High-accuracy measurement of atomic polarizability in an optical lattice clock

Search for Ultralight Dark Matter from Long-Term Frequency Comparisons of Optical and Microwave Atomic Clocks

We search for ultralight scalar dark matter candidates that induce oscillations of the fine structure constant, the electron and quark masses, and the quantum chromodynamics energy scale with frequency comparison data between a ^{171}Yb optical lattice clock and a ^{133}Cs fountain microwave clock that span 298 days with an uptime of 15.4%. New limits on the couplings of the scalar dark matter to electrons and gluons in the mass range from 10^{-22} to 10^{-20}  eV/c^{2} are set, assuming that each of these couplings is the dominant source of the modulation in the frequency ratio. The absolute frequency of the ^{171}Yb clock transition is also determined as 518 295 836 590 863.69(28) Hz, which is one of the important contributions toward a redefinition of the second in the International System of Units.

Vibration modes of a transportable optical cavity

Many factors still need to be evaluated to fully understand the physical mechanisms determining optical cavity vibration, which are crucial for designing and constructing a transportable ultra-stable laser. Herein, a detailed dynamic analysis is used to characterize the vibration modes of a transportable optical cavity. The first five resonance modes are identified in the presence of a cavity support, and the guidelines to achieve a high first-order resonance frequency are proposed; thereby, high robustness is described using a 50 mm length optical cavity. The results demonstrate that the first-order resonance of up to 681 Hz with a gross weight of 2.51 kg can be achieved using an optimization strategy for given cavity support. The theoretical results are consistent with simulation and experiment. With the optimal group, a 1.34 Hz linewidth transportable ultra-stable laser at 1550 nm is established, and a linewidth of 1.5 Hz and frequency instability of 9.5×10^-15@1s are obtained after the test including 100 km actual road transportation and 34 min continuous vibration. The test condition is equivalent to ∼ 1000 km road transportation. Our method can be readily extended to other transportable optical cavities, providing a powerful tool for improving the robustness of vibration, particularly important for transportable environments.

Uncertainty Evaluation of an 171Yb Optical Lattice Clock at NMIJ

We report an uncertainty evaluation of an ¹⁷¹Yb optical lattice clock with a total fractional uncertainty of 3.6×10^-16 , which is mainly limited by the lattice-induced light shift and the blackbody radiation shift. Our evaluation of the lattice-induced light shift, the density shift, and the second-order Zeeman shift is based on an interleaved measurement where we measure the frequency shift using the alternating stabilization of a clock laser to the 6s^{2 1}S₀-6s6p ³P₀ clock transition with two different experimental parameters. In the present evaluation, the uncertainties of two sensitivity coefficients for the lattice-induced hyperpolarizability shift d incorporated in a widely used light shift model by RIKEN and the second-order Zeeman shift a_Z are improved compared with the uncertainties of previous coefficients. The hyperpolarizability coefficient d is determined by investigating the trap potential depth and the light shifts at the lattice frequencies near the two-photon transitions 6s6p³P₀-6s8p³P₀, 6s8p³P₂, and 6s5f³F₂. The obtained values are d=-1.1(4) μ Hz and a_Z=-6.6(3) Hz/mT². These improved coefficients should reduce the total systematic uncertainties of Yb lattice clocks at other institutes.

Dual-Mode Operation of an Optical Lattice Clock Using Strontium and Ytterbium Atoms

We have developed an optical lattice clock that can operate in dual modes: a strontium (Sr) clock mode and an ytterbium (Yb) clock mode. Dual-mode operation of the Sr-Yb optical lattice clock is achieved by alternately cooling and trapping ⁸⁷Sr and ¹⁷¹Yb atoms inside the vacuum chamber of the clock. Optical lattices for Sr and Yb atoms were arranged with horizontal and vertical configurations, respectively, resulting in a small distance of the order of between the trapped Sr and Yb atoms. The ¹S₀-³P₀ clock transitions in the trapped atoms were interrogated in turn and the clock lasers were stabilized to the transitions. We demonstrated the frequency ratio measurement of the Sr and Yb clock transitions by using the dual-mode operation of the Sr-Yb optical lattice clock. The dual-mode operation can reduce the uncertainty of the blackbody radiation shift in the frequency ratio measurement, because both Sr and Yb atoms share the same blackbody radiation.

Atomic clocks for geodesy

We review experimental progress on optical atomic clocks and frequency transfer, and consider the prospects of using these technologies for geodetic measurements. Today, optical atomic frequency standards have reached relative frequency inaccuracies below 10^-17, opening new fields of fundamental and applied research. The dependence of atomic frequencies on the gravitational potential makes atomic clocks ideal candidates for the search for deviations in the predictions of Einstein's general relativity, tests of modern unifying theories and the development of new gravity field sensors. In this review, we introduce the concepts of optical atomic clocks and present the status of international clock development and comparison. Besides further improvement in stability and accuracy of today's best clocks, a large effort is put into increasing the reliability and technological readiness for applications outside of specialized laboratories with compact, portable devices. With relative frequency uncertainties of 10^-18, comparisons of optical frequency standards are foreseen to contribute together with satellite and terrestrial data to the precise determination of fundamental height reference systems in geodesy with a resolution at the cm-level. The long-term stability of atomic standards will deliver excellent long-term height references for geodetic measurements and for the modelling and understanding of our Earth.

Systematic evaluation of a 171Yb optical clock by synchronous comparison between two lattice systems

Optical clocks are the most precise measurement devices. Here we experimentally characterize one such clock based on the ¹S₀-³P₀ transition of neutral ¹⁷¹Yb atoms confined in an optical lattice. Given that the systematic evaluation using an interleaved stabilization scheme is unable to avoid noise from the clock laser, synchronous comparisons against a second ¹⁷¹Yb lattice system were implemented to accelerate the evaluation. The fractional instability of one clock falls below 4 × 10⁻¹⁷ after an averaging over a time of 5,000 seconds. The systematic frequency shifts were corrected with a total uncertainty of 1.7 × 10⁻¹⁶. The lattice polarizability shift currently contributes the largest source. This work paves the way to measuring the absolute clock transition frequency relative to the primary Cs standard or against the International System of Units (SI) second.

Rydberg-Dressed Magneto-optical Trap

We propose and demonstrate the laser cooling and trapping of Rydberg-dressed Sr atoms. By off-resonantly coupling the excited state of a narrow (7 kHz) cooling transition to a high-lying Rydberg state, we transfer Rydberg properties such as enhanced electric polarizability to a stable magneto-optical trap operating at <1  μK. Simulations show that it is possible to reach a regime where the long-range interaction between Rydberg-dressed atoms becomes comparable to the kinetic energy, opening a route to combining laser cooling with tunable long-range interactions.

Faraday-Shielded dc Stark-Shift-Free Optical Lattice Clock

We demonstrate the absence of a dc Stark shift in an ytterbium optical lattice clock. Stray electric fields are suppressed through the introduction of an in-vacuum Faraday shield. Still, the effectiveness of the shielding must be experimentally assessed. Such diagnostics are accomplished by applying high voltage to six electrodes, which are grounded in normal operation to form part of the Faraday shield. Our measurements place a constraint on the dc Stark shift at the 10^{-20} level, in units of the clock frequency. Moreover, we discuss a potential source of error in strategies to precisely measure or cancel nonzero dc Stark shifts, attributed to field gradients coupled with the finite spatial extent of the lattice-trapped atoms. With this consideration, we find that Faraday shielding, complemented with experimental validation, provides both a practically appealing and effective solution to the problem of dc Stark shifts in optical lattice clocks.

Blackbody radiation shift assessment for a lutetium ion clock

The accuracy of state-of-the-art atomic clocks is derived from the insensitivity of narrow optical atomic resonances to environmental perturbations. Two such resonances in singly ionized lutetium have been identified with potentially lower sensitivities compared to other clock candidates. Here we report measurement of the most significant unknown atomic property of both transitions, the static differential scalar polarizability. From this, the fractional blackbody radiation shift for one of the transitions is found to be −1.36(9) × 10⁻¹⁸ at 300 K, the lowest of any established optical atomic clock. In consideration of leading systematic effects common to all ion clocks, both transitions compare favorably to the most accurate ion-based clocks reported to date. This work firmly establishes Lu⁺ as a promising candidate for a future generation of more accurate optical atomic clocks.

There is a continuous effort to improve the accuracy of atomic clocks. Here the authors measure the static differential scalar polarizability of Lutetium ion resonant transitions and its lower light shift from blackbody radiation makes it a promising candidate for ion-based atomic clocks.

Measuring absolute frequencies beyond the GPS limit via long-haul optical frequency dissemination

Global Positioning System (GPS) dissemination of frequency standards is ubiquitous at present, providing the most widespread time and frequency reference for the majority of industrial and research applications worldwide. On the other hand, the ultimate limits of the GPS presently curb further advances in high-precision, scientific and industrial applications relying on this dissemination scheme. Here, we demonstrate that these limits can be reliably overcome even in laboratories without a local atomic clock by replacing the GPS with a 642-km-long optical fiber link to a remote primary caesium frequency standard. Through this configuration we stably address the ¹S₀-³P₀ clock transition in an ultracold gas of ¹⁷³Yb, with a precision that exceeds the possibilities of a GPS-based measurement, dismissing the need for a local clock infrastructure to perform beyond-GPS high-precision tasks. We also report an improvement of two orders of magnitude in the accuracy on the transition frequency reported in literature.

Towards a Mg Lattice Clock: Observation of the ^{1}S_{0}-^{3}P_{0} Transition and Determination of the Magic Wavelength

We optically excite the electronic state 3s3p ^{3}P_{0} in ^{24}Mg   atoms, laser cooled and trapped in a magic-wavelength lattice. An applied magnetic field enhances the coupling of the light to the otherwise strictly forbidden transition. We determine the magic wavelength, the quadratic magnetic Zeeman shift, and the transition frequency to be 468.46(21) nm, -206.6(2.0)  MHz/T^{2}, and 655 058 646 691(101) kHz, respectively. These are compared with theoretical predictions and results from complementary experiments. We also develop a high-precision relativistic structure model for magnesium, give an improved theoretical value for the blackbody radiation shift, and discuss a clock based on bosonic magnesium.

Atomic clock with 1×10(-18) room-temperature blackbody Stark uncertainty

The Stark shift due to blackbody radiation (BBR) is the key factor limiting the performance of many atomic frequency standards, with the BBR environment inside the clock apparatus being difficult to characterize at a high level of precision. Here we demonstrate an in-vacuum radiation shield that furnishes a uniform, well-characterized BBR environment for the atoms in an ytterbium optical lattice clock. Operated at room temperature, this shield enables specification of the BBR environment to a corresponding fractional clock uncertainty contribution of 5.5×10(-19). Combined with uncertainty in the atomic response, the total uncertainty of the BBR Stark shift is now 1×10(-18). Further operation of the shield at elevated temperatures enables a direct measure of the BBR shift temperature dependence and demonstrates consistency between our evaluated BBR environment and the expected atomic response.

High-accuracy measurement of the differential scalar polarizability of a 88Sr+ clock using the time-dilation effect

We report a high-accuracy measurement of the differential static scalar polarizability Δα(0) of the 5s(2)S(1/2)-4d(2)D(5/2) transition of the (88)Sr(+) ion. The high accuracy is obtained by comparing the micromotion-induced positive scalar Stark shift to the negative time-dilation shift. Measurement of the trap drive frequency where these shifts cancel is used to determine Δα(0) without the need to determine the electric field. Δα(0) is a critical parameter for the operation of frequency standards as it determines the blackbody radiation frequency shift coefficient, the largest source of uncertainty in the (88)Sr(+) ion clock. The measured value of Δα(0) is -4.7938(71) × 10(-40) J m(2)/V(2). Taking into account the dynamic correction, the blackbody shift at 300 K is 0.247,99(37) Hz. The contribution of the blackbody shift coefficient to the uncertainty of the ion standard has been reduced by a factor of 24, from 2 × 10(-17) to 8.3 × 10(-19). The revised total uncertainty of our reference standard is 1.2 × 10(-17), limited by the blackbody field evaluation. An additional benefit of the low uncertainty of Δα(0) is the ability to suppress, by a factor of about 200, the net micromotion frequency shifts.

Experimental realization of an optical second with strontium lattice clocks

Progress in realizing the SI second had multiple technological impacts and enabled further constraint of theoretical models in fundamental physics. Caesium microwave fountains, realizing best the second according to its current definition with a relative uncertainty of 2-4 × 10(-16), have already been overtaken by atomic clocks referenced to an optical transition, which are both more stable and more accurate. Here we present an important step in the direction of a possible new definition of the second. Our system of five clocks connects with an unprecedented consistency the optical and the microwave worlds. For the first time, two state-of-the-art strontium optical lattice clocks are proven to agree within their accuracy budget, with a total uncertainty of 1.5 × 10(-16). Their comparison with three independent caesium fountains shows a degree of accuracy now only limited by the best realizations of the microwave-defined second, at the level of 3.1 × 10(-16).

Absolute polarization measurement using a vector light shift

We have measured the vector light shift due to a cavity built-up optical lattice by using a variation of the Hanle effect with trapped Cs atoms, where the time-evolving population of all magnetic sublevels is measured in situ. The measurement is linearly sensitive to the electric field of the nonlinearly polarized light, which allows unprecedented sensitivity to absolute linear polarization quality, to the level of 10(-10) in fractional intensity. Our approach to measuring and improving linear polarization can be applied to electron electric dipole moment searches, optical lattice clocks, magnetometery, and quantum computing.

Optical-frequency transfer over a single-span 1840 km fiber link

To compare the increasing number of optical frequency standards, highly stable optical signals have to be transferred over continental distances. We demonstrate optical-frequency transfer over a 1840-km underground optical fiber link using a single-span stabilization. The low inherent noise introduced by the fiber allows us to reach short term instabilities expressed as the modified Allan deviation of 2×10(-15) for a gate time τ of 1 s reaching 4×10(-19) in just 100 s. We find no systematic offset between the sent and transferred frequencies within the statistical uncertainty of about 3×10(-19). The spectral noise distribution of our fiber link at low Fourier frequencies leads to a τ(-2) slope in the modified Allan deviation, which is also derived theoretically.

High accuracy correction of blackbody radiation shift in an optical lattice clock

We have determined the frequency shift that blackbody radiation is inducing on the 5s2 (1)S0-5s5p (3)P0 clock transition in strontium. Previously its uncertainty limited the uncertainty of strontium lattice clocks to 1×10(-16). Now the uncertainty associated with the blackbody radiation shift correction translates to a 5×10(-18) relative frequency uncertainty at room temperature. Our evaluation is based on a measurement of the differential dc polarizability of the two clock states and on a modeling of the dynamic contribution using this value and experimental data for other atomic properties.

Precision measurement of transition matrix elements via light shift cancellation

We present a method for accurate determination of atomic transition matrix elements at the 10(-3) level. Measurements of the ac Stark (light) shift around "magic-zero" wavelengths, where the light shift vanishes, provide precise constraints on the matrix elements. We make the first measurement of the 5s - 6p matrix elements in rubidium by measuring the light shift around the 421 and 423 nm zeros through diffraction of a condensate off a sequence of standing wave pulses. In conjunction with existing theoretical and experimental data, we find 0.3235(9)ea(0) and 0.5230(8)ea(0) for the 5s - 6p(1/2) and 5s - 6p(3/2) elements, respectively, an order of magnitude more accurate than the best theoretical values. This technique can provide needed, accurate matrix elements for many atoms, including those used in atomic clocks, tests of fundamental symmetries, and quantum information.

Ytterbium in quantum gases and atomic clocks: van der Waals interactions and blackbody shifts

We evaluated the C(6) coefficients of Yb-Yb, Yb-alkali, and Yb-group II van der Waals interactions with 2% uncertainty. The only existing experimental result for such quantities is for the Yb-Yb dimer. Our value, C(6)=1929(39) a.u., is in excellent agreement with the recent experimental determination of 1932(35) a.u. We have also developed a new approach for the calculation of the dynamic correction to the blackbody radiation shift. We have calculated this quantity for the Yb 6s(2) (1)S(0)-6s6p (3)P(0)(o) clock transition with 3.5% uncertainty. This reduces the fractional uncertainty due to the blackbody radiation shift in the Yb optical clock at 300 K to the 10(-18) level.

Comparison of two independent Sr optical clocks with 1×10(-17) stability at 10(3) s

Many-particle optical lattice clocks have the potential for unprecedented measurement precision and stability due to their low quantum projection noise. However, this potential has so far never been realized because clock stability has been limited by frequency noise of optical local oscillators. By synchronously probing two ^{87}Sr lattice systems using a laser with a thermal noise floor of 1×10(-15), we remove classically correlated laser noise from the intercomparison, but this does not demonstrate independent clock performance. With an improved optical oscillator that has a 1×10(-16) thermal noise floor, we demonstrate an order of magnitude improvement over the best reported stability of any independent clock, achieving a fractional instability of 1×10(-17) in 1000 s of averaging time for synchronous or asynchronous comparisons. This result is within a factor of 2 of the combined quantum projection noise limit for a 160 ms probe time with ~10(3) atoms in each clock. We further demonstrate that even at this high precision, the overall systematic uncertainty of our clock is not limited by atomic interactions. For the second Sr clock, which has a cavity-enhanced lattice, the atomic-density-dependent frequency shift is evaluated to be -3.11×10(-17) with an uncertainty of 8.2×10(-19).

Neutral atom frequency reference in the deep ultraviolet with fractional uncertainty = 5.7×10(-15)

We present an assessment of the (6s2) (1)S0 ↔ (6s6p)(3)P0 clock transition frequency in 199Hg with an uncertainty reduction of nearly 3 orders of magnitude and demonstrate an atomic quality factor Q of ∼10(14). The 199Hg atoms are confined in a vertical lattice trap with light at the newly determined magic wavelength of 362.5697±0.0011  nm and at a lattice depth of 20E(R). The atoms are loaded from a single-stage magneto-optical trap with cooling light at 253.7 nm. The high Q factor is obtained with an 80 ms Rabi pulse at 265.6 nm. We find the frequency of the clock transition to be 1,128,575,290,808,162.0±6.4(syst)±0.3(stat)  Hz (i.e., with fractional uncertainty=5.7×10(-15)). Neither an atom number nor second order Zeeman dependence has yet been detected. Only three laser wavelengths are used for the cooling, lattice trapping, probing, and detection.