Marc-Oliver Mewes, Gabriele Ferrari, Florian Schreck, Alice Sinatra, Christophe Salomon
We confine 4 10^8 fermionic 6Li atoms simultaneously with 9 10^9 bosonic 7Li atoms in a magneto-optical trap based on an all-semiconductor laser system. We optimize the two-isotope sample for sympathetic evaporative cooling. This is an essential step towards the production of a quantum-degenerate gas of fermionic lithium atoms.
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The near resonant cooling mechanism have offered for the experiment with laser induced excitation of Lithium isotopes and its ionization by collisions.
The electric dipole polarizabilities and hyperpolarizabilities for the lithium isotopes $^6$Li and $^7$Li in the ground state $2^2S$ and the excited states $2^2P$ and $3^2D$, as well as the leading resonance and dispersion long-range coefficients for the Li($2^2S$)--Li($2^2S$) and Li($2^2S$)--Li($2^2P$) systems, are calculated nonrelativistically using variational wave functions in Hylleraas basis sets. Comparisons are made with published results, where available. We find that the value of the second hyperpolarizability of the $2^2S$ state is sensitive to the isotopic mass due to a near cancel…
We have successfully implemented the first simultaneous magneto-optical trapping (MOT) of lithium ($^6$Li) and ytterbium ($^{174}$Yb) atoms, towards production of ultracold polar molecules of LiYb. For this purpose, we developed the dual atomic oven which contains both atomic species as an atom source and successfully observed the spectra of the Li and Yb atoms in the atomic beams from the dual atomic oven. We constructed the vacuum chamber including the glass cell with the windows made of zinc selenium (ZnSe) for the CO$_2$ lasers, which are the useful light sources of optical trapping for ev…
We demonstrate simultaneous deceleration and trapping of a cold atomic and molecular mixture. This is the first step towards studies of cold atom-molecule collisions at low temperatures as well as application of sympathetic cooling. Both atoms and molecules are cooled in a supersonic expansion and are loaded into a moving magnetic trap which brings them to rest via the Zeeman interaction from an initial velocity of 375 m/s. We use a beam seeded with molecular Oxygen, and entrain it with Lithium atoms by laser ablation prior to deceleration. The deceleration ends with loading of the mixture int…
We demonstrate an ultrastable CO2 laser trap that provides tight confinement of neutral atoms with negligible optical scattering and minimal laser-noise- induced heating. Using this method, fermionic 6Li atoms are stored in a 0.4 mK deep well with a 1/e trap lifetime of 300 sec, consistent with a background pressure of 10^(-11) Torr. To our knowledge, this is the longest storage time ever achieved with an all-optical trap, comparable to the best reported magnetic traps.
Changes in the mean-square nuclear charge radii along the lithium isotopic chain were determined using a combination of precise isotope shift measurements and theoretical atomic structure calculations. Nuclear charge radii of light elements are of high interest due to the appearance of the nuclear halo phenomenon in this region of the nuclear chart. During the past years we have developed a new laser spectroscopic approach to determine the charge radii of lithium isotopes which combines high sensitivity, speed, and accuracy to measure the extremely small field shift of an 8 ms lifetime isotope…
Bound state properties of the four-electron lithium ion Li$^{-}$ in its ground $2^{2}S-$state and isotope-subsistuted ${}^{6}$Li$^{-}$ and ${}^{7}$Li$^{-}$ ions in their ground $2^1S-$state(s) are determined from the results of accurate, variational computations. Another closely related problem discussed in this study is accurate numerical evaluation of the half-life of the beryllium-7 isotope. This problem is of paramount importance for modern radiochemistry.
We present studies of resonance-enhanced photo-ionization for isotope-selective loading of Ca+ into a Paul trap. The 4s^2 ^1S_0 <-> 4s4p ^1P_1 transition of neutral calcium is driven by a 423nm laser and the atoms are photo-ionized by a second laser at 389nm. Isotope-selectivity is achieved by using crossed atomic and laser beams to reduce the Doppler width significantly below the isotope shifts in the 423nm transition. The loading rate of ions into the trap is studied under a range of experimental parameters for the abundant isotope 40Ca+. Using the fluorescence of the atomic beam at 423nm as…
It was recently shown that dielectronic recombination measurements can be used for accurately inferring changes in the nuclear mean-square charge radii of highly-charged lithium-like neodymium [Brandau et al., Phys. Rev. Lett. 100 073201 (2008)]. To make use of this method to derive information about the nuclear charge distribution for other elements and isotopes, accurate electronic isotope shift parameters are required. In this work, we calculate and discuss the relativistic mass- and field-shift factors for the two $2s ^{2}S_{1/2} - 2p ^{2}P^{o}_{1/2,3/2}$ transitions along the lithium isoe…
Optical trapping techniques are an efficient way to probe limited quantities of rare isotopes. In order to achieve the highest possible measurement precision, it is critical to optimize the optical trapping efficiency. This work presents the development of a three-dimensional semi-classical Monte Carlo simulation of the optical trapping process and its application to optimizing the optical trapping efficiency of Radium for use in the search of the permanent electric dipole moment of $^{225}$Ra. The simulation includes an effusive-oven atomic beam source, transverse cooling and Zeeman slowing o…
Trapping lithium with a big number in a simplified experimental setup has difficulties and challenges today. In this paper, we experimentally demonstrate the enhancement of \textsuperscript{6}Li trapping efficiency in a three-dimensional magneto-optical trap (3D MOT) by using the multiple-sideband cooling in a two-dimensional magneto-optical trap (2D MOT). To improve the number of trapped atoms, we broaden the cooling light spectrum to 102 MHz composed of seven frequency components and then trap atoms with a number of $6.0\times10^8$ which is about 4 times compared to that in the single-freque…
Isotope-selective Ion Trapping via Sympathetic Cooling using a Surface-Electrode Trap with a Hole for Collimated Atomic Loading
通过表面电极陷阱的孔进行协同冷却实现同位素选择性离子捕获，用于高效制备同位素离子对和离子链。
We have successfully loaded a magneto-optic trap for Yb atoms from a thermal source without the use of a Zeeman slower. The source is placed close to the trapping region so that it provides a large flux of atoms that can be cooled and captured. The atoms are cooled on the ${^1S_0} \leftrightarrow {^1P_1}$ transition at 398.8 nm. We have loaded all seven stable isotopes of Yb into the trap. For the most abundant isotope ($^{174}$Yb), we load more than $10^7$ atoms into the trap within 1 s. For the rarest isotope ($^{168}$Yb) with a natural abundance of only 0.13%, we still load about $4 \times …
Resonant photoionization dynamics during optical trapping of lithium atoms
本研究利用反应显微镜结合逐事件时间重建技术，探究全光阱中激光冷却锂原子的低强度多色光电离，识别5p、5f态共振激发及额外电离通道，揭示光电离产额的偏振依赖机制。
Magneto-optical trapping of Zinc
本文报道了利用213.9纳米跃迁实现锌原子的激光冷却与磁光囚禁，成功囚禁所有稳定同位素，包括可能用于光学原子钟的费米子同位素，为高精度光谱和量子信息处理奠定基础。
We report a vapor-cell magneto-optical trapping of Hg isotopes on the ${}^1S_0-{}^3P_1$ intercombination transition. Six abundant isotopes, including four bosons and two fermions, were trapped. Hg is the heaviest non-radioactive atom trapped so far, which enables sensitive atomic searches for ``new physics'' beyond the standard model. We propose an accurate optical lattice clock based on Hg and evaluate its systematic accuracy to be better than $10^{-18}$. Highly accurate and stable Hg-based clocks will provide a new avenue for the research of optical lattice clocks and the time variation of t…
Using first-principles calculations, we identify magic wavelengths for the 2s-2p and 2s-3p transitions in lithium. The ns and np atomic levels have the same ac Stark shifts at the corresponding magic wavelength, which facilitates state-insensitive optical cooling and trapping. Tune-out wavelengths for which the ground-state frequency-dependent polarizability vanishes are also calculated. Differences of these wavelengths between 6Li and 7Li are reported. Our approach uses high-precision, relativistic all-order methods in which all single, double, and partial triple excitations of the Dirac-Fock…
The determination of isotope ratios of noble gas atoms has many applications e.g. in physics, nuclear arms control, and earth sciences. For several applications, the concentration of specific noble gas isotopes (e.g. Kr and Ar) is so low that single atom detection is highly desirable for a precise determination of the concentration. As an important step in this direction, we demonstrate operation of a krypton Atom Trap Trace Analysis (ATTA) setup based on a magneto-optical trap (MOT) for metastable Kr atoms excited by all-optical means. Compared to other state-of-the-art techniques for prepari…
We present a realization of a magneto-optical trap of mercury atoms on the intercombination line. We report on trapping of all stable mercury isotopes. We characterize the effect of laser detuning, laser intensity, and gradient field on the trapping performance of our system. The atom number for the most abundant isotope Hg-202 is 50 million atoms. Moreover, we study the difference in cooling processes for bosonic and fermionic isotopes. We observe agreement with the Doppler cooling theory for the bosonic species and show sub-Doppler cooling for the fermionic species. We reach a phase space de…
Lithium is an important element in atomic quantum gas experiments because its interactions are highly tunable, due to broad Feshbach resonances and zero-crossings, and because it has two stable isotopes, $^6$Li, a fermion, and $^7$Li, a boson. Although lithium has special value for these reasons, it also presents experimental challenges. In this article, we review some of the methods that have been developed or adapted to confront these challenges, including beam and vapor sources, Zeeman slowers, sub-Doppler laser cooling, laser sources at 671 nm, and all-optical methods for trapping and cool…
Compact structures for single-beam magneto-optical trapping of ytterbium
本文提出两种紧凑消色差反射镜结构，实现镱原子单光束磁光阱，并在准平面结构中首次实现费米子碱土类同位素的两级冷却与囚禁。
We have magneto-optically trapped all three stable neon isotopes, including the rare Ne-21, and all two-isotope combinations. The atoms are prepared in the metastable ^3P_2 state and manipulated via laser interaction on the ^3P_2 to ^3D_3} transition at 640.2nm. These cold (T = 1mK) and environmentally decoupled atom samples present ideal objects for precision measurements and the investigation of interactions between cold and ultracold metastable atoms. In this work, we present accurate measurements of the isotope shift of the ^3P_2 to ^3D_3 transition and the hyperfine interaction constants …
In this contribution we present calculations performed for interacting electron systems within a non-perturbative formulation of the cluster theory. Extrapolation of the model to describe the time dependence of the interacting systems is feasible and planed. The theory is based on the unitary operator $e^{iS}$ ({\it S} is the correlation operator) formalism which, in this paper, is treated non perturbatively within many-particle correlations. The application of the derived equations to few-body systems is realized in terms of Generalized Linearization Approximations (GLA) and via the Cluster F…
Hyperfine quenching rates of the lowest-energy metastable $^3P_0$ and $^3P_2$ states of Mg, Ca, Sr, and Yb atoms are computed. The calculations are carried out using ab initio relativistic many-body methods. The computed lifetimes may be useful for designing novel ultra-precise optical clocks and trapping experiments with the $3P_2$ fermionic isotopes. The resulting natural widths of the $^3P_0 -> ^1S_0$ clock transition are 0.44 mHz for $^{25}$Mg, 2.2 mHz for $^{43}$Ca, 7.6 mHz for $^{87}$Sr, 43.5 mHz for $^{171}$Yb, and 38.5 mHz for $^{173}$Yb. Compared to the bosonic isotopes, the lifetime …
We present the first simultaneous trapping of two different ultracold atomic species in a conservative trap. Lithium and cesium atoms are stored in an optical dipole trap formed by the focus of a CO$_2$ laser. Techniques for loading both species of atoms are discussed and observations of elastic and inelastic collisions between the two species are presented. A model for sympathetic cooling of two species with strongly different mass in the presence of slow evaporation is developed. From the observed Cs-induced evaporation of Li atoms we estimate a cross section for cold elastic Li-Cs collision…
A new beamline for Resonant Excitation of Beams with Electromagnetic fields and Lasers (REBEL) and Stopping and Trapping of Radioactive Isotopes for Precision Experiments (STRIPE)
本研究介绍了集成于同一离线束流线的REBEL与STRIPE两套实验装置，分别用于快离子束高灵敏度光谱测量和离子囚禁精密光谱，共享稳定基础设施，初步性能良好，可支撑相关技术研发并适配未来放射性束设施。
We present a Dual Isotope Magneto Optical Trap produced using a single diode laser. We generate all the optical frequencies needed for trapping both species using a fiber intensity modulator. All the optical frequencies are amplified simultaneously using a tapered amplifier. The independent control of each frequency is on the RF side rather than on the optical side. This introduces an enormous simplification for laser cooling applications that often require an acousto-optic modulator for each laser beam. Frequency changing capabilities are limited by the modulator bandwidth (10 GHz). Traps for…
We present the accurate measurement of the frequency of the $7S-7P$ laser-trapping transition for three francium isotopes. Our approach is based on an interferometric comparison to deduce the unknown laser frequency from a secondary laser frequency-standard. After careful investigation of systematics, with samples of about 100 atoms the final accuracy reaches 8 MHz, an order of magnitude better than the best previous measurement for $^{210}$Fr, and opens the way to improved tests of the theoretical computation of Fr atomic structure.
We present a continuous-wave, 810 nm laser with watt-level powers. Our system is based on difference-frequency generation of 532 nm and 1550 nm fiber lasers in a single pass through periodically poled lithium niobate (PPLN). We measure the broadband spectral noise and residual intensity noise to be compatible with off-resonant dipole trapping of ultracold atoms. Given the large bandwidth of the fiber amplifiers, the output can be optimized for a range of wavelengths, including the strontium clock-magic wavelength of 813 nm. Furthermore, with the exploration of more appropriate nonlinear crysta…
Magnetic trapping of an ultracold $^{39}$K-$^{40}$K mixture with a versatile potassium laser system
本文提出一种多功能钾激光系统，在单腔装置中实现$^{39}$K-$^{40}$K玻色-费米混合气体的双同位素磁光阱、亚多普勒冷却与磁囚禁，并通过声光调制器实现微秒级同位素切换。
Two efficient and isotope-selective resonant two-photon ionization techniques for loading barium ions into radio-frequency (RF)-traps are demonstrated. The scheme of using a strong dipole-allowed transition at λ=553 nm as a first step towards ionization is compared to the established technique of using a weak intercombination line (λ=413 nm). An increase of two orders of magnitude in the ionization efficiency is found favoring the transition at 553 nm. This technique can be implemented using commercial all-solid-state laser systems and is expected to be advantageous compared to other narrowban…
We investigate oscillation frequencies for simultaneous trapping of more than one type of alkali atoms in a common optical lattice. For this purpose, we present numerical results for magic trapping conditions, where the oscillation frequencies for two different kind of alkali atoms using laser lights in the wavelength range 500-1200 nm are same. These wavelengths will be of immense interest for studying static and dynamic properties of boson-boson, boson-fermion, fermion-fermion, and boson-boson-boson mixtures involving different isotopes of Li, Na, K, Rb, Cs and Fr alkali atoms. In addition t…
Dissipative pure-optical trap for laser cooling and trapping of neutral atoms
本文提出一种具有宏观周期的深耗散纯光学晶格，其深度与磁光阱（MOT）相当，能通过耗散摩擦力实现中性原子的俘获与冷却，为开发无需磁场的紧凑冷原子系统提供了新方法。
Thorium ions exhibit unique nuclear properties with high relevance for testing symmetries of nature, and Paul traps feature an ideal experimental platform for performing high precision quantum logic spectroscopy. Loading of stable or long-lived isotopes is well-established and relies on ionization from an atomic beam. A different approach allows trapping short-lived isotopes available as alpha-decay daughters, which recoil from a thin sample of the precursor nuclide. A prominent example is the short-lived $^{229\text{m}}$Th, populated in a decay of long-lived $^{233}$U. Here, ions are provided…
Survey of hyperfine structure measurements in alkali atoms
该综述汇总所有碱金属原子的光谱超精细常数，涵盖锂至铯的长寿命同位素及钫的可得同位素，并结合标度律与超精细异常开展全局分析。
The neutron-rich 6He and 8He isotopes exhibit an exotic nuclear structure that consists of a tightly bound 4He-like core with additional neutrons orbiting at a relatively large distance, forming a halo. Recent experimental efforts have succeeded in laser trapping and cooling these short-lived, rare helium atoms, and have measured the atomic isotope shifts along the 4He-6He-8He chain by performing laser spectroscopy on individual trapped atoms. Meanwhile, the few-electron atomic structure theory, including relativistic and QED corrections, has reached a comparable degree of accuracy in the calc…
High-power and narrow-linewidth laser light is a vital tool for atomic physics, being used for example in laser cooling and trapping and precision spectroscopy. Here we produce Watt-level laser radiation at 457.49 nm and 460.86 nm of respective relevance for the cooling transitions of cadmium and strontium atoms. This is achieved via the frequency doubling of a kHz-linewidth vertical-external-cavity surface-emitting laser (VECSEL), which is based on a novel gain chip design enabling lasing at > 2 W in the 915-928 nm region. Following an additional doubling stage, spectroscopy of the $^1S_0\to{…
An ultra-stable optical clock based on coherent population trapping effect of alkaline-earth ions, such as Ca$^+$, Sr$^+$, Ba$^+$, is analyzed here. The proposed transitions use the odd isotopes, so that the frequency shift is insensitive to the applied magnetic field. To enhance the signal, a large number of ions are trapped in a linear Paul trap, and laser cooled to crystallize such that the ions are in the Lamb-Dicke regime to avoid first order Doppler shift. Other relevant frequency shifts are also analyzed. Further techniques to improve the stability of the clock signal are discussed.
Optical Dipole Trap for Hg Atoms
该研究实现了汞原子的光偶极阱，完成了汞同位素从磁光阱到光偶极阱的转移与表征，为同位素相关碰撞等研究及量子简并探索提供了新途径。
Isotope separation is one of the grand challenges of modern society and holds great potential for basic science, medicine, energy, and defense. We consider here a new and general approach to isotope separation. The method is based on an irreversible change of the mass-to-magnetic moment ratio of a particular isotope in an atomic beam, followed by a magnetic multipole whose gradients deflect and guide the atoms. The underlying mechanism is a reduction of the entropy of the beam by the information of a single-scattered photon for each atom that is separated. We numerically simulate isotope separ…
When two of three pairs of the Gaussian laser beams of a traditional MOT are misaligned in the racetrack configuration the effective coordinate-dependent vortex force do arise. Then an atom is accelerated by this vortex force until its velocity not balanced by the damping force. This situation may produce a stable ring of revolving atoms of a certain radius. Due to the different frequency and laser beams intensity dependences of the vortex, damping and trapping forces it is possible to equalize the radii of two orbiting groups of atoms in two-species or dual-isotope magneto-optical trap and so…
We report the first efficient trapping of rare-earth Yb atoms with a high-power violet laser diode (LD). An injection-locked violet LD with a 25 mW frequency-stabilized output was used for the magneto-optical trapping (MOT) of fermionic as well as bosonic Yb isotopes. A typical number of $4\times 10^6$ atoms for $^{174}$Yb with a trap density of $\sim 1\times10^8/$cm$^3$ was obtained. A 10 mW violet external-cavity LD (ECLD) was used for the one-dimensional (1D) slowing of an effusive Yb atomic beam without a Zeeman slower resulting in a 35-fold increase in the number of trapped atoms. The ove…
Hyperfine spectroscopy and laser cooling of the fermionic isotopes $^{47}$Ti and $^{49}$Ti
该研究通过超精细结构和激光冷却跃迁的测量，实现了$^{47}$Ti和$^{49}$Ti的磁光陷阱制备，为费米同位素的冷却和光谱研究提供了关键数据。
Ultracold dysprosium gases, with a magnetic moment ten times that of alkali atoms and equal only to terbium as the most magnetic atom, are expected to exhibit a multitude of fascinating collisional dynamics and quantum dipolar phases, including quantum liquid crystal physics. We report the first laser cooling and trapping of half a billion Dy atoms using a repumper-free magneto-optical trap (MOT) and continuously loaded magnetic confinement, and we characterize the trap recycling dynamics for bosonic and fermionic isotopes. The first inelastic collision measurements in the few partial wave, 10…
We have studied magneto-optical traps (MOTs) for efficient on-line trapping of radioactive atoms. After discussing a model of the trapping process in a vapor cell and its efficiency, we present the results of detailed experimental studies on Rb MOTs. Three spherical cells of different sizes were used. These cells can be easily replaced, while keeping the rest of the apparatus unchanged: atomic sources, vacuum conditions, magnetic field gradients, sizes and power of the laser beams, detection system. By direct comparison, we find that the trapping efficiency only weakly depends on the MOT cell …
We have demonstrated Zeeman slowing and capture of neutral Ra-225 and Ra-226 atoms in a magneto-optical trap (MOT). The intercombination transition 1S0-3P1 is the only quasi-cycling transition in radium and was used for laser-cooling and trapping. Repumping along the 3D1-1P1 transition extended the lifetime of the trap from milliseconds to seconds. Room-temperature blackbody radiation was demonstrated to provide repumping from the metastable 3P0 level. We measured the isotope shift and hyperfine splittings on the 3D1-1P1 transition with the laser-cooled atoms, and set a limit on the lifetime o…
Precision optical spectroscopy of exotic ions reveals accurate information about nuclear properties such as charge radii and magnetic and quadrupole moments. Thorium ions exhibit unique nuclear properties with high relevance for testing symmetries of nature. We report loading and trapping of single $^{232}$Th$^+$ ions in a linear Paul trap, embedded into and sympathetically cooled by small crystals of trapped $^{40}$Ca$^+$ ions. Trapped Th ions are identified in a non-destructive manner from the voids in the laser-induced Ca fluorescence pattern emitted by the crystal, and alternatively, by me…
We report the design and performance of a Littrow-type 671 nm External Cavity Diode Laser (ECDL) that delivers output power greater than 150 mW and features enhanced passive stability. The main body of the ECDL is constructed using titanium to minimize temperature related frequency drifts. The laser diode is mounted in a cylindrical mount that allows vertical adjustments while maintaining thermal contact with the temperature stabilized base plate. The wavelength tuning is achieved by horizontal displacement of the diffraction grating about an optimal pivot point. The compact design increases t…
A self-aligning recirculated crossed optical dipole trap for lithium atoms
本文提出一种具有固有稳定性的自对准循环交叉光偶极阱设计，通过精确调谐放大率为一的成像系统实现光阱移动且保持对准，并利用$^6$Li原子验证了4.3 mm移动范围内的对准稳定性。
Continuous-wave output at 229 nm for the application of laser cooling of Cd atoms was generated by the 4th harmonic using two successive second harmonic generation stages. Employing a single-frequency optically pumped semiconductor laser as a fundamental source, 0.56 W of output at 229 nm was observed with a 10-mm long, Brewster-cut BBO crystal in an external cavity with 1.62 W of 458 nm input. Conversion efficiency from 458 nm to 229 nm was more than 34%. By applying a tapered amplifier as a fundamental source, we demonstrated magneto-optical trapping of all stable Cd isotopes including isoto…
We report on an efficient production scheme for a large quantum degenerate sample of fermionic lithium. The approach is based on our previous work on narrow-line $ 2S_{1/2}\rightarrow 3P_{3/2} $ laser cooling resulting in a high phase-space density of up to $3\times10^{-4}$. This allows utilizing a large volume crossed optical dipole trap with a total power of $45\,\textrm{W}$, leading to high loading efficiency and $8\times10^6$ trapped atoms. The same optical trapping configuration is used for rapid adiabatic transport over a distance of $25\,\textrm{cm}$ in $0.9\,\textrm{s}$, and subsequent…
Achromatic, planar Fresnel-Reflector for a Single-beam Magneto-optical Trap
提出一种受菲涅尔透镜启发的消色差平面菲涅尔反射器，用于单光束磁光阱，解决了衍射光栅的色差与成本问题，实现了锶同位素多级冷却与多物种俘获，推动冷原子系统微型化。
Single-atom imaging of ${}^{173}$Yb in optical tweezers loaded by a five-beam magneto-optical trap
本文利用正交五光束磁光阱向光镊阵列高效装载并冷却镱原子，结合非魔幻波长双色成像首次实现 ${}^{173}$Yb 单原子分辨探测，保真度达 $99.96(1)\\%$。
This paper presents the first realisation of a simultaneous $^{87}$Rb -$^{85}$Rb Mach-Zehnder atom interferometer with Bose-condensed atoms. A number of ambitious proposals for precise terrestrial and space based tests of the Weak Equivalence Principle rely on such a system. This implementation utilises hybrid magnetic-optical trapping to produce spatially overlapped condensates with a duty cycle of 20s. A horizontal optical waveguide with co-linear Bragg beamsplitters and mirrors is used to simultaneously address both isotopes in the interferometer. We observe a non-linear phase shift on a no…
A sharp resonance line that appears in three-photon transitions between the $^{1}S_{0}$ and $^{3}P_{0}$ states of alkaline earth and Yb atoms is proposed as an optical frequency standard. This proposal permits the use of the even isotopes, in which the clock transition is narrower than in proposed clocks using the odd isotopes and the energy interval is not affected by external magnetic fields or the polarization of trapping light. The method has the unique feature that the width and rate of the clock transition can be continuously adjusted from the $MHz$ level to sub-$mHz$ without loss of sig…
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