kunselman, P. Roberson, and H. K. Walter, “An experimental study of muonic x-ray transitions in mercury isotopes,” Nucl. Phys. A 314(2–3), 361–386 (1979).
[Crossref]

1978 (1)

P. L. Lee, F. Boehm, and A. A. Hahn, “Variations of nuclear charge radii in mercury isotopes with A=198, 199, 200, 201, 202, and 204 from x-ray isotope shifts,” Phys. Rev. C 17(5), 1859–1861 (1978).
[Crossref]

1977 (3)

S. Gerstenkorn, J. J. Labarthe, and J. Vergès, “Fine and hyperfine structures and isotope shifts in the arc spectrum of mercury. Part I. Experimental study of the infrared spectrum by Fourier transform spectroscopy,” Phys. Scripta 15(3), 167–172 (1977).
[Crossref]

J. Szudy and W. Baylis, “Asymmetry in pressure-broadened spectral lines,” J. Quant. Spectrosc. Radiat. Transf. 17(5), 681 – 684 (1977).
[Crossref]

C. Bouchiat, “Parity violation in atomic processes,” J. Phys. G: Nucl. Phys. 3(2), 183–197 (1977).
[Crossref]

1974 (1)

K. Heilig and A. Steudel, “Changes in mean-square nuclear charge radii from optical isotope shifts,” At. Data Nucl. Data Tables 14(5–6), 613–638 (1974).
[Crossref]

1963 (2)

1962 (1)

1961 (4)

R. L. Barger and K. G. Kessler, “Kr 86 and atomic-beam-emitted Hg 198 wavelengths,” J. Opt. Soc. Am. 51(8), 827–829 (1961).
[Crossref]

C. F. Bruce and R. M. Hill, “Wavelengths of krypton 86, mercury 198, and cadmium 114,” Aust. J. Phys. 14(1), 64–88 (1961).
[Crossref]

R. H. Kohler, “Detection of double resonance by frequency change: application to Hg 201,” Phys. Rev. 121(4), 1104–1111 (1961).
[Crossref]

W. G. Schweitzer, “Hyperfine structure and isotope shifts in the 2537-A line of mercury,” J. Opt. Soc. Am. 51(6), 692–693 (1961).
[Crossref]

1960 (1)

C. V. Stager and R. H. Kohler, “Hyperfine structure of Hg 199 and Hg 201 in the  3P 1 state,” Bull. Am. Phys. Soc. Ser. II 5(4), 274 (1960).

1952 (2)

1950 (1)

1891 (1)

H. Kayser and C. Runge, “Ueber die spectra der elemente der zweiten Mendelejeff’schen gruppe,” Annalen der Physik 279(6), 385–409 (1891).
[Crossref]

Ablewski, P.

Adams, K. B.

Ahmad, S. A.

G. Ulm, S. K. Bhattacherjee, P. Dabkiewicz, G. Huber, H. J. Kluge, T. Kühl, H. Lochmann, E. W. Otten, K. Wendt, S. A. Ahmad, W. Klempt, R. Neugart, and ISOLDE Collaboration, “Isotope shift of  182Hg and an update of nuclear moments and charge radii in the isotope range  181Hg- 206Hg,” Zeitschrift für Physik A Atomic Nuclei 325(3), 247–259 (1986).
[Crossref]

Allard, N.

N. Allard and J. Kielkopf, “The effect of neutral nonresonant collisions on atomic spectral lines,” Rev. Mod. Phys. 54(4), 1103–1182 (1982).
[Crossref]

Aminoff, C. G.

Angom, D.

K. V. P. Latha, D. Angom, B. P. Das, and D. Mukherjee, “Probing CP violation with the electric dipole moment of atomic mercury,” Phys. Rev. Lett. 103, 083001 (2009).
[Crossref] [PubMed]

Angstmann, E. J.

E. J. Angstmann, V. A. Dzuba, and V. V. Flambaum, “Relativistic effects in two valence-electron atoms and ions and the search for variation of the fine-structure constant,” Phys. Rev. A 70, 014102 (2004).
[Crossref]

Arias, E. F.

Z. Jiang, A. Czubla, J. Nawrocki, W. Lewandowski, and E. F. Arias, “Comparing a GPS time link calibration with an optical fibre self-calibration with 200 ps accuracy,” Metrologia 52(2), 384–391 (2015).
[Crossref]

Atkins, A. J.

E. J. Baerends, T. Ziegler, A. J. Atkins, J. Autschbach, D. Bashford, O. Baseggio, A. Bérces, F. M. Bickelhaupt, C. Bo, P. M. Boerritger, L. Cavallo, C. Daul, D. P. Chong, D. V. Chulhai, L. Deng, R. M. Dickson, J. M. Dieterich, D. E. Ellis, M. van Faassen, A. Ghysels, A. Giammona, S. J. A. van Gisbergen, A. Goez, A. W. Götz, S. Gusarov, F. E. Harris, P. van den Hoek, Z. Hu, C. R. Jacob, H. Jacobsen, L. Jensen, L. Joubert, J. W. Kaminski, G. van Kessel, C. König, F. Kootstra, A. Kovalenko, M. Krykunov, E. van Lenthe, D. A. McCormack, A. Michalak, M. Mitoraj, S. M. Morton, J. Neugebauer, V. P. Nicu, L. Noodleman, V. P. Osinga, S. Patchkovskii, M. Pavanello, C. A. Peeples, P. H. T. Philipsen, D. Post, C. C. Pye, H. Ramanantoanina, P. Ramos, W. Ravenek, J. I. Rodríguez, P. Ros, R. Rüger, P. R. T. Schipper, D. Schlüns, H. van Schoot, G. Schreckenbach, J. S. Seldenthuis, M. Seth, J. G. Snijders, M. Solà, M. Stener, M. Swart, D. Swerhone, G. te Velde, V. Tognetti, P. Vernooijs, L. Versluis, L. Visscher, O. Visser, F. Wang, T. A. Wesolowski, E. M. van Wezenbeek, G. Wiesenekker, S. K. Wolff, T. K. Woo, and A. L. Yakovlev, “ADF2017, SCM, Theoretical Chemistry, Vrije Universiteit, Amsterdam, The Netherlands,” (2017).

Autschbach, J.

E. J. Baerends, T. Ziegler, A. J. Atkins, J. Autschbach, D. Bashford, O. Baseggio, A. Bérces, F. M. Bickelhaupt, C. Bo, P. M. Boerritger, L. Cavallo, C. Daul, D. P. Chong, D. V. Chulhai, L. Deng, R. M. Dickson, J. M. Dieterich, D. E. Ellis, M. van Faassen, A. Ghysels, A. Giammona, S. J. A. van Gisbergen, A. Goez, A. W. Götz, S. Gusarov, F. E. Harris, P. van den Hoek, Z. Hu, C. R. Jacob, H. Jacobsen, L. Jensen, L. Joubert, J. W. Kaminski, G. van Kessel, C. König, F. Kootstra, A. Kovalenko, M. Krykunov, E. van Lenthe, D. A. McCormack, A. Michalak, M. Mitoraj, S. M. Morton, J. Neugebauer, V. P. Nicu, L. Noodleman, V. P. Osinga, S. Patchkovskii, M. Pavanello, C. A. Peeples, P. H. T. Philipsen, D. Post, C. C. Pye, H. Ramanantoanina, P. Ramos, W. Ravenek, J. I. Rodríguez, P. Ros, R. Rüger, P. R. T. Schipper, D. Schlüns, H. van Schoot, G. Schreckenbach, J. S. Seldenthuis, M. Seth, J. G. Snijders, M. Solà, M. Stener, M. Swart, D. Swerhone, G. te Velde, V. Tognetti, P. Vernooijs, L. Versluis, L. Visscher, O. Visser, F. Wang, T. A. Wesolowski, E. M. van Wezenbeek, G. Wiesenekker, S. K. Wolff, T. K. Woo, and A. L. Yakovlev, “ADF2017, SCM, Theoretical Chemistry, Vrije Universiteit, Amsterdam, The Netherlands,” (2017).

Azoubib, J.

J. Azoubib, J. Nawrocki, and W. Lewandowski, “Independent atomic timescale in Poland-organization and results,” Metrologia 40(3), S245–S248 (2003).
[Crossref]

Baerends, E. J.

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Giammona, A.

E. J. Baerends, T. Ziegler, A. J. Atkins, J. Autschbach, D. Bashford, O. Baseggio, A. Bérces, F. M. Bickelhaupt, C. Bo, P. M. Boerritger, L. Cavallo, C. Daul, D. P. Chong, D. V. Chulhai, L. Deng, R. M. Dickson, J. M. Dieterich, D. E. Ellis, M. van Faassen, A. Ghysels, A. Giammona, S. J. A. van Gisbergen, A. Goez, A. W. Götz, S. Gusarov, F. E. Harris, P. van den Hoek, Z. Hu, C. R. Jacob, H. Jacobsen, L. Jensen, L. Joubert, J. W. Kaminski, G. van Kessel, C. König, F. Kootstra, A. Kovalenko, M. Krykunov, E. van Lenthe, D. A. McCormack, A. Michalak, M. Mitoraj, S. M. Morton, J. Neugebauer, V. P. Nicu, L. Noodleman, V. P. Osinga, S. Patchkovskii, M. Pavanello, C. A. Peeples, P. H. T. Philipsen, D. Post, C. C. Pye, H. Ramanantoanina, P. Ramos, W. Ravenek, J. I. Rodríguez, P. Ros, R. Rüger, P. R. T. Schipper, D. Schlüns, H. van Schoot, G. Schreckenbach, J. S. Seldenthuis, M. Seth, J. G. Snijders, M. Solà, M. Stener, M. Swart, D. Swerhone, G. te Velde, V. Tognetti, P. Vernooijs, L. Versluis, L. Visscher, O. Visser, F. Wang, T. A. Wesolowski, E. M. van Wezenbeek, G. Wiesenekker, S. K. Wolff, T. K. Woo, and A. L. Yakovlev, “ADF2017, SCM, Theoretical Chemistry, Vrije Universiteit, Amsterdam, The Netherlands,” (2017).

Goez, A.

E. J. Baerends, T. Ziegler, A. J. Atkins, J. Autschbach, D. Bashford, O. Baseggio, A. Bérces, F. M. Bickelhaupt, C. Bo, P. M. Boerritger, L. Cavallo, C. Daul, D. P. Chong, D. V. Chulhai, L. Deng, R. M. Dickson, J. M. Dieterich, D. E. Ellis, M. van Faassen, A. Ghysels, A. Giammona, S. J. A. van Gisbergen, A. Goez, A. W. Götz, S. Gusarov, F. E. Harris, P. van den Hoek, Z. Hu, C. R. Jacob, H. Jacobsen, L. Jensen, L. Joubert, J. W. Kaminski, G. van Kessel, C. König, F. Kootstra, A. Kovalenko, M. Krykunov, E. van Lenthe, D. A. McCormack, A. Michalak, M. Mitoraj, S. M. Morton, J. Neugebauer, V. P. Nicu, L. Noodleman, V. P. Osinga, S. Patchkovskii, M. Pavanello, C. A. Peeples, P. H. T. Philipsen, D. Post, C. C. Pye, H. Ramanantoanina, P. Ramos, W. Ravenek, J. I. Rodríguez, P. Ros, R. Rüger, P. R. T. Schipper, D. Schlüns, H. van Schoot, G. Schreckenbach, J. S. Seldenthuis, M. Seth, J. G. Snijders, M. Solà, M. Stener, M. Swart, D. Swerhone, G. te Velde, V. Tognetti, P. Vernooijs, L. Versluis, L. Visscher, O. Visser, F. Wang, T. A. Wesolowski, E. M. van Wezenbeek, G. Wiesenekker, S. K. Wolff, T. K. Woo, and A. L. Yakovlev, “ADF2017, SCM, Theoretical Chemistry, Vrije Universiteit, Amsterdam, The Netherlands,” (2017).

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E. J. Baerends, T. Ziegler, A. J. Atkins, J. Autschbach, D. Bashford, O. Baseggio, A. Bérces, F. M. Bickelhaupt, C. Bo, P. M. Boerritger, L. Cavallo, C. Daul, D. P. Chong, D. V. Chulhai, L. Deng, R. M. Dickson, J. M. Dieterich, D. E. Ellis, M. van Faassen, A. Ghysels, A. Giammona, S. J. A. van Gisbergen, A. Goez, A. W. Götz, S. Gusarov, F. E. Harris, P. van den Hoek, Z. Hu, C. R. Jacob, H. Jacobsen, L. Jensen, L. Joubert, J. W. Kaminski, G. van Kessel, C. König, F. Kootstra, A. Kovalenko, M. Krykunov, E. van Lenthe, D. A. McCormack, A. Michalak, M. Mitoraj, S. M. Morton, J. Neugebauer, V. P. Nicu, L. Noodleman, V. P. Osinga, S. Patchkovskii, M. Pavanello, C. A. Peeples, P. H. T. Philipsen, D. Post, C. C. Pye, H. Ramanantoanina, P. Ramos, W. Ravenek, J. I. Rodríguez, P. Ros, R. Rüger, P. R. T. Schipper, D. Schlüns, H. van Schoot, G. Schreckenbach, J. S. Seldenthuis, M. Seth, J. G. Snijders, M. Solà, M. Stener, M. Swart, D. Swerhone, G. te Velde, V. Tognetti, P. Vernooijs, L. Versluis, L. Visscher, O. Visser, F. Wang, T. A. Wesolowski, E. M. van Wezenbeek, G. Wiesenekker, S. K. Wolff, T. K. Woo, and A. L. Yakovlev, “ADF2017, SCM, Theoretical Chemistry, Vrije Universiteit, Amsterdam, The Netherlands,” (2017).

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B. Graner, Y. Chen, E. G. Lindahl, and B. R. Heckel, “Reduced limit on the permanent electric dipole moment of  199Hg,” Phys. Rev. Lett. 116, 161601 (2016).
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M. D. Swallows, T. H. Loftus, W. C. Griffith, B. R. Heckel, E. N. Fortson, and M. V. Romalis, “Techniques used to search for a permanent electric dipole moment of the  199Hg atom and the implications for CP violation,” Phys. Rev. A 87, 012102 (2013).
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Heckel, B. R.

B. Graner, Y. Chen, E. G. Lindahl, and B. R. Heckel, “Reduced limit on the permanent electric dipole moment of  199Hg,” Phys. Rev. Lett. 116, 161601 (2016).
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R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B Photophysics Laser Chem. 31(2), 97–105 (1983).
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Hu, Z.

E. J. Baerends, T. Ziegler, A. J. Atkins, J. Autschbach, D. Bashford, O. Baseggio, A. Bérces, F. M. Bickelhaupt, C. Bo, P. M. Boerritger, L. Cavallo, C. Daul, D. P. Chong, D. V. Chulhai, L. Deng, R. M. Dickson, J. M. Dieterich, D. E. Ellis, M. van Faassen, A. Ghysels, A. Giammona, S. J. A. van Gisbergen, A. Goez, A. W. Götz, S. Gusarov, F. E. Harris, P. van den Hoek, Z. Hu, C. R. Jacob, H. Jacobsen, L. Jensen, L. Joubert, J. W. Kaminski, G. van Kessel, C. König, F. Kootstra, A. Kovalenko, M. Krykunov, E. van Lenthe, D. A. McCormack, A. Michalak, M. Mitoraj, S. M. Morton, J. Neugebauer, V. P. Nicu, L. Noodleman, V. P. Osinga, S. Patchkovskii, M. Pavanello, C. A. Peeples, P. H. T. Philipsen, D. Post, C. C. Pye, H. Ramanantoanina, P. Ramos, W. Ravenek, J. I. Rodríguez, P. Ros, R. Rüger, P. R. T. Schipper, D. Schlüns, H. van Schoot, G. Schreckenbach, J. S. Seldenthuis, M. Seth, J. G. Snijders, M. Solà, M. Stener, M. Swart, D. Swerhone, G. te Velde, V. Tognetti, P. Vernooijs, L. Versluis, L. Visscher, O. Visser, F. Wang, T. A. Wesolowski, E. M. van Wezenbeek, G. Wiesenekker, S. K. Wolff, T. K. Woo, and A. L. Yakovlev, “ADF2017, SCM, Theoretical Chemistry, Vrije Universiteit, Amsterdam, The Netherlands,” (2017).

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Jacob, C. R.

E. J. Baerends, T. Ziegler, A. J. Atkins, J. Autschbach, D. Bashford, O. Baseggio, A. Bérces, F. M. Bickelhaupt, C. Bo, P. M. Boerritger, L. Cavallo, C. Daul, D. P. Chong, D. V. Chulhai, L. Deng, R. M. Dickson, J. M. Dieterich, D. E. Ellis, M. van Faassen, A. Ghysels, A. Giammona, S. J. A. van Gisbergen, A. Goez, A. W. Götz, S. Gusarov, F. E. Harris, P. van den Hoek, Z. Hu, C. R. Jacob, H. Jacobsen, L. Jensen, L. Joubert, J. W. Kaminski, G. van Kessel, C. König, F. Kootstra, A. Kovalenko, M. Krykunov, E. van Lenthe, D. A. McCormack, A. Michalak, M. Mitoraj, S. M. Morton, J. Neugebauer, V. P. Nicu, L. Noodleman, V. P. Osinga, S. Patchkovskii, M. Pavanello, C. A. Peeples, P. H. T. Philipsen, D. Post, C. C. Pye, H. Ramanantoanina, P. Ramos, W. Ravenek, J. I. Rodríguez, P. Ros, R. Rüger, P. R. T. Schipper, D. Schlüns, H. van Schoot, G. Schreckenbach, J. S. Seldenthuis, M. Seth, J. G. Snijders, M. Solà, M. Stener, M. Swart, D. Swerhone, G. te Velde, V. Tognetti, P. Vernooijs, L. Versluis, L. Visscher, O. Visser, F. Wang, T. A. Wesolowski, E. M. van Wezenbeek, G. Wiesenekker, S. K. Wolff, T. K. Woo, and A. L. Yakovlev, “ADF2017, SCM, Theoretical Chemistry, Vrije Universiteit, Amsterdam, The Netherlands,” (2017).

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E. J. Baerends, T. Ziegler, A. J. Atkins, J. Autschbach, D. Bashford, O. Baseggio, A. Bérces, F. M. Bickelhaupt, C. Bo, P. M. Boerritger, L. Cavallo, C. Daul, D. P. Chong, D. V. Chulhai, L. Deng, R. M. Dickson, J. M. Dieterich, D. E. Ellis, M. van Faassen, A. Ghysels, A. Giammona, S. J. A. van Gisbergen, A. Goez, A. W. Götz, S. Gusarov, F. E. Harris, P. van den Hoek, Z. Hu, C. R. Jacob, H. Jacobsen, L. Jensen, L. Joubert, J. W. Kaminski, G. van Kessel, C. König, F. Kootstra, A. Kovalenko, M. Krykunov, E. van Lenthe, D. A. McCormack, A. Michalak, M. Mitoraj, S. M. Morton, J. Neugebauer, V. P. Nicu, L. Noodleman, V. P. Osinga, S. Patchkovskii, M. Pavanello, C. A. Peeples, P. H. T. Philipsen, D. Post, C. C. Pye, H. Ramanantoanina, P. Ramos, W. Ravenek, J. I. Rodríguez, P. Ros, R. Rüger, P. R. T. Schipper, D. Schlüns, H. van Schoot, G. Schreckenbach, J. S. Seldenthuis, M. Seth, J. G. Snijders, M. Solà, M. Stener, M. Swart, D. Swerhone, G. te Velde, V. Tognetti, P. Vernooijs, L. Versluis, L. Visscher, O. Visser, F. Wang, T. A. Wesolowski, E. M. van Wezenbeek, G. Wiesenekker, S. K. Wolff, T. K. Woo, and A. L. Yakovlev, “ADF2017, SCM, Theoretical Chemistry, Vrije Universiteit, Amsterdam, The Netherlands,” (2017).

Jensen, L.

E. J. Baerends, T. Ziegler, A. J. Atkins, J. Autschbach, D. Bashford, O. Baseggio, A. Bérces, F. M. Bickelhaupt, C. Bo, P. M. Boerritger, L. Cavallo, C. Daul, D. P. Chong, D. V. Chulhai, L. Deng, R. M. Dickson, J. M. Dieterich, D. E. Ellis, M. van Faassen, A. Ghysels, A. Giammona, S. J. A. van Gisbergen, A. Goez, A. W. Götz, S. Gusarov, F. E. Harris, P. van den Hoek, Z. Hu, C. R. Jacob, H. Jacobsen, L. Jensen, L. Joubert, J. W. Kaminski, G. van Kessel, C. König, F. Kootstra, A. Kovalenko, M. Krykunov, E. van Lenthe, D. A. McCormack, A. Michalak, M. Mitoraj, S. M. Morton, J. Neugebauer, V. P. Nicu, L. Noodleman, V. P. Osinga, S. Patchkovskii, M. Pavanello, C. A. Peeples, P. H. T. Philipsen, D. Post, C. C. Pye, H. Ramanantoanina, P. Ramos, W. Ravenek, J. I. Rodríguez, P. Ros, R. Rüger, P. R. T. Schipper, D. Schlüns, H. van Schoot, G. Schreckenbach, J. S. Seldenthuis, M. Seth, J. G. Snijders, M. Solà, M. Stener, M. Swart, D. Swerhone, G. te Velde, V. Tognetti, P. Vernooijs, L. Versluis, L. Visscher, O. Visser, F. Wang, T. A. Wesolowski, E. M. van Wezenbeek, G. Wiesenekker, S. K. Wolff, T. K. Woo, and A. L. Yakovlev, “ADF2017, SCM, Theoretical Chemistry, Vrije Universiteit, Amsterdam, The Netherlands,” (2017).

Jiang, Z.

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Raczynski, A.

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Ramos, P.

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Romalis, M. V.

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E. J. Baerends, T. Ziegler, A. J. Atkins, J. Autschbach, D. Bashford, O. Baseggio, A. Bérces, F. M. Bickelhaupt, C. Bo, P. M. Boerritger, L. Cavallo, C. Daul, D. P. Chong, D. V. Chulhai, L. Deng, R. M. Dickson, J. M. Dieterich, D. E. Ellis, M. van Faassen, A. Ghysels, A. Giammona, S. J. A. van Gisbergen, A. Goez, A. W. Götz, S. Gusarov, F. E. Harris, P. van den Hoek, Z. Hu, C. R. Jacob, H. Jacobsen, L. Jensen, L. Joubert, J. W. Kaminski, G. van Kessel, C. König, F. Kootstra, A. Kovalenko, M. Krykunov, E. van Lenthe, D. A. McCormack, A. Michalak, M. Mitoraj, S. M. Morton, J. Neugebauer, V. P. Nicu, L. Noodleman, V. P. Osinga, S. Patchkovskii, M. Pavanello, C. A. Peeples, P. H. T. Philipsen, D. Post, C. C. Pye, H. Ramanantoanina, P. Ramos, W. Ravenek, J. I. Rodríguez, P. Ros, R. Rüger, P. R. T. Schipper, D. Schlüns, H. van Schoot, G. Schreckenbach, J. S. Seldenthuis, M. Seth, J. G. Snijders, M. Solà, M. Stener, M. Swart, D. Swerhone, G. te Velde, V. Tognetti, P. Vernooijs, L. Versluis, L. Visscher, O. Visser, F. Wang, T. A. Wesolowski, E. M. van Wezenbeek, G. Wiesenekker, S. K. Wolff, T. K. Woo, and A. L. Yakovlev, “ADF2017, SCM, Theoretical Chemistry, Vrije Universiteit, Amsterdam, The Netherlands,” (2017).

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Figures (9)

Fig. 1
Fig. 1 A simplified scheme of the laser setup. A fourth harmonic generation laser system delivers up to 30 mW of the 253.7 nm laser light which is frequency shifted by a double-pass transition in the acousto-optical modulator AOM1 and then directed to a mercury cell. A Doppler-free saturation absorption signal is used to monitor a deviation of the UV laser frequency from an atomic transition of a given Hg isotope. A part of the 1014.8 nm laser light is transferred through an AOM2 to a transfer cavity. The cavity length is stabilized to the wavelength of a 689 nm laser while the 1014.8 nm laser wavelength is locked to one of the cavity modes. The frequency of the 1014.8 nm laser is compared via the optical frequency comb to the frequencies of UTC(AOS) and UTC(PL) [29, 30] via the stabilized fibre optic link [31] of the OPTIME network [32, 33]. DDS stands for a direct digital synthesizer, PC – a desktop computer, μ-c – a microcontroller, PD – a photodiode, and PDH – Pound-Drever-Hall locking technique.
Fig. 2
Fig. 2 Schematic illustration of the background-induced frequency shift of the typical saturated absorption spectral line. a) a symmetrical profile; the red solid curve shows the slope-dependent SNR in the digital locking technique. b) a profile with a linear background. c) a profile with a linear (grey) and a non-linear (black) background. The red (panel b) and green (panel c) circles correspond to the probed range 2δf in the linear and the non-linear background case, respectively. The inflection points of the profile are marked with the blue circles. f0 (blue arrow) is a non-shifted frequency, fSNR (red arrow) and fSNR+NL (green arrow) are the frequencies obtained with f+ and f calculated from maximal SNR of fUV signal with the linear and the non-linear background, respectively.
Fig. 3
Fig. 3 Top: structure of the 254 nm line in the natural isotopic composition of mercury based on the data published by Schweitzer [35] and Zadnik [36]. Red and blue colour corresponds to bosons and fermions, respectively. The letters indicate the following hyperfine components: F = 1/2 (a), F = 3/2 (b), and F = 5/2 (c). The line strengths are normalized to the most abundant isotope, i.e. 202Hg. Bottom: a typical saturated absorption spectroscopy signal recorded in our measurements, averaged about ten times and power broadened for better visibility.
Fig. 4
Fig. 4 A scheme of the relevant frequencies, both radio (denoted by f) and optical (denoted by ν), used in the experimental setup. The coloured arrows indicate schematic paths of the laser beams while the black arrows correspond to the RF signalssent to a PC-based data acquisition system.
Fig. 5
Fig. 5 Results of the absolute frequency measurements for 1S03P1 transition in Hg isotopes. Both sample standard deviation (red error bars) and mean standard deviation (black error bars) for a given measurement are shown. The red dotted lines and the blue dashed lines are statistical and total (including statistical and systematic) uncertainties, respectively, as listed in Table 2.
Fig. 6
Fig. 6 Results of a sample AC-Stark shift measurement in the 1S0-3P1 transition of 204Hg. f204Hg is the absolute frequency of the transition. Each point represents the average of measurements for a given power of the UV light. Black and red error bars correspond to the mean and the sample standard deviation, respectively. The dashed blue lines indicate linear regression bands. The black solid line is the linear regression fit to the data weighted by the mean standard deviations.
Fig. 7
Fig. 7 Comparison of present work results to the previous determinations of the 1S03P1 frequency for different Hg isotopes. The experimental results are referenced to the following lines: 198Hg 546 nm (green circle), 86Kr 606 nm (red square) and 198Hg 185 nm (blue triangle). (1), (2) Burns and Adams [49, 50], (3) Gerstenkorn et al. eGerstenkorn1977, (4) Meggers and Kessler [52], (5) Barger and Kessler [53], (6) Barger and Kessler result corrected according to the Bruce and Hill data [54], (7) correction of the Barger result [53] made by Kramida [9] based on the measurement of 313.2749895 nm 198Hg [55] as a reference, (8) Kaufman [56], (9) Schweitzer [35], (10) Schweitzer’s result [35] corrected according to the Bruce and Hill data [54]. Black points are our results while the orange ones (cross) correspond to the corrected measurements.
Fig. 8
Fig. 8 A comparison of isotope shift results referenced to 198Hg. Our results (black) are compared with the data shown by Schweitzer [35] (blue circle), Crane [57] (red cross) and Gerstenkorn [51] (brown square). For better visibility, the results are separated horizontally and shifted by an isotope shift value measured in the present work for a given isotope.
Fig. 9
Fig. 9 King plot of normalised isotope shifts in the 6s6p 3P2-6s7s 3S1 (546 nm) transition (taken from [24]) versus normalised isotope shifts in the 5d10 6s2 1S0-5d10 6s6p 3P1 (254 nm) transition (our results). The isotope shifts of 199Hg were shifted to the centre of gravity of the hyperfine manifold according to the data published by Rayman [24], Sansonetti [58] (546 nm), and Stager [59] (254 nm). The red solid line is the linear fit weighted by uncertainties of isotope shifts. The common reference isotope is 198Hg.

Tables (3)

Tables Icon

Table 1 Systematic shifts and their uncertainties for typical experimental conditions, i.e. the UV laser beam intensity of 400 W/m2 and the temperature of the Hg-vapour cell of 26.1°C. All results are in MHz. Remote frequency reference characterisation, i.e. gravitational red shift between AOS laboratory and our laboratory as well as uncertainty between UTC(AOS) and TT (the SI second on the geoid) are taken from [31].

Tables Icon

Table 2 Measured absolute frequencies of the 1S0-3P1 transition.

Tables Icon

Table 3 Isotope shifts for the 1S0-3P1 transition in Hg referenced to 198Hg. The measured values are compared with the results presented by Schweitzer [35], Crane [57] and Gerstenkorn [51].

Equations (4)

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f U V = 4 ( f o + n f R ± f B 2 f A O M 2 ) + 2 f A O M 1 ,
I S i A A = A A A A M S i + E i δ r 2 A A ,
ζ 546 A A = ζ 254 A A E 546 E 254 + M S 546 E 546 E 254 M S 254 .
E i = Z e 2 6 ϵ 0 Δ ρ el ( 0 ) ,

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