Analysis of the interaction-length dependence of frequency stability in an iodine-stabilized Nd:YAG laser.

We report a numerical simulation and an experimental study on the interaction-length dependence of frequency stability in an iodine-stabilized neodymium-doped yttrium aluminum garnet (Nd:YAG) laser. A saturation spectroscopy model was used in the simulation to calculate the interaction-length dependence of the linewidth and signal-to-noise ratio of the iodine saturation spectrum. We determined that 2 m was the optimal interaction length for laser-frequency stabilization. We confirmed the simulation results by performing modulation transfer spectroscopy and laser-frequency stabilization using 45-cm- and 2-m-long iodine cells and multipass configurations. The results of this study are useful for designing compact and highly stable iodine-stabilized lasers.

Precision dual-comb spectroscopy using wavelength-converted frequency combs with low repetition rates.

Precision spectroscopy contributed significantly to the development of quantum mechanics in its early stages. In the twenty-first century, precision spectroscopy has played an important role in several fields, including fundamental physics, precision measurement, environmental monitoring, and medical diagnostics. An optical frequency comb is indispensable in determining the frequency axis in precision spectroscopy and it is useful as a light source for spectroscopy. Dual-comb spectroscopy uses two frequency combs with slightly different repetition rates and has the potential to surpass conventional Fourier-transform infrared spectrometers. The resolution of dual-comb spectroscopy is limited by the frequency spacing of the comb components, that is, the repetition rate of the comb. We demonstrate dual-comb spectroscopy in the visible-wavelength region using wavelength-converted frequency combs from Er-doped fiber combs. The repetition rates of the combs are relatively low at 19.8 MHz, resulting in relatively high resolution in the dual-comb spectroscopy. The observed spectral shape in dual-comb spectroscopy agrees well with the fitting result based on the hyperfine structure of molecular iodine. The realized dual-comb spectroscopy using wavelength-converted Er-doped fiber combs is reliable (maintenance free) and applicable in other experiments at visible wavelengths.

Frequency references based on molecular iodine for the study of Yb atoms using the 1S0 - 3P1 intercombination transition at 556 nm.

We used precision spectroscopy to analyze the R(53)24-1, P(49)24-1, and R(95)25-1 lines of molecular iodine (127I2) to establish optical frequency references for the laser cooling of Yb atoms using the 1S0 - 3P1 intercombination transition at 556 nm. A laser frequency instability of < 2 × 10-12 (for 0.01 s < τ < 3000 s, τ is the average time of the measurement) was attained using the observed Doppler-free hyperfine transitions of the iodine lines. The absolute frequencies of the observed 63 hyperfine transitions were determined with an uncertainty of 7 kHz (fractional uncertainty of 1.3 × 10-11). Highly accurate hyperfine constants were determined by fitting the measured hyperfine splittings to a four-term Hamiltonian that includes the electric quadrupole, spin-rotation, tensor spin-spin, and scalar spin-spin interactions with an uncertainty of approximately 1 kHz. The observed hyperfine transitions of molecular iodine provide new frequency references for research using atomic Yb, because these transitions are close to the intercombination transition of Yb at 556 nm.

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.

Laser frequency measurement in the short-wavelength region using an intermediate laser and a frequency noise cancellation method.

Optical frequency combs play a crucial role supporting optical frequency standards and cover a wide range of wavelengths (octaves). However, broadening the comb spectrum to the short-wavelength visible region (λ < 500 nm), where GaN-based blue diode lasers are available, is not an easy task. In this study, we propose a method for measuring the laser frequency in the short-wavelength region using an intermediate laser and a noise-canceling scheme. We demonstrate this method by measuring the frequency of a GaN-based laser at 399 nm and confirming that the frequency measurement is not affected by the frequency noise of the intermediate laser.

Entanglement on an optical atomic-clock transition.

State-of-the-art atomic clocks are based on the precise detection of the energy difference between two atomic levels, which is measured in terms of the quantum phase accumulated over a given time interval1-4. The stability of optical-lattice clocks (OLCs) is limited both by the interrupted interrogation of the atomic system by the local-oscillator laser (Dick noise5) and by the standard quantum limit (SQL) that arises from the quantum noise associated with discrete measurement outcomes. Although schemes for removing the Dick noise have been recently proposed and implemented4,6-8, performance beyond the SQL by engineering quantum correlations (entanglement) between atoms9-20 has been demonstrated only in proof-of-principle experiments with microwave clocks of limited stability. The generation of entanglement on an optical-clock transition and operation of an OLC beyond the SQL represent important goals in quantum metrology, but have not yet been demonstrated experimentally16. Here we report the creation of a many-atom entangled state on an OLC transition, and use it to demonstrate a Ramsey sequence with an Allan deviation below the SQL after subtraction of the local-oscillator noise. We achieve a metrological gain of [Formula: see text] decibels over the SQL by using an ensemble consisting of a few hundred ytterbium-171 atoms, corresponding to a reduction of the averaging time by a factor of 2.8 ± 0.3. Our results are currently limited by the phase noise of the local oscillator and Dick noise, but demonstrate the possible performance improvement in state-of-the-art OLCs1-4 through the use of entanglement. This will enable further advances in timekeeping precision and accuracy, with many scientific and technological applications, including precision tests of the fundamental laws of physics21-23, geodesy24-26 and gravitational-wave detection27.

Effects of Metacognitive Strategies on the Self-Regulated Learning Process: The Mediating Effects of Self-Efficacy.

The purpose of this study was to examine the effects of metacognitive strategies on self-regulated learning processes, focusing on the mediating effects of self-efficacy. The surveys were conducted in December 2016 (Time 1) and January 2017 (Time 2). One hundred and five undergraduates enrolled at a Japanese university participated in this survey study, consisting of two surveys conducted one month apart. The questionnaires measured the use of metacognitive strategies (i.e., planning strategy and monitoring strategy), self-efficacy, general learning behaviors (behavioral engagement and persistence), and the use of cognitive strategies (i.e., writing-repetition strategy and deep-processing strategy). First, cross-lagged structure equation modeling revealed that the use of planning strategy enhanced self-efficacy. Second, path analysis examined relationships between metacognitive strategies, general learning behaviors, and cognitive strategies. It revealed that (a) general learning behaviors were promoted by metacognitive strategies mediated by self-efficacy and (b) cognitive strategies were almost directly affected by the monitoring strategy. The current study reveals that general learning behaviors and cognitive strategies involve different processes than metacognitive strategies.

Near-Unitary Spin Squeezing in

Spin squeezing can improve atomic precision measurements beyond the standard quantum limit (SQL), and unitary spin squeezing is essential for improving atomic clocks. We report substantial and nearly unitary spin squeezing in ^{171}Yb, an optical lattice clock atom. The collective nuclear spin of ∼10^{3} atoms is squeezed by cavity feedback, using light detuned from the system's resonances to attain unitarity. The observed precision gain over the SQL is limited by state readout to 6.5(4) dB, while the generated states offer a gain of 12.9(6) dB, limited by the curvature of the Bloch sphere. Using a squeezed state within 30% of unitarity, we demonstrate an interferometer that improves the averaging time over the SQL by a factor of 3.7(2). In the future, the squeezing can be simply transferred onto the optical-clock transition of ^{171}Yb.

Development of 8-branch Er:fiber frequency comb for Sr and Yb optical lattice clocks.

We demonstrate an 8-branch Er:fiber frequency comb with seven application ports, which can be individually optimized for applications with different wavelengths. The beat between the comb and a cw laser has a signal-to-noise ratio exceeding 30 dB at a resolution bandwidth of 300 kHz. The 8-branch frequency comb is used to perform frequency locking for four repumping and lattice lasers, and the frequency measurement of two clock lasers of strontium and ytterbium optical lattice clocks. We have achieved reliable optical lattice clock operation, thanks to the stable frequency locking and measurement obtained by using the 8-branch frequency comb. The developed frequency comb is a powerful experimental tool for various applications, including not only optical lattice clocks, but also research on quantum optics that use many frequency-stabilized lasers.

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 6s2 1S0-6s6p 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 aZ 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 aZ=-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.

Second harmonic generation at 399 nm resonant on the 1S0-1P1 transition of ytterbium using a periodically poled LiNbO3 waveguide.

We demonstrate a compact and robust method for generating a 399-nm light resonant on the 1S0 - 1P1 transition in ytterbium using a single-pass periodically poled LiNbO3 waveguide for second harmonic generation (SHG). The obtained output power at 399 nm was 25 mW when a 798-nm fundamental power of 380 mW was coupled to the waveguide. We observed no degradation of the SHG power for 13 hours with a low power of 6 mW. The obtained SHG light has been used as a seed light for injection locking, which provides sufficient power for laser cooling ytterbium.

Compact iodine-stabilized laser operating at 531 nm with stability at the 10(-12) level and using a coin-sized laser module.

We demonstrate a compact iodine-stabilized laser operating at 531 nm using a coin-sized light source consisting of a 1062-nm distributed-feedback diode laser and a frequency-doubling element. A hyperfine transition of molecular iodine is observed using the light source with saturated absorption spectroscopy. The light source is frequency stabilized to the observed iodine transition and achieves frequency stability at the 10(-12) level. The absolute frequency of the compact laser stabilized to the a(1) hyperfine component of the R(36)32 - 0 transition is determined as 564074632419(8) kHz with a relative uncertainty of 1.4×10(-11). The iodine-stabilized laser can be used for various applications including interferometric measurements.

Binary phase oscillation of two mutually coupled semiconductor lasers.

A two-site Ising model is implemented as an injection-locked laser network consisting of a single master laser and two mutually coupled slave lasers. We observed ferromagnetic and antiferromagnetic orders in the in-phase and out-of-phase couplings between the two slave lasers. Their phase difference is locked to either 0 or π even if the coupling path is continuously modulated. The system automatically selects the oscillation frequency to satisfy the in-phase or out-of-phase coupling condition, when the mutual coupling dominates over the injection-locking by the master laser.

Frequency ratio measurement of 171Yb and 87Sr optical lattice clocks.

The frequency ratio of the (1)S(0)(F = 1/2)-(3)P(0)(F = 1/2) clock transition in (171)Yb and the (1)S(0)(F = 9/2)-(3)P(0)(F = 9/2) clock transition in (87)Sr is measured by an optical-optical direct frequency link between two optical lattice clocks. We determined the ratio (ν(Yb)/ν(Sr)) to be 1.207 507 039 343 341 2(17) fractional standard uncertainty of 1.4 × 10(-15) [corrected]. The measurement uncertainty of the frequency ratio is smaller than that obtained from absolute frequency measurements using the International Atomic Time (TAI) link. The measured ratio agrees well with that derived from the absolute frequency measurement results obtained at NIST and JILA, Boulder, CO using their Cs-fountain clock. Our measurement enables the first international comparison of the frequency ratios of optical clocks. The measured frequency ratio will be reported to the International Committee for Weights and Measures for a discussion related to the redefinition of the second.

Errata: Frequency ratio measurement of 171Yb and 87Sr optical lattice clocks.

We correct the errors in the uncertainty budget. The determined ratio (νYb/νSr) is corrected to be 1.207 507 039 343 341 2(17) with a fractional standard uncertainty of 1.4 × 10-15.

Spectroscopy of 171Yb in an optical lattice based on laser linewidth transfer using a narrow linewidth frequency comb.

We propose a novel, high-performance, and practical laser source system for optical clocks. The laser linewidth of a fiber-based frequency comb is reduced by phase locking a comb mode to an ultrastable master laser at 1064 nm with a broad servo bandwidth. A slave laser at 578 nm is successively phase locked to a comb mode at 578 nm with a broad servo bandwidth without any pre-stabilization. Laser frequency characteristics such as spectral linewidth and frequency stability are transferred to the 578-nm slave laser from the 1064-nm master laser. Using the slave laser, we have succeeded in observing the clock transition of (171)Yb atoms confined in an optical lattice with a 20-Hz spectral linewidth.

Narrow linewidth laser system realized by linewidth transfer using a fiber-based frequency comb for the magneto-optical trapping of strontium.

A narrow linewidth diode laser system at 689 nm is realized by phase-locking an extended cavity diode laser to one tooth of a narrow linewidth optical frequency comb. The optical frequency comb is phase-locked to a narrow linewidth laser at 1064 nm, which is frequency stabilized to a high-finesse optical cavity. We demonstrate the magneto-optical trapping of Sr using an intercombination transition with the developed laser system.

A compact light source at 461 nm using a periodically poled LiNbO3 waveguide for strontium magneto-optical trapping.

We have developed a compact light source at 461 nm using a single-pass periodically poled LiNbO3 waveguide for second-harmonic (SH) generation. The obtained optical power at 461 nm is 76 mW when the power of the 922-nm fundamental light coupled into the waveguide is 248 mW. Although a narrowing of the phase-matching temperature acceptance bandwidth is observed at a high SH power, stable overnight operation is realized by carefully controlling the device temperature within an uncertainty of 0.01 °C.

Storage and retrieval of a squeezed vacuum.

Storage and retrieval of a squeezed vacuum was successfully demonstrated using electromagnetically induced transparency. The squeezed vacuum pulse having a temporal width of 930 ns was incident on the laser cooled 87Rb atoms with an intense control light in a coherent state. When the squeezed vacuum pulse was slowed and spatially compressed in the cold atoms, the control light was switched off. After 3 mus of storage, the control light was switched on again, and the squeezed vacuum was retrieved, as was confirmed using the time-domain homodyne method.