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We report the absolute frequency measurement of the 5 s 2 1 S 0 → 5 s 5 p 3 P 0 transition in 87Sr optical lattice clock (Sr1) at National Time Service Center. Its systematic frequency shifts are evaluated carefully with a total relative uncertainty of 5.1 × 10 − 17 . The measured absolute frequency is 429 228 004 229 872.91(18) Hz with a relative uncertainty of 4.1 × 10 − 16 , with reference to the ensemble of primary and secondary frequency standards published in the Circular T bulletin by BIPM through a global navigation satellite system link.

The quantum system under periodical modulation is the simplest path to understand the quantum non-equilibrium system, because it can be well described by the effective static Floquet Hamiltonian. Under the stroboscopic measurement, the initial phase is usually irrelevant. However, if two uncorrelated parameters are modulated, their relative phase can not be gauged out, so that the physics can be dramatically changed. Here, we simultaneously modulate the frequency of the lattice laser and the Rabi frequency in an optical lattice clock (OLC) system. Thanks to ultra-high precision and ultra-stability of OLC, the relative phase could be fine-tuned. As a smoking gun, we observed the interference between two Floquet channels. Finally, by experimentally detecting the eigen-energies, we demonstrate the relation between effective Floquet Hamiltonian and 1-D topological insulator with high winding number. Our experiment not only provides a direction for detecting the phase effect, but also paves a way in simulating quantum topological phase in OLC platform., 7 pages, 4 figures, almost published version, comments are welcome and more information at http://cqutp.org/users/xfzhang/

In this paper, we demonstrate in situ synchronous frequency comparison between distinct regions in a one-dimensional optical lattice. The synchronous comparison instability is well below the Dick limit and agrees with the limit induced by atomic detection noise. The absolute atom number is extracted from the synchronous comparison instability with an uncertainty below 3%. Surpassing the performance of absorption imaging, this method provides a way to directly and precisely determine the absolute atom number from detection noise. Taking advantage of the inhomogeneous density distribution over the whole lattice, the density shift can also be conveniently measured by this synchronous frequency comparison method. Inconsistent with the expectation of the linear relationship between density shift and atom number difference, nonlinearity is observed, indicating that the assumption of an identical density shift coefficient over the whole lattice is not always safe.

In this paper, we demonstrate a frequency modulation technique to accurately measure the probe Stark shift of optical clocks. The effective coupling strength of the probe laser to the clock transition is precisely controlled by this frequency modulation technique, which is different from the traditional method by controlling the effective coupling strength via changing the probe light power. In an 87Sr optical lattice clock, the probe Stark shifts are measured as a function of the square of the bare state coupling strength. The probe Stark shift coefficient of 87Sr is experimentally determined as −6.0(5)×10−7/Hz using this frequency modulation technique. With the help of frequency modulation, the probe light power can be as large as possible without decreasing the measurement precision and the achieved measurement lever arm is improved by more than one order of magnitude compared with previous results.

We periodically modulate the lattice trapping potential of a $^{87}$Sr optical clock to Floquet engineer the clock transition. In the context of atomic gases in lattices, Floquet engineering has been used to shape the dispersion and topology of Bloch quasi-energy bands. Differently from these previous works manipulating the external (spatial) quasi-energies, we target the internal atomic degrees of freedom. We shape Floquet spin quasi-energies and measure their resonance profiles with Rabi spectroscopy. We provide the spectroscopic sensitivity of each band by measuring the Fisher information and show that this is not depleted by the Floquet dynamical modulation. The demonstration that the internal degrees of freedom can be selectively engineered by manipulating the external degrees of freedom inaugurates a novel device with potential applications in metrology, sensing and quantum simulations., 6 pages, 4 figures, including supplementary material, comments are welcome and more information at http://cqutp.org/users/xfzhang/

The self-comparison method is a powerful tool in the uncertainty evaluation of optical lattice clocks, but any drifts will cause a frequency offset between the two compared clock loops and thus lead to incorrect measurement result. We propose a drift-insensitive self-comparison method to remove this frequency offset by adjusting the clock detection sequence. We also experimentally demonstrate the validity of this method in a one-dimensional 87Sr optical lattice clock. As the clock laser frequency drift exists, the measured frequency difference between two identical clock loops is (240 ± 34) mHz using the traditional self-comparison method, while it is (−15 ± 16) mHz using the drift-insensitive self-comparison method, indicating that this frequency offset is cancelled within current measurement precision. We further use the drift-insensitive self-comparison technique to measure the collisional shift and the second-order Zeeman shift of our clock and the results show that the fractional collisional shift and the second-order Zeeman shift are 4.54(28) × 10−16 and 5.06(3) × 10−17, respectively.

We present a synchronous frequency comparison method based on one cold-atom ensemble by using the dual-excitation spectrum technique, which can simultaneously detect the probabilities of two different clock transitions. We experimentally verify this synchronous frequency comparison method between | m F | = 9 / 2 and | m F | = 7 / 2 in a one-dimensional 87Sr optical lattice clock and the comparison instability is well below the Dick limit. We also extend the dual-excitation spectrum method to shorten the clock feedback cycle by a half in optical lattice clocks and experimentally demonstrate that the interleaved self-comparison instability is 1.4 times lower than that of the traditional operation method.

We report a transportable one-dimensional optical lattice clock based on 87Sr at the National Time Service Center. The transportable apparatus consists of a compact vacuum system and compact optical subsystems. The vacuum system with a size of 90 cm× 20 cm× 42 cm and the beam distributors are assembled on a double-layer optical breadboard. The modularized optical subsystems are integrated on independent optical breadboards. By using a 230 ms clock laser pulse, spin-polarized spectroscopy with a linewidth of 4.8 Hz is obtained which is close to the 3.9 Hz Fourier-limit linewidth. The time interleaved self-comparison frequency instability is determined to be 6.3 × 10–17 at an averaging time of 2000 s.

The frequency-drift-induced self-comparison measurement error was experimentally demonstrated by measuring the frequency difference between two interleaved clock loops with the same systemic parameters in the 87Sr optical lattice clock at the National Time Service Center of China. Combining the experimental and simulated results, this error was precisely determined by the total clock laser frequency drift during the time interval between two adjacent operations of interleaved clock loops.

We review recent experimental progress concerning the 87Sr optical lattice clock at the National Time Service Center in China. Hertz-level spectroscopy of the 87Sr clock transition for the optical lattice clock was performed, and closed-loop operation of the optical lattice clock was realized. A fractional frequency instability of 2.8 &times, 10&minus, 17 was attained for an averaging time of 2000 s. The Allan deviation is found to be 1.6 &times, 15/&tau, 1/2 and is limited mainly by white-frequency-noise. The Land&eacute, g-factors of the (5s2)1S0 and (5s5p)3P0 states in 87Sr were measured experimentally, they are important for evaluating the clock&rsquo, s Zeeman shifts. We also present recent work on the miniaturization of the strontium optical lattice clock for space applications.

The work presented in this paper is based on an optical frequency comb injection-locking, active filtering and amplification method to build a narrow linewidth laser for second cooling of the strontium atoms in an optical lattice clock. An optical femtosecond laser comb with mode spacing of 250 MHz as master laser is applied to directly inject into an external cavity semiconductor laser at 689 nm called slave laser, a single mode is selected and amplified from the optical femtosecond laser comb.

In the ultra-cold 87Sr atomic system, the Zeeman shift of the clock transition was measured with the σ±-polarized interrogation to accurately determine the g-factors of the 5s2 1S0 and 5s5p 3P0 states.

We show that single-layer graphene presents negative irradiance-dependent nonlinear refraction. We discriminate between a low-irradiance regime, where the conventional Kerr effect applies and a high-irradiance regime where the nonlinear refraction becomes irradiance-dependent.

We report experiments on the observation of the 1S0-3P0 transition spectrum of 88Sr in the Lamb-Dicke regime. After going through a two-stage magneto-optical trap (MOT), 88Sr cold atoms with number of about 1 \times 105 and a longitudinal temperature of 8.4 μK are loaded into a one-dimensional (1D) optical lattice, which is realized with a semiconductor laser at 813.4 nm. Using the magnetic field-inducing 3P1 state mixing into 3P0 state, the spectroscopy of the 1S0-3P0 transition with a linewidth of 180 Hz is detected.

We presented experimental and theoretical studies of the effect of an external magnetic field on the forbidden transition in the bosonic Sr atom. In our ultra-cold atomic system, the excitation fraction of $5s5p$~$^3P_0$~-~$5s^2$~$^1S_0$ forbidden transition was measured under the circumstance of the different magnetic field strengths by using the normalized detection method. Based on perturbation theory, we calculated the magnetic-field-induced $5s5p$~$^3P_0$~-~$5s^2$~$^1S_0$ transition rate. The excitation fraction as a function of the magnetic field strength was deduced according to the calculated results. A good agreement was found between the experimental measurements and the calculations. This study should be helpful in evaluating the magnetic field effects on the forbidden transition rate with higher accuracy. Moreover, it can help to understand the ultra-cold atomic interaction in the external magnetic field., 17 pages, 4 figures, 055017

We describe a dual-entropy-source quantum random number generator based on atomic spontaneous emission. Using the intensity fluctuations of a coherent beam to modulate the detuning frequency of the driving field, the atomic ensemble exhibits larger fluctuations of the spontaneous emission noise. The quantum-to-classical-noise ratio of the measured noise is increased to 10.14 dB. After post-processing, a string of random numbers at rates up to 5.12 Mb/s is extracted, which passes all the NIST tests. The presented scheme shows the feasibility to combine multiple independent randomness sources to produce secure quantum random bits.

We present an experimental determination on the Lande g-factors for the 5s2 1S0 and 5s5p 3 P0 states in ultra-cold atomic systems, which is important for evaluating the Zeeman shift of the clock transition in the 87Sr optical lattice clock. The Zeeman shift of the 5s5p 3P0–5s2 1S0 forbidden transition is measured with the π-polarized and σ±-polarized interrogations at different magnetic field strengths. Moreover, in the g-factor measurement with the σ±-transition spectra, it is unnecessary to calibrate the external magnetic field. By this means, the ground state 5s2 1S0 g-factor for the 87Sr atom is −1.306(52)×10−4, which is the first experimental determination to the best of our knowledge, and the result matches very well with the theoretical estimation. The differential g-factor δg between the 5s5p 3P0 state and the 5s2 1S0 state of the 87Sr atoms is measured in the experiment as well, which are −7.67(36) × 10−5 with π-transition spectra and −7.72(43) × 10−5 with σ±-transition spectra, in good agreement with the previous report [Phys. Rev. A 76 (2007) 022510]. This work can also be used for determining the differential g-factor of the clock states for the optical clocks based on other atoms.

We report the 87Sr optical lattice clock developed at the National Time Service Center. We achieved a closed-loop operation of the optical lattice clock based on 87Sr atoms. The linewidth of the spin-polarized clock peak is 3.9 Hz with a clock laser pulse length of 300 ms, which corresponds to a Fourier-limited linewidth of 3 Hz. The fitting of the in-loop error signal data shows that the instability is approximately , affected primarily by the white noise. The fractional frequency difference averages down to for an averaging time of 3000 s.

A new layered compound within the nominal composition range of Y2SrCo2−xCuxO6.5(0.5

We report on frequency measurement of the intercombination (5s2)1S0–(5s5p)3P1 transition of the four natural isotopes of strontium, including 88Sr (82.58%), 87Sr (7.0%), 86Sr (9.86%), and 84Sr (0.56%). A narrow-linewidth laser that is locked to an ultra-low expansion (ULE) optical cavity with a finesse of 12000 is evaluated at a linewidth of 200 Hz with a fractional frequency drift of 2.8×10−13 at an integration time of 1 s. The fluorescence collector and detector are specially designed, based on a thermal atomic beam. Using a double-pass acousto-optic modulator (AOM) combined with a fiber and laser power stabilization configuration to detune the laser frequency enables high signal-to-noise ratios and precision saturated spectra to be obtained for the six transition lines, which allows us to determine the transition frequency precisely. The optical frequency is measured using an optical frequency synthesizer referenced to an H maser. Both the statistical values and the final values, including the corrections and uncertainties, are derived for a comparison with the values given in other works.