A pair of 87Sr optical lattice clocks with a statistical agreement of 2 × 10−18 within 6,000 s has been developed. To this end, the behaviour of the blackbody radiation—a major perturbation for optical lattice clocks—was directly investigated. The accuracy of atomic clocks relies on the superb reproducibility of atomic spectroscopy, which is accomplished by careful control and the elimination of environmental perturbations on atoms. To date, individual atomic clocks have achieved a 10−18 level of total uncertainties1,2, but a two-clock comparison at the 10−18 level has yet to be demonstrated. Here, we demonstrate optical lattice clocks with 87Sr atoms interrogated in a cryogenic environment to address the blackbody radiation-induced frequency shift3, which remains the primary source of systematic uncertainty2,4,5,6 and has initiated vigorous theoretical7,8 and experimental9,10 investigations. The systematic uncertainty for the cryogenic clock is evaluated to be 7.2 × 10−18, which is expedited by operating two such cryo-clocks synchronously11,12. After 11 measurements performed over a month, statistical agreement between the two cryo-clocks reached 2.0 × 10−18. Such clocks' reproducibility is a major step towards developing accurate clocks at the low 10−18 level, and is directly applicable as a means for relativistic geodesy13.

Cryogenic optical lattice clocks

We describe an optical atomic clock based on quantum-logic spectroscopy of the ^{1}S_{0}↔^{3}P_{0} transition in ^{27}Al^{+} with a systematic uncertainty of 9.4×10^{-19} and a frequency stability of 1.2×10^{-15}/sqrt[τ]. A ^{25}Mg^{+} ion is simultaneously trapped with the ^{27}Al^{+} ion and used for sympathetic cooling and state readout. Improvements in a new trap have led to reduced secular motion heating, compared to previous ^{27}Al^{+} clocks, enabling clock operation with ion secular motion near the three-dimensional ground state. Operating the clock with a lower trap drive frequency has reduced excess micromotion compared to previous ^{27}Al^{+} clocks. Both of these improvements have led to a reduced time-dilation shift uncertainty. Other systematic uncertainties including those due to blackbody radiation and the second-order Zeeman effect have also been reduced.

https://link.aps.org/accepted/10.1103/PhysRevLett.123.033201

^{27}Al^{+} Quantum-Logic Clock with a Systematic Uncertainty below 10^{-18}.

Atomic polarization phenomena impinge upon a number of areas and processes in physics. The dielectric constant and refractive index of any gas are examples of macroscopic properties that are largely determined by the dipole polarizability. When it comes to microscopic phenomena, the existence of alkaline-earth anions and the recently discovered ability of positrons to bind to many atoms are predominantly due to the polarization interaction. An imperfect knowledge of atomic polarizabilities is presently looming as the largest source of uncertainty in the new generation of optical frequency standards. Accurate polarizabilities for the group I and II atoms and ions of the periodic table have recently become available by a variety of techniques. These include refined many-body perturbation theory and coupled-cluster calculations sometimes combined with precise experimental data for selected transitions, microwave spectroscopy of Rydberg atoms and ions, refractive index measurements in microwave cavities, ab initio calculations of atomic structures using explicitly correlated wavefunctions, interferometry with atom beams and velocity changes of laser cooled atoms induced by an electric field. This review examines existing theoretical methods of determining atomic and ionic polarizabilities, and discusses their relevance to various applications with particular emphasis on cold-atom physics and the metrology of atomic frequency standards.

https://iopscience.iop.org/article/10.1088/0953-4075/43/20/202001/pdf

Theory and applications of atomic and ionic polarizabilities

We describe and review the current state of the art in atomic fountain clocks. These clocks provide the best realization of the SI second possible today, with relative uncertainties of a few parts in 1016.

/pdf/atomic-fountain-clocks-5dx9m391lj.pdf

Atomic fountain clocks

We propose high-resolution laser spectroscopy of the 3.5 eV nuclear transition in Th-229 in isolated atoms. Laser excitation of the nucleus can be detected efficiently in a double-resonance method by probing the hyperfine structure of a transition in the electron shell. It is shown that for a suitably chosen electronic level, the frequency of the nuclear transition is independent of external magnetic fields to first order and of electric fields to second order. This makes Th-229 a possible reference for an optical clock of very high accuracy. The nuclear-electronic double-resonance method can be conveniently applied to a laser-cooled ion of 229Th3+ in a radiofrequency trap. Further applications of nuclear laser spectroscopy are discussed.

https://iopscience.iop.org/article/10.1209/epl/i2003-00210-x/pdf

Nuclear laser spectroscopy of the 3.5 eV transition in Th-229

Frequency shifts of hyperfine splittings of $^{2}S_{\frac{1}{2}}$ states due to the blackbody radiation field are calculated It is shown that they can be estimated from the dc hyperfine Stark shifts, which have previously been measured in the ground states of hydrogen and the alkali atoms The shift at 300 K is large enough to be significant in primary Cs atomic beam frequency standards, and should be measurable A simple method of calculating the hyperfine Stark shifts is described, which is based on the Bates-Damgaard method for determining radial matrix elements and the Fermi-Segr\`e formula for determining the contact hyperfine matrix elements It is applied to ${\mathrm{Ba}}^{+}$ and ${\mathrm{Hg}}^{+}$, for which no experimental data are yet available, and which are currently of interest for frequency standards

Shift of S 1 2 2 hyperfine splittings due to blackbody radiation

Frequency shifts of hyperfine splittings of 2S1/2 states due to the blackbody electric field are calculated. It is shown that they can be estimated from the dc hyperfine Stark shifts, which have previously been measured in the ground states of hydrogen and the alkali atoms. The shifts scale as T4. The fractional shift for Cs at 300 K is -1.7 x 10-14, which is large enough to be significant in primary frequency standards, and should be measurable. A simple method of calculating the hyperfine Stark shifts is described, which is based on the Bates-Damgaard method for determining radial matrix elements and the Fermi-Segre formula for determining the contact hyperfine matrix elements. It agrees with the experiment to within 12% for the entire alkali series. It is applied to Ba+ and Hg+, for which no experimental data are yet available, and which are currently of interest for frequency standards. At 300 K, the fractional shifts are -9.9 x 10-17 and -2.4 x 10-15 for Hg+ and Ba+, respectively. The shift due to the blackbody magnetic field is -1.3 x 10-17 [T(K)/300]2 for any 2S1/2 state.

https://hal.archives-ouvertes.fr/jpa-00221731/document

SHIFT OF 2Sl/2 HYPERFINE SPLITTINGS DUE TO BLACKBODY RADIATION AND ITS INFLUENCE ON FREQUENCY STANDARDS

Lasers available at new wavelengths, powers, linewidths, and stabilities have made possible advances in precision atomic frequency standards and spectroscopy. Laser spectrometers with resolving power exceeding 1011 have been constructed qnd used to measure the photon recoil structure of spectral lines and in new tests of relativity. Recent progress in frequency stabilation methods and in laser-cooled ions indicates the possibility of an optical frequency standard with an accuracy and stability of less than 10-Is. Diode lasers may enable the construction of an optically-pumped cesium standard with an order-ofmagnitude improvement in accuracy over existing primary standards. I. CESIUM PRIMARY STANDARDS RESEARCH Introduction. The U.S. primary frequency standard, NBS-6, is a cesium atomicbeam apparatus with an interaction length of 3.74 meters. The experimental uncertainty that limits its accuracy is the microwave cavity phase shift [l]. This shift is cancelled to some degree by averaging the clock rates obtained from the two directions of atomic beam propagation in the standard. However, the degree of cancellation is limited by the faithfulness of the atomic beam retrace, which is affected by factors of beam axial symmetry. Since the frequency shift produced by a given cavity phase shift is proportional to the resonance linewidth, one way to improve this standard would be to increase the microwave Q. This factor can be increased in a cesium clock only by lengthening the interaction time with the atoms. It is unlikely that a new primary standard could be made physically longer than NBS-6, because magnetic shielding becomes difficult to achieve for such large dimensions. In addition, a suitable means of cooling neutral atoms in an atomic beam has not yet been developed. Therefore, the microwave linewidth in future cesium clocks will probably not decrease, and any improvement in accuracy must come from a direct assault on the sources of error. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981834 C8-272 JOURNAL DE PHYSIQUE I n recent years, the development o f r e l i a b l e single-mode diode lasers has made poss ib le new methods t h a t may s i g n i f i c a n t l y reduce t h e e r r o r s found i n a cesium c lock o f g iven length. While much admirable work has been performed i n t h e pas t us ing labora to ry -qua l i t y diode lasers [ Z ] , the advent o f low-cost, l o n g l i f e , commercial l asers w i t h exce l len t q u a l i t y now makes long-term operat ion o f an opt ical ly-pumped labora to ry standard feas ib le . Cesium Opt i ca l Pumping. The atomic-state-preparat ion technique o f most i n t e r e s t a t t h e Nat ional Bureau o f Standards (NBS) i s one which promises t o change the s t a t e o f near l y every cesium atom w i t h i n t h e atomic beam t o a s i n g l e magnetic sublevel [3,4]. Two lasers can be used f o r t h i s purpose, one tuned t o t h e (2S4, F = 3 -, 2P3,2, F = 4) t r a n s i t i o n , and the other ad justed t o the (2S+, F = 4 -, 2P3,2, F = 4) l i n e , both a t 852 nm wavelength. The l a t t e r l a s e r i s plane po la r ized, w i t h the vector o f the e l e c t r i c f i e l d p a r a l l e l t o a small magnetic f i e l d , which establ ishes a quan t i za t ion ax is . Wi th bo th lasers cross ing the atomic beam, atoms move from each energy l e v e l i n t o every o ther l e v e l , w i t h the except i o n o f the (2S+, F = 4, M = 0) ground-state sublevel. I n t h i s case, s e l e c t i o n r u l e s p r o h i b i t e x c i t a t i o n o f t h e atom, and even tua l l y near l y a l l atoms should f a l l i n t o t h i s substate. A s i m i l a r arrangement o f l asers w i l l a l l o w the pumping o f atoms i n t o the F = 3, M = 0 s tate. A number o f advantages r e s u l t from t h i s process. The most obvious i s t h a t t h e s igna l should increase considerably, since, ins tead o f being r e j e c t e d by s t a t e s e l e c t i o n magnets, atoms are converted t o the des i red s t a t e by o p t i c a l pumping. I n the case of NBS-6, which uses both the (F = 3, M = 0) and (F = 4, M = 0) substates, t h e increase i n s igna l i s a f a c t o r o f e igh t , and the expected increase i n s ignal to-noise r a t i o i s consequent1 y a. A more s i g n i f i c a n t bene f i t o f o p t i c a l pumping i s the generat ion o f a h i g h l y symmetrical cesium beam, s ince o p t i c a l pumping i s l a r g e l y independent o f v e l o c i t y and pos i t i on . This feature, combined w i t h a new Cs oven design, should permi t a much b e t t e r re t race o f the atomic beam upon reversal . Improved microwave c a v i t y design w i t h smal ler c a v i t y windows may he lp reduce t h e actual s i z e o f phase s h i f t s which vary across c a v i t y windows [5] and lower the t o t a l uncer ta in ty i n frequency due t o c a v i t y phase s h i f t by an order o f magnitude. Another uncer ta in ty of unknown magnitude i n present Cs standards i s t h a t in t roduced by Majorana t r a n s i t i o n s as atoms pass from t h e la rge (1 T) f i e l d s of t h e s t a t e s e l e c t i o n magnets t o t h e small (0.1 T) f i e l d o f t h e C f i e l d reg ion 161. Since t h e C f i e l d can now be extended t o inc lude the o p t i c a l pumping region, such Majorana t r a n s i t i o n s should n o t occur. I n add i t i on , pumping o f the atoms i n t o a s i n g l e magnetic sublevel w i l l pe rmi t study o f Majorana t r a n s i t i o n s , which should appear as changes i n Rabi resonances adjacent t o the c e n t r a l c lock t r a n s i t i o n . The present s t reng th of t h e C f i e l d i s mandated by t h e presence o f asymmetry i n the s i ze o f microwave resonances near t h e c l o c k t r a n s i t i o n . AS atoms a re pumped i n t o the (F = 4, M = 0) l e v e l , these a u x i l i a r y features w i l l fade, permi t t i n g the reduc t ion o f the C f i e l d t o a smaller, more s tab le value. Also, the s i g n o f the C f i e l d i s i r r e l e v a n t i n t h i s scheme; therefore, t h e f i e l d can be reversed w i t h no a n t i c i p a t e d s h i f t s i n c lock frequency. This check on systematics i s n o t poss ib le w i t h the cu r ren t system, s ince improper s ign o f t h e C f i e l d would r e s u l t i n Majorana t r a n s i t i o n s o f unknown e f fec t . Fluorescence Detect ion. Complete removal o f s ta te -se lec t ion magnets i s poss ib le i f l a s e r methods a re employed t o de tec t atoms t h a t have made the microwave t r a n s i t i o n . Perhaps t h e s implest way t o accomplish t h i s i s w i t h f luorescence detect ion. I n t h e case where atoms are pumped t o t h e F = 3, M = 0 l e v e l , a " f l o p i n " i n t e r roga t ion i s poss ib le w i t h a laser tuned t o t h e F = 4 + F = 5 t r a n s i t i o n . The advantage o f us ing o f t h i s p a r t i c u l a r t r a n s i t i o n i s t h a t atoms exc i ted t o the 2S,,,, F = 5 l e v e l must decay t o the F = 4 l e v e l , where they are repeatedly exc i t e d , c o n t r i b u t i n g many photons per atom t o the f luorescence s ignal . It i s poss ib le i n t h i s manner t o ob ta in 100% t o t a l de tec t ion e f f i c i e n c y even when the c o l l e c t i o n e f f i c i e n c y i s considerably l e s s than one. By appropr ia te adjustment o f l a s e r frequency and angle o f c ross ing o f the atomic beam, d i f f e r e n t atomic v e l o c i t y d i s t r i b u t i o n s a1 so may be se lected us ing such f luorescence detect ion. A device const ructed w i t h laserinduced de tec t ion and opt ical-pumping regions could, perhaps, be operated simultaneously w i t h counter-propagati ng atomic beams. With appropr ia te arrangement o f pumping and de tec t ion regions, on ly atoms which have made a microwave t r a n s i t i o n w i l l con t r ibu te t o the f luorescence s ignal ; t h i s a l lows d i s t i n c t i o n between the two beam d i rec t ions . One d i r e c t i o n could be used f o r lock ing the microwave frequency, and the o ther d i r e c t i o n f o r l o c k i n g t h e c a v i t y phase s h i f t value. Th is may even permi t the use o f separate c a v i t i e s f o r t h e two ends o f the Ramsey resonance region. Even i f d i f f i c u l t i e s w i t h background l e v e l s and c o l l i s i o n s prevent implementation of t h i s technique, sw i tch ing o f the two d i r e c t i o n s should be much f a s t e r w i t h t h e l a s e r methods, s ince the cesium ovens can be operated continuously. There are c e r t a i n disadvantages o f the new methods. One, t h e l i g h t s h i f t o f t h e cesium atoms as they pass through the microwave region, due t o t h e f l u o r escence l i g h t coming from the two l a s e r regions, may be as l a r g e as Av 10-14. The magnitude o f t h i s e f f e c t was f i r s t est imated by A. B r i l l e t (Un ive rs i t6 Par isSud). E. Smith (NBS) has a l s o ca lcu la ted the s h i f t us ing a t e n s o r i a l analys is , which accounts f o r d i f fe rences i n f luorescence p o l a r i z a t i o n . Care must be taken t o reduce t h e i n t e n s i t y o f t h i s f luorescence r a d i a t i o n through t h e use o f apert u r e s and by p roper l y spacing the l a s e r regions from t h e microwave regions. A second problem i s photon-recoi l beam d e f l e c t i o n [7]. Since slower atoms a re de f lec ted more than f a s t e r ones, a velocity-dependent s p a t i a l d i s t r i b u t i o n may be formed. The value o f frequency s h i f t s due t o t h i s e f f e c t can be reduced below 10l5 by symmetric l a s e r i l l u m i n a t i o n o f the beam and proper c a v i t y design [4]. C8-274 JOURNAL DE PHYSIQUE Laser Requirements. The characteristics of diode lasers appropriate for this task include properties essential to attainment of good signal-to-noise ratio and complete optical pumping, as

/pdf/impact-of-lasers-on-primary-frequency-standards-and-40t1mdu6mv.pdf

Impact of lasers on primary frequency standards and precision spectroscopy

Mark  Feldman, J. C. Bergquis t , L L. Lewis, and F. L. Walls Frequency and Time Standards Group Time and Frequency D i v i s i o n Nat ional Bureau of Standards Boulder.  Colorado 80303 Summary We a r e s t u d y i n g t w o t y p e s o f o p t i c a l l y pumped g l a s s c e l l s w h i c h do n o t c o n t a i n a b u f f e r gas  and have no w a l l c o a t i n g i n w h i c h b e a m l i k e p r o p e r t i e s a re exp lo i t ed . The f i r s t d e v i c e i s a sealed  g lass tube  o f  abou t 1 cm diameter  and 20 cm leng th . A sinal 1 amount o f 87Rb metal i s l o c a l i z e d a t one  end by  temperature  gradients  which  a lso  cont ro l  the vapor  pressure. The c e l l has t h e  p r o p e r t i e s  o f a broad  atomic beam f o r t h e t r a n s p o r t o f o p t i c a l l y pumped atoms from one nd t o t h e o t h e r with c o l l i m a t i o n  g i v e n  b y  t h e  a s p e c t  r a t i o  o f  t h e  t u b e . A t each  end  the Rb "beam" i s crossed  by a l ase r . I n each i n t e r a c t i o n  r e g i o n ,  t h e  l a s e r  o p t i c a l l y pumps atoms i n t o one o f t h e 5 2 S h y p e r f i n e l e v e l s , as  we l l as detects  populat ion  kanges  between  the h y p e r f i n e  l e v e l s .  I n a second  device,  graphi te i n s e r t s  a r e i n c l u d e d i n the  g lass  tube. The g r a p h i t e  s t r o n g l y  g e t t e r s Rb, the reby  p rov id ing c o l l i m a t i o n and s i g n i f i c a n t l y r e d u c i n g s c a t t e r i n g o f l a s e r l i g h t f r o m background Rb atoms. A TE m i c r o w a v e  c a v i t y  i s  p o s i t i o n e d between  the w l a s e r i n t e r a c t i o n r e g i o n s . I n t h e b r o a d beam device we have observed the t r a n s p o r t  o f  o p t i c a l l y pumped atoms  between t h e ends w i t h a S/N r a t i o o f 300:l i n 1 S . A tunable dye  laser was used f o r  t h e pumping  and  signal d e t e c t i o n . I n t h e c o l l i m a t e d beam device, we have obsewed microwave t rans i t ions us ing a d iode lase r f o r pumping and f luorescence detection.

https://tf.boulder.nist.gov/general/pdf/564.pdf

Preliminary Investigation of a New Optically Pumped Atomic Rubidium Standard

The cons t ruc t ion and performance o f NBS-6, t h e U.S. cesium primary frequency standard, are summarized. A b r i e f d e s c r i p t i o n o f eva lua t ion procedures and sources o f uncer ta in ty are given. In t roduc t ion . The Uni ted States' pr imary frequency standard, NBS-6, was p laced i n t o serv ice i n 1975. The cesium c lock was b u i l t upon the bas ic framework prov ided by NBS-5, b u t var ious improvements o f the device were r a d i c a l enough t o warrant a new standard designation. The basic design uses dipole-magnet s t a t e se lectors , a conventional U-shaped, rectangular cross-sect ion Ramsey c a v i t y , and r e v e r s i b l e mu1 ti channel c o l l imator and hot-wi re detector . For the l a s t several years, annual evaluat ions o f NBS-6 have been made i n order t o prov ide s teer ing in fo rmat ion t o the Nat ional Bureau o f Standards (NBS) embodiment o f atomic time, AT(NBS). The standard has n o t been operated continuous ly as a p a r t i c i p a n t i n the NBS t ime scale. This phi losophy has been supported by recent data g i v i n g the r e l a t i v e performance o f NBS-4 (which i s operated cont i n u o u s l y as p a r t o f the NBS t ime scale); t h e u n o f f i c i a l working t ime scale a t NBS, UTC(8/S); and a small passive hydrogen maser (SPHM). F igure 1 shows the s t a b i l i t y obtained by comparing SPHM w i t h NBS-4 and w i t h UTC(8/S). NBS-4 i s normally a la rge c o n t r i b u t o r t o UTC(8/S). However, much o f t h i s p a r t i c u l a r data was taken when NBS-4 was turned off fo r maintenance. These curves i n d i c a t e no t on ly t h a t the j o i n t s t a b i l i t y o f SPHM vs. NBS-4 i s about 2 x t-' f o r t < l o 5 s, b u t t h a t the long-term s t a b i l i t y o f UTC(8/S) i s about 2 x 10l4 fo r t < l o 6 s. An e f f o r t i s i n progress t o complete a d d i t i o n a l masers t o add t o the NBS t ime scale. When these c locks j o i n t h e scale, i t w i l l become even more unnecessary t o operate a pr imary standard cont inuously. The shortterm and long-term s t a b i l i t y o f NBS-6 were designed t o enable us t o achieve the accuracy l i m i t e d by c a v i t y phase s h i f t i n t h e clock. The accuracy i s l i m i t e d by the degree o f r e t r a c e upon beam reversal , which r e s t r i c t s the l e v e l o f cance l la t ion o f c a v i t y phase s h i f t . The most uncer ta in component o f t h e c a v i t y phase s h i f t i s the d i s t r i b u t e d s h i f t across the microwave c a v i t y windows. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981829

L.L. Lewis

Papers

Shift of S 1 2 2 hyperfine splittings due to blackbody radiation

SHIFT OF 2Sl/2 HYPERFINE SPLITTINGS DUE TO BLACKBODY RADIATION AND ITS INFLUENCE ON FREQUENCY STANDARDS

Impact of lasers on primary frequency standards and precision spectroscopy

Preliminary Investigation of a New Optically Pumped Atomic Rubidium Standard

Design considerations and performance of nbs-6, the nbs primary frequency standard