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A liquid-nitrogen-cryogenic 40Ca+ optical clock is presented that is designed to greatly reduce the blackbody radiation (BBR) shift. The ion trap, the electrodes, and the in-vacuum BBR shied are installed under the liquid nitrogen container, keeping the ions in a cryogenic environment of liquid-nitrogen temperature. Compared to the first design in our previous work, many improvements have been made to increase performance. The liquid nitrogen maintenance time has been increased for about three times by increasing the volume of the liquid nitrogen container; the trap position recovery time after the liquid nitrogen container refilled has been decreased more than three times by a better fixing scheme for the liquid-nitrogen container; and the magnetic field noise felt by the ion has been decreased more than three times by a better design of the magnetic shielding system. These optimizations make the scheme for reducing the BBR shift uncertainty of liquid-nitrogen-cooled optical clocks more mature and stable, and develop a stable lock with a narrower linewidth spectrum, which would be very beneficial for further reducing the overall systematic uncertainty of optical clocks.

We constructed a transportable 40Ca+ optical clock (with an estimated minimum systematic shift uncertainty of 1.3*10^(-17) and a stability of 5*10^(-15)/sqrt{tau} ) that can operate outside the laboratory. We transported it from the Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan to the National Institute of Metrology, Beijing. The absolute frequency of the 729 nm clock transition was measured for up to 35 days by tracing its frequency to the second of International System of Units. Some improvements were implemented in the measurement process, such as the increased effective up-time of 91.3 % of the 40Ca+ optical clock over a 35-day-period, the reduced statistical uncertainty of the comparison between the optical clock and hydrogen maser, and the use of longer measurement times to reduce the uncertainty of the frequency traceability link. The absolute frequency measurement of the 40Ca+ optical clock yielded a value of 411042129776400.26 (13) Hz with an uncertainty of 3.2*10^(-16), which is reduced by a factor of 1.7 compared with our previous results. As a result of the increase in the operating rate of the optical clock, the accuracy of 35 days of absolute frequency measurement can be comparable to the best results of different institutions in the world based on different optical frequency measurements., Comment: 15 pages, 5 figures

We present a robust, transportable Ca+ optical clock, with a systematic uncertainty of 1.3 × 10−17 limitedby the black-body radiation (BBR) field evaluation and an uptime rate of >75% over a 20-day period. Theclock is then installed in an air-conditioned car trailer, making it more convenient for applications. Referencedto a stationary laboratory clock, geopotential measurements are made with the transportable clock with a totaluncertainty of 0.33 m (statistically 0.25 m and systematically 0.22 m) and agree with the spirit level measurement.After being moved >1200 km, the absolute frequency of the Ca+ optical clock transition is measuredas 411 042 129 776 400.41(23) Hz, with a fractional uncertainty of 5.6 × 10−16, which is about one orderof magnitude smaller than our previous measurement. The transportable built can be used for sub-meter-levelelevation measurements, comparing intercontinental optical clocks, verifying basic physical theories, etc.

Here we present a liquid nitrogen-cooled Ca^+ optical clock with an overall systematic uncertainty of 3*10^-18. In contrast with the room-temperature Ca^+ optical clock that we have reported previously, the temperature of the blackbody radiation (BBR) shield in vacuum has been reduced to 82(5) K using liquid nitrogen. An ion trap with a lower heating rate and improved cooling lasers were also introduced. This allows cooling the ion temperature to the Doppler cooling limit during the clock operation, and the systematic uncertainty due to the ion's secular (thermal) motion is reduced to < 1*10^-18. The uncertainty due to the probe laser light shift and the servo error are also reduced to < 1*10^-19 and 4*10^-19 with the hyper-Ramsey method and the higher-order servo algorithm, respectively. By comparing the output frequency of the cryogenic clock to that of a room-temperature clock, the differential BBR shift between the two was measured with a fractional statistical uncertainty of 7*10^-18. The differential BBR shift was used to calculate the static differential polarizability, and it was found in excellent agreement with our previous measurement with a different method. This work suggests that the BBR shift of optical clocks can be well suppressed in a liquid nitrogen environment. This is advantageous because conventional liquid-helium cryogenic systems for optical clocks are more expensive and complicated. Moreover, the proposed system can be used to suppress the BBR shift significantly in other types of optical clocks such as Yb^+, Sr^+, Yb, Sr, etc., 15 pages, 5 figures

Optical clocks are important for precise measurements in the field of physics. As reported, both the instability and uncertainty of optical lattice clocks are more than two orders of magnitude smaller than those of the best microwave clocks. Therefore, in the near future, optical clocks could be used to redefine the second. Nevertheless, an optical clock with reliability comparable to microwave clocks has not been achieved thus far. In this paper, we compared the frequencies of two Ca^+ optical clocks that were nearly continuously operated for 31 days. Through the comparison experiment, the frequency stability of a single clocks was found to be 6.3×10^-18 at an averaging time of 520 000 s and 7.9×10^-18 at averaging time of 262000 s, while the operating uptime rate reached more than 90% in the period of around 5 days. Thus, our experiment demonstrated that it is possible to increase the stability of single-ion optical clocks to the 10^-18 level, while still maintaining quasi-continuous operation with a high operating rate. This result further confirms that optical clocks can potentially be used to redefine the second.

Highly charged ions (HCIs) are promising candidates for the next generation of atomic clocks, owing to their tightly bound electron cloud, which significantly suppresses the common environmental disturbances to the quantum oscillator. Here we propose and pursue an experimental strategy that, while focusing on various HCIs of a single atomic element, keeps the number of candidate clock transitions as large as possible. Following this strategy, we identify four adjacent charge states of nickel HCIs that offer as many as six optical transitions. Experimentally, we demonstrated the essential capability of producing these ions in the low-energy compact Shanghai-Wuhan Electron Beam Ion Trap. We measured the wavelengths of four magnetic-dipole ($M$1) and one electric-quadrupole ($E$2) clock transitions with an accuracy of several ppm with a novel calibration method; two of these lines were observed and characterized for the first time in controlled laboratory settings. Compared to the earlier determinations, our measurements improved wavelength accuracy by an order of magnitude. Such measurements are crucial for constraining the range of laser wavelengths for finding the "needle in a haystack" narrow lines. In addition, we calculated frequencies and quality factors, evaluated sensitivity of these six transitions to the hypothetical variation of the electromagnetic fine structure constant $\alpha$ needed for fundamental physics applications. We argue that all the six transitions in nickel HCIs offer intrinsic immunity to all common perturbations of quantum oscillators, and one of them has the projected fractional frequency uncertainty down to the remarkable level of 10$^{-19}$., Comment: To be published in Physical Review A

We present a robust, transportable ${\mathrm{Ca}}^{+}$ optical clock, with a systematic uncertainty of $1.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ limited by the black-body radiation (BBR) field evaluation and an uptime rate of $g75%$ over a 20-day period. The clock is then installed in an air-conditioned car trailer, making it more convenient for applications. Referenced to a stationary laboratory clock, geopotential measurements are made with the transportable clock with a total uncertainty of 0.33 m (statistically 0.25 m and systematically 0.22 m) and agree with the spirit level measurement. After being moved $g1200$ km, the absolute frequency of the ${\mathrm{Ca}}^{+}$ optical clock transition is measured as 411 042 129 776 400.41(23) Hz, with a fractional uncertainty of $5.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$, which is about one order of magnitude smaller than our previous measurement. The transportable built can be used for sub-meter-level elevation measurements, comparing intercontinental optical clocks, verifying basic physical theories, etc.

The hyperfine structures of the $2{^{3}S}_{1}$ states of the $^{6}{\mathrm{Li}}^{+}$ and $^{7}{\mathrm{Li}}^{+}$ ions are investigated theoretically to extract the Zemach radii of the $^{6}\mathrm{Li}$ and $^{7}\mathrm{Li}$ nuclei by comparing with precision measurements. The obtained Zemach radii are larger than the previous values of Puchalski and Pachucki [Phys. Rev. Lett. 111, 243001 (2013)] and disagree with them by about 1.5 and 2.2 standard deviations for $^{6}\mathrm{Li}$ and $^{7}\mathrm{Li}$, respectively. Furthermore, our Zemach radius of $^{6}\mathrm{Li}$ differs significantly from the nuclear physics value, derived from the nuclear charge and magnetic radii [Phys. Rev. A 78, 012513 (2008)] by more than $6\ensuremath{\sigma}$, indicating an anomalous nuclear structure for $^{6}\mathrm{Li}$. The conclusion that the Zemach radius of $^{7}\mathrm{Li}$ is about 40% larger than that of $^{6}\mathrm{Li}$ is confirmed. The obtained Zemach radii are used to calculate the hyperfine splittings of the $2{^{3}P}_{J}$ states of $\text{ }{^{6,7}\mathrm{Li}}^{+}$, where an order of magnitude improvement over the previous theory has been achieved for $^{7}{\mathrm{Li}}^{+}$.

Precision spectroscopy of ${\mathrm{Li}}^{+}$ is a promising testing ground for bound-state quantum electrodynamics (QED) and for measurements of nuclear properties such as the Zemach radius. We investigate the hyperfine and fine-structure splittings of the $2\phantom{\rule{0.16em}{0ex}}^{3}S_{1}$ and $2{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{J}$ states of $^{7}\mathrm{Li}^{+}$ using saturated fluorescence spectroscopy based on a $\ensuremath{\sim}460\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$ metastable ion beam. We measure in particular the $2\phantom{\rule{0.16em}{0ex}}^{3}S_{1}--2\phantom{\rule{0.16em}{0ex}}^{3}P_{J}$ transitions in $^{7}\mathrm{Li}^{+}$. With a triple nested loop scanning method, the long-term drift and systematic uncertainties are reduced or eliminated, resulting in a total uncertainty of less than 100 kHz. Our results are in good agreement with QED calculations. For the hyperfine splittings of $2\phantom{\rule{0.16em}{0ex}}^{3}S_{1}$, our measured values have a similar accuracy to previous measurements and theoretical calculations. For the $2{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{J}$ fine and hyperfine splittings, our measured results are one order of magnitude more accurate than those of previous measurements and have a similar accuracy to the theoretical values. The measurements lay the foundation for future work on the ${\mathrm{Li}}^{+}$ isotopes and their theoretical interpretation in terms of nuclear charge radii and the Zemach radii.

Edge states emerge in diverse areas of science, offering promising opportunities for the development of future electronic or optoelectronic devices, sound and light propagation control in acoustics and photonics. Previous experiments on edge states in photonics were carried out mostly in linear regimes, but the current belief is that nonlinearity introduces more striking features into physics of edge states, leading to the formation of edge solitons, optical isolation, making possible stable lasing in such states, to name a few. Here we report the observation of edge solitons at the zigzag edge of a reconfigurable photonic graphene lattice created via the effect of electromagnetically induced transparency in an atomic vapor cell with controllable nonlinearity. To obtain edge solitons, Raman gain is introduced to compensate strong absorption experienced by the edge state during propagation. Our observations may open the way for future experimental exploration of topological photonics on this nonlinear, reconfigurable platform., Edge states are excitations existing at the boundary of truncated periodic materials with specific spectral degeneracies, and their properties are enriched when materials possess a nonlinear response. Here, the authors provide experimental evidence of edge soliton formation in a nonlinear photonic graphene lattice induced in an atomic vapour cell.

In this work, we carry out experimental measurements and theoretical calculations of the branching fractions for the $4{P}_{3/2}$ state of $^{40}\mathrm{Ca}^{+}$. The measurements are based on counting photon numbers emitted from hundreds of ions trapped in a linear Paul trap, as their being affected by lasers. The calculations are performed using the relativistic coupled-cluster method at different approximations. The measured values for the decays of the $4{P}_{3/2}$ state into the $4{S}_{1/2}$, $3{D}_{5/2}$, and $3{D}_{3/2}$ states are, respectively, 0.9350(4), 0.0587(4), and 0.0063(2), which agree well with our recommended theoretical values 0.9344(13), 0.0590(12), and 0.0066(1). Our measured values are also consistent with the experimental values of Gerritsma et al. [R. Gerritsma, G. Kirchmair, F. Z\"ahringer, J. Benhelm, R. Blatt, and C. F. Roos, Eur. Phys. J. D 50, 13 (2008)] using a completely different method. Furthermore, we also calculate the branching fractions of the $4{P}_{1/2}$ state using the same method, and compare to the available experimental and theoretical data.

In this review, the improvements made in the past two decades for 40Ca+ optical clocks in China are presented. Uncertainty of below 1.3×10−17 was achieved by applying the “magic” RF trapping frequency and introducing a generalized Ramsey excitation scheme. The stability of 40Ca+ optical clocks has been improved to 2.5×10−15/τ with an uptime rate of 93.8% by implementing two ameliorated lock algorithms in the Ramsey excitation scheme. A long-term clock frequency comparison shows a clock stability of 6.3 × 10−18 in an averaging time of 524 000 s. A robust and transportable clock installed in an air-conditioned car trailer can achieve almost the same performance of laboratory clocks. A height difference between transportable and laboratory clocks was measured with an uncertainty of 0.33 m and the absolute frequency of 40Ca+ optical clock transitions was remeasured as 411 042 129 776 400.41(23) Hz, with a fractional uncertainty of 5.6×10−16 based on a Cs fountain clock in the National Institute of Metrology after the transportable clock was transported from Wuhan to Beijing. The author predicts that transportable single-ion optical clocks especially based on the 40Ca+ will make a significant contribution to the construction of a world-wide optical clock network and the redefinition of the unit of time in the future.

Laser frequency stabilization plays an important role in high-precision spectroscopic measurements. Since high-accuracy commercial wavemeters became available, wavemeter-based frequency stabilization has found a broad application due to its convenience, flexibility, and wide applicability. However, such stabilization schemes frequently suffer from long-term drift, since the accuracy of the wavelength measurement of a wavemeter is affected by ambient temperature fluctuation. In this work, we demonstrate that such long-term drift can be suppressed by regularly calibrating the frequency of a wavemeter-locked laser utilizing an optical frequency comb, which has much better long-term stability. Under this dual-referenced locking scheme, the Allan deviation is reduced to 3.5 E-12 at 4000 s for a fiber laser operated at 548 nm, which when used in the optical Ramsey spectroscopic measurement of 7 L i + , reduces the standard deviation by as much as 40%, compared to the case when only wavemeter locking is applied.

We investigate the process of pulsed laser cooling using a self-constructed molecular dynamics simulation (MD-Simulation) program. We simulate the Doppler cooling process and pulsed laser Doppler cooling process of a single 40Ca+ ion, and the comparison with the experimental results shows that this self-constructed MD-Simulation program works well in the weak laser intensity situation. Furthermore, we analyze the pulsed laser Doppler cooling process of a single 27Al+ ion. This program can be used to analyze the molecular dynamic process of various situations of Doppler cooling in an ion trap, which could give predictions and experimental guidance.

Micromotion induced by the radio-frequency field contributes greatly to the systematic frequency shifts of optical frequency standards. Although different strategies for mitigating this effect have been proposed, trapping ions optically has the potential to provide a generic solution to the elimination of micromotion. This could be achieved by trapping a single ion in the dipole trap composed of a highpower laser field. Here, we present the setup of the dipole trap composed of a 532 nm laser at a power of 10 W aiming to optically trap a single 40Ca+ and we observe an AC-Stark shift of the fluorescence spectrum line of ∼22 MHz caused by the 532 nm dipole beam. The beam waist of the dipole laser is several microns, which would provide a dipole potential strong enough for all-optical trapping of a single 40Ca+ ion.

A low-energy, compact and superconducting electron beam ion trap (the Shanghai-Wuhan EBIT or SW-EBIT) for extraction of highly charged ions is presented. The magnetic field in the central drift tube of the SW-EBIT is approximately 0.21 T produced by a pair of high-temperature superconducting coils. The electron-beam energy of the SW-EBIT is in the range of 30-4000 eV, and the maximum electron-beam current is up to 9 mA. Acting as a source of highly charged ions, the ion-beam optics for extraction is integrated, including an ion extractor and an einzel lens. A Wien filter is then used to measure the charge-state distribution of the extracted ions. In this work, the tungsten ions below the charge state of 15 have been produced, extracted, and analyzed. The charge-state distributions and spectra in the range of 530-580 nm of tungsten ions have been measured simultaneously with the electron-beam energy of 279 eV and 300 eV, which preliminarily indicates that the 549.9 nm line comes from $W^{14+}$., This article has been published on Review of Scientific Instruments. Available at https://doi.org/10.1063/1.5112154

The apparatus for fluorescence spectroscopy measurement is developed to determine the fine structure (FS)/hyperfine structure (HFS) splittings of 1s2p

The fractional uncertainty of the 40Ca+ optical clock in our laboratory has been evaluated to be 2.2 × 10 − 17, but it is difficult to evaluate the statistical uncertainty of the output frequency at this level, limited by the frequency stability associated with the quantum projection noise (QPN). A reduction in the stability is required to shorten the averaging time for a certain statistical uncertainty level. To improve the stability, the Ramsey method is introduced in the locking process. To improve the reliability and continuity, we introduce the idea of using auxiliary Rabi probes to avoid fringe slips in the Ramsey interrogation and to automatically search for resonance. The stability of a single 40Ca+ ion frequency standard is improved from 6.3 × 10 − 15 / τ to 2.5 × 10 − 15 / τ, where τ is the averaging time in seconds, which is close to the QPN limit for an 80-ms-long Ramsey interrogation. We obtain a stability of 1.5 × 10 − 17 at an averaging time of 21 000 s and an uptime rate of 93.8% for a 34-h-long run. These methods can easily be applied to other ion or neutral atom optical clocks.

Sympathetic cooling is a method used to lower the kinetic energy of ions with complicated energy-level structures, via Coulomb interactions with laser-cooled ions in an ion trap. The ion to be sympathetically cooled is sometimes prepared outside of the trap, and it is critical to introduce this ion into the trap by temporarily lowering the potential of one endcap without allowing the coolant ion to escape. We study the time required for a laser-cooled ion to escape from a linear Paul trap when the voltage of one endcap is lowered. The escape time is on the order of a few microseconds, and varies significantly when the low-level voltage changes. A re-cooling time of a maximum of 13 s was measured, which can be reduced to approximately one hundred of milliseconds by decreasing the duration of the low-level voltage. The measurement of these critical values lays the foundation for the smooth injection and cooling of the ion to be sympathetically cooled.

Ion deceleration has played a critical role in ion-related research when the ions are produced in the form of a high-energy beam. We present a deceleration method combining electrostatic lens and ion trap technique, which can effectively decelerate ions to energy below the trapping potential of a typical ion trap. The experiments were performed on metastable 1s2s 3 S 1 Li+ ions, and demonstrated that the kinetic energy could easily be reduced from ∼450 eV to a few eV, with the latter being confirmed using the Doppler-shifted fluorescence spectra.

Progress of the 40Ca+ ion optical clock based on the 42S1/2 – 3d 2D5/2 electric quadrupole transition is reported. By setting the drive frequency to the “magic” frequency Ω 0, the frequency uncertainty caused by the scalar Stark shift and second-order Doppler shift induced by micromotion is reduced to the 10−19 level. By precisely measuring the differential static scalar polarizability Δα 0, the uncertainty due to the blackbody radiation (BBR) shift (coefficient) is reduced to the 10−19 level. With the help of a second-order integrating servo algorithm, the uncertainty due to the servo error is reduced to the 10−18 level. The total fractional uncertainty of the 40Ca+ ion optical clock is then improved to 2.2× 10−17, whereas this value is mainly restricted by the uncertainty of the BBR shift due to temperature fluctuations. The state preparation is introduced together with improvements in the pulse sequence, and furthermore, a better signal to noise ratio (SNR) and less dead time are achieved. The clock stability of a single clock is improved to 4.8 × 10 − 15 / τ ( in seconds ) .

We recently reported a 5×10−17 level frequency comparison of two 40Ca+ optical clocks, one of which has fractional frequency uncertainty of 3.4×10−17, limited by the BBR effect. Here we present progress towards a 40Ca+ optical clock with uncertainty at the 10−18 level. The differential static scalar polarizability Δα0 of the 40Ca+ ion clock transition is obtained by precisely measuring the “magic” rf drive frequency. Δα0 is measured as −7.2653(44)x10−40 J m2/V2, the blackbody radiation shift is then calculated to be 0.3790(2) Hz at 300 K. The contribution of the blackbody shift coefficient to the uncertainty of the optical clock at room temperature is reduced to 5.6×10−19, the excess micromotion induced clock uncertainty is also reduced to the 10−19 level by choosing the appropriate trap drive frequency. With a suppression of the BBR field temperature uncertainty to the sub-Kelvin level and improved clock stability, a robust, relatively low-cost 40Ca+ ion clock with uncertainty at 10−18 level can be made.

The apparatus for fluorescence spectroscopy measurement is developed to determine the fine structure (FS)/hyperfine structure (HFS) splittings of 1s2p 3PJ(J=0,1,2) states of Li+. The instrument is composed of a low energy Li+ ion source and a saturated fluorescence spectroscopic probing system. A low energy Li+ ion source, containing 1.8(7)% of 1s2s 3S1 metastable ions with an energy of ∼500 eV, is obtained by an electron bombardment process. The ion current can stay more than 250 h with the variation of ∼0.3%, and the divergence of ion beam is ∼0.5 mrad. The symmetric profile of Lamb dip signals of 1s2s 3S1−−1s2p 3PJ transitions with linewidths of ∼50 MHz are obtained after subtracting Doppler background from the saturated fluorescence signals. A back-and-forth scan method is adopted to determine the FS/HFS splittings of 1s2p 3PJ states. Under these conditions, as a preliminary test, several splittings of 7Li+ are measured. The statistical uncertainties of the FS/HFS splittings are estimated to be less than 50 kHz, and the results are one order of magnitude better than previous results. The apparatus is feasible to precisely determine the splittings of energy levels of alkali and alkaline earth ions.

A Ti:sapphire laser at 729 nm is frequency stabilized to an ultra-stable ultra-low thermal expansion coefficient (ULE) cavity by means of Pound-Drever-Hall method. An acousto-optic modulator is used as the fast frequency feedback component. 1 Hz linewidth and 2 × 10(-15) frequency stability at 1-100 s are characterized by optical beating with a separated Fabry-Perot cavity stabilized diode laser. Compared to the universal method that the error signal feedback to inject current of a diode laser, this scheme is demonstrated to be simple and also effective for linewidth narrowing. The temperature of zero coefficient of the thermal expansion of the ULE cavity is measured with the help of a femto-second frequency comb. And the performance of the laser is well defined by locking it to the unperturbed clock transition line-center of 4 S1/2-3 D5/2 clock transition of a single laser cooled (40)Ca(+) ion. A Fourier-transform limited resonance of 6 Hz (Δv/v = 1.5 × 10(-14)) is observed. This laser is also used as the local oscillator for the comparison experiment of two (40)Ca(+) ion optical clocks and improves the stability of comparison for an order of magnitude better than the previous results.

In this paper, we present a detailed method for rapidly and effectively loading a single 40Ca+ ion into a miniature linear Paul trap. Calcium atoms are generated by laser ablation, and the single ion is loaded and specific isotopes are selected by a two-step photo-ionization method. Compared to the traditional photo-ionization method in which atoms are typically emitted from a resistively heated oven, the advantages of laser ablation are that it can be precisely controlled, it can effectively avoid the problem of fluxed calcium deposition on the trap electrodes, and it restricts the generation of dark ions, which can influence atomic-precision spectroscopy measurements. With its short loading time, it is possible to load an ion in few seconds with the appropriate parameters. The technique of laser ablation has been applied to generate several species of atoms and ions at present, it will potentially benefit in the studies of optical frequency standards, quantum simulation and quantum information processing in an ultra-high vacuum condition and cryogenic system.

Stability is one of most important performances of an atomic clock. Here we describe our recent work on improving the stability of our 40 Ca + optical clock. State preparation is adopted to transfer the ion to the ground-state magnetic sublevel of the clock transition, after the quenching laser transfers the ion to the ground state at each cycle. Using this method, the stability for 40 Ca + optical clock is improved to about . Compared with in previous work, the averaging time is decreased to reach a given level of statistical uncertainty in a clock comparison.

Potential distribution is an important characteristic for evaluating the performance of an ion trap. Here, we analyze and optimize the potential distribution of an endcap ion trap for single-ion trapping. We obtain an optimal endcap radius of 225 μm–250 μm, endcap-shield gap of ~ 250 μm, and inter-endcap distance of 540 μm–590 μm. The simulation method for analysis can also be applied to other ion traps, which is useful for improving the design and assembly of ion traps.

We demonstrate experimentally the existence of magic wavelengths and determine the ratio of oscillator strengths for a single trapped ion. For the first time, two magic wavelengths near 396 nm for the Ca-40(+) clock transition are measured simultaneously with high precision. By tuning the applied laser to an intermediate wavelength between transitions 4s(1/2) -> 4p(1/2) and 4s(1/2) -> 4p(3/2), the sensitivity of the clock transition Stark shift to the oscillator strengths is greatly enhanced. Furthermore, with the measured magic wavelengths, we determine the ratio of the oscillator strengths with a deviation of less than 0.5%. Our experimental method may be applied to measure magic wavelengths for other ion clock transitions. Promisingly, the measurement of these magic wavelengths paves the way to building all-optical trapped ion clocks.

In light of the diverse range of reported values for the lifetimes of metastable states of Ca-40(+), we have carried out afresh both measurements and theoretical investigation to confirm the lifetime of its 3d D-2(5/2) state (tau(3d5/2)). A high-efficiency quantum state detection method by monitoring the quantum jumps of a laser-cooled single Ca+ ion in a miniature ring Paul trap was employed in the measurement. Also, sophisticated calculations were performed considering higher order nonlinear terms in the relativistic coupled-cluster (RCC) method with all possible single and double excitations, but accounting only for the important triple excitations from both the core and the valence orbitals. Systematic factors affecting measurement, such as collision with background gases, heating effects, the power of the 866-nm laser, and state detection errors were carefully analyzed. Our observational and theoretical values for tau(3d5/2) are 1174(10) ms and 1172(3) ms, respectively, which agree well with the experimental results reported by P. A. Barton et al. [Phys. Rev. A 62, 032503 (2000)] and A. Kreuter et al. [Phys. Rev. A 71, 032504 (2005)]. The present theoretical analysis demonstrates that the contributions from the core triples and Breit interaction are notable, as they improve the theoretical results obtained in the previous RCC calculations [B. K. Sahoo, Phys. Rev. A 74, 062504 (2006)].

Ac-Stark shift of atom levels is caused by an ac-electromagnetic field. As an electromagnetic wave, laser light does induce ac-Stark shift. It is proved experimentally that if the light is linearly polarized, the dynamic polarizability changes with polarization direction. The polarization direction of the linearly-polarized laser is tuned by 720 degrees, and the ac-Stark shifts of the 4S(1/2), m = (+/- 1/2) -> 3D(5/2), (m = +/- 1/2) clock transitions in Ca-40(+) are measured in steps of 10 degrees. The frequency shifts change with laser polarization in a periodical manner and have values opposite to each other.

The experimental study at Wuhan Institute of Physics and Mathematics (WIPM), Chinese Academy of Scienses (CAS) on the precision spetroscopy based on single trapped Ca+ ion is described in this paper. A single Ca+ ion is trapped in a miniature Paul trap and laser cooled to Lamb-Dicke regime, and the ion can be trapped more than 2 months. The linewidth of the 729 nm laser for probing the Ca+ 4 s 2 S 1/2-3 d 2 D 5/2 clock transition is reduced to lessthan 1 Hz by locked to a super cavity, and the 729 nm laser can be locked more than 1 month continuously. Two similar Ca + ion optical frequency standards are set up for frequency comparison. The systematic uncertainty is evaluated to be ´ 10−17 for both ftrquency standards. The frequency difference of two frequency standards is measured to be 3.0 (5.5) ´ 10−17 within 42 d. The Allan deviation for a single clock is measured to be 1×10−14 τ −1/2 with a 3-d-continuous comparison, the stability for a reaches 7 ´ 10−17 at an averaging time of 20000 s. Meanwhile, the absolute frequency of the Ca+ 4 s 2 S 1/2-3 d 2 D 5/2 clock transition is measured to be 411042129776401.7(1.1) Hz with respect to the SI second through the Global Positioning System (GPSx). The precision spectroscopy experiments are carried out based on the single Ca+ ion system. The magic wavelengths for the Ca+ optical frequency standardare measured to be λ | mj |=1/2=395.7992(7) nm and λ | mj |=3/2=395.7990(7) nm, which agrees with theoretical calculation made by Tang et al. The lifetime of the 3 d 2 D 5/2 is measured to be 1174(10) ms, which is agree with the experimental measurement made by University of Oxford and University of Innsbruck and the recent theoretical calculation made by Sahoo.