Reflection-type vapor cell for micro atomic clocks using local anodic bonding of 45° mirrors.

This Letter reports the design, fabrication, and evaluation of reflection-type planar vapor cells for chip-scale atomic clocks. The cell with 2-8 mm cavity length contains two 45° Bragg reflector mirrors assembled using a local anodic bonding. Coherent population trapping resonance of Rb atoms is observed, realizing an atomic clock operation. Allan deviations at an averaging time of 1 s are ${2.2} \times {{1}}{{{0}}^{- 10}}$ and ${9.5} \times {{1}}{{{0}}^{- 11}}$ for 2 mm long and 6 mm long vapor cells, respectively. These results show that planar vapor cells compatible with a system-in-package are feasible without degradation of clock stabilities compared to conventional vertically stacked cells.

Frequency ratio of an 115In+ ion clock and a 87Sr optical lattice clock.

We report on the first, to the best of our knowledge, frequency ratio measurement of an 115In+ singleion clock and a 87Sr optical lattice clock. A hydrogen maser serves as a flywheel oscillator to measure the ratio by independent optical combs. From 89,000 s of measurement time, the frequency ratio fIn/fSr is determined to be 2.952 748 749 874 863 3(23) with 7.7×10-16 relative uncertainty. The measurement creates a new connection in the network of frequency ratios of optical clocks.

Frequency measurement of the clock transition of an indium ion sympathetically-cooled in a linear trap.

We report frequency measurement of the clock transition in an 115In+ ion sympathetically-cooled with Ca+ ions in a linear rf trap. The Ca+ ions are used as a probe of the external electromagnetic field and as the coolant for preparing the cold In+. The frequency is determined to be 1 267 402 452 901 049.9 (6.9) Hz by averaging 36 measurements using an optical frequency comb referenced to the frequency standards located in the same site.

SI-traceable measurement of an optical frequency at the low 10-16 level without a local primary standard.

SI-traceable measurements of optical frequencies using International Atomic Time (TAI) do not require a local primary frequency reference, but suffer from an uncertainty in tracing to the SI second. For the measurement of the 87Sr lattice clock transition, we have reduced this uncertainty to the low 10-16 level by averaging three sets of ten-day intermittent measurements, in which we operated the lattice clock for 104 s on each day. Moreover, a combined oscillator of two hydrogen masers was employed as a local flywheel oscillator (LFO) in order to mitigate the impact of sporadic excursion of LFO frequency. The resultant absolute frequency with fractional uncertainty of 4.3 × 10-16 agrees with other measurements based on local state-of-the-art cesium fountains.

Dissemination of optical-comb-based ultra-broadband frequency reference through a fiber network.

We disseminated an ultra-broadband optical frequency reference based on a femtosecond (fs)-laser optical comb through a kilometer-scale fiber link. Its spectrum ranged from 1160 nm to 2180 nm without additional fs-laser combs at the end of the link. By employing a fiber-induced phase noise cancellation technique, the linewidth and fractional frequency instability attained for all disseminated comb modes were of order 1 Hz and 10-18 in a 5000 s averaging time. The ultra-broad optical frequency reference, for which absolute frequency is traceable to Japan Standard Time, was applied in the frequency stabilization of an injection-seeded Q-switched 2051 nm pulse laser for a coherent light detection and ranging LIDAR system.

Direct comparison of a Ca+ single-ion clock against a Sr lattice clock to verify the absolute frequency measurement.

Optical frequency comparison of the (40)Ca(+) clock transition ν(Ca)((2)S(1/2-)(2D(5/2), 729 nm) against the (87)Sr optical lattice clock transition ν(Sr) ((1)S(0)-(3)P(0), 698 nm) has resulted in a frequency ratio ν(Ca) / ν(Sr) = 0.957 631 202 358 049 9(2 3). The rapid nature of optical comparison allowed the statistical uncertainty of frequency ratio ν(Ca) / ν(Sr) to reach 1 × 10(-15) in 1000s and yielded a value consistent with that calculated from separate absolute frequency measurements of ν(Ca) using the International Atomic Time (TAI) link. The total uncertainty of the frequency ratio using optical comparison (free from microwave link uncertainties) is smaller than that obtained using absolute frequency measurement, demonstrating the advantage of optical frequency evaluation. We note that the absolute frequency of (40)Ca(+) we measure deviates from other published values by more than three times our measurement uncertainty.

All-optical link for direct comparison of distant optical clocks.

We developed an all-optical link system for making remote comparisons of two distant ultra-stable optical clocks. An optical carrier transfer system based on a fiber interferometer was employed to compensate the phase noise accumulated during the propagation through a fiber link. Transfer stabilities of 2 × 10(-15) at 1 second and 4 × 10(-18) at 1000 seconds were achieved in a 90-km link. An active polarization control system was additionally introduced to maintain the transmitted light in an adequate polarization, and consequently, a stable and reliable comparison was accomplished. The instabilities of the all-optical link system, including those of the erbium doped fiber amplifiers (EDFAs) which are free from phase-noise compensation, were below 2 × 10(-15) at 1 second and 7 × 10(-17) at 1000 seconds. The system was available for the direct comparison of two distant (87)Sr lattice clocks via an urban fiber link of 60 km. This technique will be essential for the measuring the reproducibility of optical frequency standards.

Months-long real-time generation of a time scale based on an optical clock.

Time scales consistently provide precise time stamps and time intervals by combining atomic frequency standards with a reliable local oscillator. Optical frequency standards, however, have not been applied to the generation of time scales, although they provide superb accuracy and stability these days. Here, by steering an oscillator frequency based on the intermittent operation of a 87Sr optical lattice clock, we realized an "optically steered" time scale TA(Sr) that was continuously generated for half a year. The resultant time scale was as stable as International Atomic Time (TAI) with its accuracy at the 10-16 level. We also compared the time scale with TT(BIPM16). TT(BIPM) is computed in deferred time each January based on a weighted average of the evaluations of the frequency of TAI using primary and secondary frequency standards. The variation of the time difference TA(Sr) - TT(BIPM16) was 0.79 ns after 5 months, suggesting the compatibility of using optical clocks for time scale generation. The steady signal also demonstrated the capability to evaluate one-month mean scale intervals of TAI over all six months with comparable uncertainties to those of primary frequency standards (PFSs).

Advanced Satellite-Based Frequency Transfer at the 10-16 Level.

Advanced satellite-based frequency transfers by two-way carrier-phase (TWCP) and integer precise point positioning have been performed between the National Institute of Information and Communications Technology and Korea Research Institute of Standards and Science. We confirm that the disagreement between them is less than at an averaging time of several days. In addition, an overseas frequency ratio measurement of Sr and Yb optical lattice clocks was directly performed by TWCP. We achieved an uncertainty at the mid-10-16 level after a total measurement time of 12 h. The frequency ratio was consistent with the recently reported values within the uncertainty.

Frequency Measurement System of Optical Clocks Without a Flywheel Oscillator.

We developed a system for the remote frequency comparison of optical clocks. The system does not require a flywheel oscillator at the remote end, making it possible to evaluate optical frequencies even in laboratories, where no stable microwave reference, such as an Rb clock, a Cs clock, or a hydrogen maser exists. The system is established by the integration of several systems: a portable carrier-phase two-way satellite frequency transfer station and a microwave signal generation system by an optical frequency comb from an optical clock. The measurement was as quick as a conventional method that employs a local microwave reference. We confirmed the system uncertainty and instability to be at the low 10-15 level using an Sr lattice clock.

87Sr lattice clock with inaccuracy below 10 -15.

Aided by ultrahigh resolution spectroscopy, the overall systematic uncertainty of the 1S0-3P0 clock resonance for lattice-confined 87Sr has been characterized to 9 x 10(-16). This uncertainty is at a level similar to the Cs-fountain primary standard, while the potential stability for the lattice clocks exceeds that of Cs. The absolute frequency of the clock transition has been measured to be 429 228 004 229 874.0(1.1) Hz, where the 2.5 x 10(-15) fractional uncertainty represents the most accurate measurement of a neutral-atom-based optical transition frequency to date.

Optical atomic coherence at the 1-second time scale.

Highest-resolution laser spectroscopy has generally been limited to single trapped ion systems because of the rapid decoherence that plagues neutral atom ensembles. Precision spectroscopy of ultracold neutral atoms confined in a trapping potential now shows superior optical coherence without any deleterious effects from motional degrees of freedom, revealing optical resonance linewidths at the hertz level with a good signal-to-noise ratio. The resonance quality factor of 2.4 x 10(14) is the highest ever recovered in any form of coherent spectroscopy. The spectral resolution permits direct observation of the breaking of nuclear spin degeneracy for the 1S0 and 3P0 optical clock states of 87Sr under a small magnetic bias field. This optical approach for excitation of nuclear spin states allows an accurate measurement of the differential Landé g factor between 1S0 and 3P0. The optical atomic coherence demonstrated for collective excitation of a large number of atoms will have a strong impact on quantum measurement and precision frequency metrology.

Systematic study of the 87Srclock transition in an optical lattice.

With ultracold 87Srconfined in a magic wavelength optical lattice, we present the most precise study (2.8 Hz statistical uncertainty) to date of the 1S0-3P0 optical clock transition with a detailed analysis of systematic shifts (19 Hz uncertainty) in the absolute frequency measurement of 429 228 004 229 869 Hz. The high resolution permits an investigation of the optical lattice motional sideband structure. The local oscillator for this optical atomic clock is a stable diode laser with its hertz-level linewidth characterized by an octave-spanning femtosecond frequency comb.

High-accuracy optical clock via three-level coherence in neutral bosonic 88Sr.

An optical atomic clock scheme is proposed that utilizes two lasers to establish coherent coupling between the 5s2 1S0 ground state of 88Sr and the first excited state, 5s5p 3P0. The coupling is mediated by the broad 5s5p 1P1 state, exploiting the phenomenon of electromagnetically induced transparency. The effective linewidth of the clock transition can be chosen at will by adjusting the laser intensity. By trapping the 88Sr atoms in an optical lattice, long interaction times with the two lasers are ensured; Doppler and recoil effects are eliminated. Based on a careful analysis of systematic errors, a clock accuracy of better than 2 x 10(-17) is expected.

Precision spectroscopy and density-dependent frequency shifts in ultracold Sr.

By varying the density of an ultracold 88Sr sample from 10(9) to>10(12) cm(-3), we make the first definitive measurement of the density-related frequency shift and linewidth broadening of the 1S0-3P1 optical clock transition in an alkaline earth system. In addition, we report the most accurate measurement to date of the 88Sr 1S0-3P1 optical clock transition frequency. Including a detailed analysis of systematic errors, the frequency is [434 829 121 312 334+/-20(stat)+/-33(syst)] Hz.

Recoil-free spectroscopy of neutral Sr atoms in the Lamb-Dicke regime.

Recoil-free as well as Doppler-free spectroscopy was demonstrated on the 1S0-3P1 transition of Sr atoms confined in a one-dimensional optical lattice. By investigating the wavelength and polarization dependence of the ac Stark shift acting on the 1S0 and 3P1(m(J)=0) states, we determined the wavelength where the Stark shifts for both states coincide. This Stark-free optical lattice, allowing the purturbation-free spectroscopy of trapped atoms, may keep neutral-atom based optical standards competitive with single-ion standards.

Narrow line cooling: finite photon recoil dynamics.

We present an extensive study of the unique thermal and mechanical dynamics for narrow-line cooling on the 1S0-3P1 88Sr transition. For negative detuning, trap dynamics reveal a transition from the semiclassical regime to the photon-recoil-dominated quantum regime, yielding an absolute minima in the equilibrium temperature below the single-photon-recoil limit. For positive detuning, the cloud divides into discrete momentum packets whose alignment mimics lattice points on a face-centered-cubic crystal. This novel behavior arises from velocity selection and "positive feedback" acceleration due to a finite number of photon recoils. Cooling is also achieved with blue-detuned light around a velocity where gravity balances the radiative force.

Recoil-limited laser cooling of 87Sr atoms near the Fermi temperature.

A dynamic magneto-optical trap, which relies on the rapid randomization of population in Zeeman substates, has been demonstrated for fermionic strontium atoms on the 1S0-3P1 intercombination transition. The obtained sample, 1x10(6) atoms at a temperature of 2 microK in the trap, was further Doppler cooled and polarized in a far-off resonant optical lattice to achieve 2 times the Fermi temperature.