Search

In a previous work [J. Chem. Phys. 140, 174105 (2014)], we have shown that a mixed quantum classical (MQC) rate theory can be derived to investigate the quantum tunneling effects in the proton transfer reactions. However, the method is based on the high temperature approximation of the hierarchical equation of motion (HEOM) with the Debye-Drude spectral density, and results in a multistate Zusman type of equation. We now extend this theory to include quantum effects of the bath degrees of freedom. By writing the full HEOM into a multidimensional partial differential equation in phase space, we can define a new reaction coordinate, and the previous method can be generalized to the full quantum regime. The validity of the new method is demonstrated by using numerical examples, including the spin-Boson model, and the double well model for proton transfer reaction. The new method is found to resolve some key problems of the previous theory based on high temperature approximation, including possible numerical instability in long time simulation and wrong rate constant at low temperatures.

The paper predicts the power frequency electric field (PFEF), audible noise (AN), and radio interference (RI) of double-circuit 220kV and double-circuit 110kV four-circuit lines on the same tower erected on the same tower through the numerical calculation method of electromagnetic environment (EME) of AC transmission lines (TLs). Through a typical tower structure, the influence of the phase sequence (PS) on the EME is analysed, and the optimal and worst PSs are obtained. The optimal PS can significantly improve the EME, especially with a good confinement effect on the electric field’s power frequency. In addition, it also focuses on analyzing the influence degree of PS when the phase spacing, conductor-to-ground height and layer spacing change and establishes the applicable range of the optimal PS.

To assess the electromagnetic environment (EME) of high-voltage AC transmission lines (TLs) across agricultural greenhouses (AGs), a program that can calculate the power frequency electromagnetic field (PFEMF) under various AC TLs is compiled based on the principle of the simulated charge method and the simulated current method, and the power frequency electric field (PFEF) and magnetic field (MF) strength of AGs are calculated and compared with the field measurement results. The results show that the field measurement values of PFEF intensity and magnetic induction intensity in AGs do not exceed the standard requirements of 10kV/m and 0.1mT. The existence of AGs has a certain influence on the electric field (EF) distribution, but has little influence on the power frequency magnetic field (PFMF). For the PFEF and PFMF in AGs, the numerical calculation results are basically consistent with the field measurement results. The above results provide a reference for the EME assessment of high-voltage AC TLs across AGs.

Absolute gravimeters have been widely used as an important instrument in geological exploration and geophysics. To achieve a required measurement precision, it is necessary to integrate a vertical vibration isolator with ultra-low resonance frequency into the gravimeter. In this paper, an active vibration isolator designed on the basis of a BM-10 passive vibration isolation platform is presented. In the isolator, a seismometer placed next to the payload on the same plate outputs a voltage signal proportional to the payload’s velocity. According to this signal, a feedback circuit based on a PID controller controls two identical voice coil actuators to drive the platform synchronously. In this way, the vibration of the payload is suppressed. The BM-10 platform has 6-DOF passive vibration isolation originally, but its horizontal vibration isolation is proved unnecessary or even harmful in absolute gravimetry. Hence, two linear bushings are applied as a horizontal constraint to ensure that the payload only moves vertically in a straight line. Experiments show the resonance period of the isolator reaches approximately 88 s. In addition, the active vibration isolator has shown a much better performance for vibrations at low frequency than the passive isolator. In the future, the vibration isolator will be improved and then be integrated in the NIM-AGRb-1 atom-interferometry absolute gravimeter for the evaluation of its performance.

A transportable fountain clock with high reliability is important for high-precision time-frequency measurements. Because of its relatively small cold atoms' collision frequency shift and ease of attaining high quantum state preparation efficiency, the rubidium atomic fountain clock has an indicated higher stability and reliability. This paper reports the design and operation of a transportable rubidium atomic fountain clock developed by the Shanghai Institute of Optical and Fine Mechanics, Chinese Academy of Science. After being transported more than 1000 km from Shanghai to the Changping Campus of the National Institute of Metrology, China, the optical platform and other hardware of the fountain clock did not need to be adjusted. The rubidium fountain clock maintained a stability of 4.0 × 10

We investigate the application of the imaginary time hierarchical equations of motion method to calculate real time quantum correlation functions. By starting from the path integral expression for the correlated system–bath equilibrium state, we first derive a new set of equations that decouple the imaginary time propagation and the calculation of auxiliary density operators. The new equations, thus, greatly simplify the calculation of the equilibrium correlated initial state that is subsequently used in the real time propagation to obtain the quantum correlation functions. It is also shown that a periodic decomposition of the bath imaginary time correlation function is no longer necessary in the new equations such that different decomposition schemes can be explored. The applicability of the new method is demonstrated in several numerical examples, including the spin-Boson model, the Holstein model, and the double-well model for proton transfer reaction.

We present a robust, transportable ${\mathrm{Ca}}^{+}$ optical clock, with a systematic uncertainty of $1.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ limited by the black-body radiation (BBR) field evaluation and an uptime rate of $g75%$ over a 20-day period. The clock is then installed in an air-conditioned car trailer, making it more convenient for applications. Referenced to a stationary laboratory clock, geopotential measurements are made with the transportable clock with a total uncertainty of 0.33 m (statistically 0.25 m and systematically 0.22 m) and agree with the spirit level measurement. After being moved $g1200$ km, the absolute frequency of the ${\mathrm{Ca}}^{+}$ optical clock transition is measured as 411 042 129 776 400.41(23) Hz, with a fractional uncertainty of $5.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$, which is about one order of magnitude smaller than our previous measurement. The transportable built can be used for sub-meter-level elevation measurements, comparing intercontinental optical clocks, verifying basic physical theories, etc.

Voltage sag often leads to interruption of industrial production processes, which brings huge economic losses to users. Taking measures from the user side is the main measure to mitigate the effects of voltage sag today. Reasonable evaluation of voltage sag immunity in industrial process is the premise of the degradation of governance. However, the current evaluation method needs to test the entire industrial process, which will cause economic losses to the users who conduct the test. Therefore, this test scheme has no practical evaluation value. This article is based on the relationship between equipment attributes and process physical attributes. Further link the equipment endurance ability with the industrial process endurance ability, through the test of single equipment to achieve the assessment of the entire industrial process endurance ability. At the same time, the case study of an industrial park shows the practicability and effectiveness of the scheme.

NIM has built three cesium fountain clocks in Beijing area. NIM5 fountain clock has been reported to BIPM since 2014. The microwave synthesizer and computer control system of NIM5 had been modified recently. The type-B uncertainty is 9×10−16, limited by the interferometric switch in the microwave chain. NIM5-M has been sent to 32 km away from NIM and compared with NIM5 via fiber link. The new NIM6 fountain clock has been built and evaluated, the results are presented in the paper. The direct comparison of NIM5 and NIM6 has also been done, a relative frequency difference of 4.4×10−16 was obtained for 20 days averaging time, consistent with the total uncertainty of the two clocks.

We investigate the numerical stability of the hierarchical equations of motion (HEOM) method applied to systems with the Brownian oscillator (BO) and multimode BO (MBO) spectral densities. It is shown that, with the increase in the system-bath coupling strength, the standard HEOM may become unstable, and a simple increase in the truncation depth of the HEOM cannot remove the instability at long times. To solve this problem, we first show that the high-temperature approximation of the HEOM with the BO spectral density is equivalent to the celebrated quantum Fokker-Planck equation (QFPE). By starting from the HEOM, we then derive a new multidimensional phase space differential equation that generalizes the QFPE to arbitrary temperature. It is further shown that the numerical instability can be removed if the new low-temperature QFPE is expanded in a basis set different than the one that leads to the conventional HEOM. The matrix product state method is also employed to propagate the new equation based on the low-temperature QFPE and to resolve the numerical instability problem for an electron transfer model with the MBO spectral density presented in the recent literature.

Two Cs fountains clocks have been built in NIM. NIM5 fountain clock has been reported to BIPM since 2014. The microwave synthesizer and computer control system of NIM5 had been modified recently. The Type-B uncertainty is 9×10-16, limited by the interferometric switch in the microwave chain. The new NIM6 fountain clock has been built and evaluated, the preliminary results are presented in the paper. With an ultra-stable microwave signal generated from an optical comb which locked to an ultra-stable laser, the frequency instability of NIM6 fountain clock reached $5 \times 10^-14$/$\tau^1/2$ at high density. The direct comparison of two fountain clocks has also been done, a relative frequency difference of $4.4 \times 10^{16}$ was obtained for 20 days averaging time, consistent with the total uncertainties of the two clocks.

The evolution history of modern time from the astronomical time to the atomic second is briefly reviewed herein. The progress and status of realizing the current definition of the second using cesium cold atomic fountain primary frequency standards, the process of generating the international atomic time (TAI) and coordinated universal time (UTC), and trend of releasing the tolerance on inserting leap-seconds into the UTC are sketched. The present situation on steering the TAI regularly from January 2016 by cesium fountain frequency standards from five countries is reported. Research progress of local and global optical frequency standards is summarized, and steering TAI by six optical frequency standards starting from 2016 is reported. Requirements and responses on steering TAI regularly by optical frequency standards are introduced according to the roadmap, which is under discussion internationally, or the future redefinition of the second. Furthermore, two types of optical frequency standards, namely the basic-research and the metrological type are suggested, and the performance and technical qualifications for the metrological type of optical frequency standards are recommended. For the optical frequency standards of the metrological type, with uncertainties better than 3×10−17, not only static relative gravity but also the alternative tide frequency shifts should be considered in their frequency evaluations. Finally, a scheme employing frequency comparison, across a long longitude-distance, between two highly stable optical frequency standards to demonstrate the relativistic tidal frequency shift directly and experimentally is proposed.

We develop new methods to efficiently propagate the hierarchical equations of motion (HEOM) by using the Tucker and hierarchical Tucker (HT) tensors to represent the reduced density operator and auxiliary density operators. We first show that by employing the split operator method, the specific structure of the HEOM allows a simple propagation scheme using the Tucker tensor. When the number of effective modes in the HEOM increases and the Tucker representation becomes intractable, the split operator method is extended to the binary tree structure of the HT representation. It is found that to update the binary tree nodes related to a specific effective mode, we only need to propagate a short matrix product state constructed from these nodes. Numerical results show that by further employing the mode combination technique commonly used in the multi-configuration time-dependent Hartree approaches, the binary tree representation can be applied to study excitation energy transfer dynamics in a fairly large system including over 104 effective modes. The new methods may thus provide a promising tool in simulating quantum dynamics in condensed phases.

A transportable fountain clock with high reliability is important for high-precision time-frequency measurements. Because of its relatively small cold atoms’ collision frequency shift and ease of attaining high quantum state preparation efficiency, the rubidium atomic fountain clock has an indicated higher stability and reliability. This paper reports the design and operation of a transportable rubidium atomic fountain clock developed by the Shanghai Institute of Optical and Fine Mechanics, Chinese Academy of Science. After being transported more than 1000 km from Shanghai to the Changping Campus of the National Institute of Metrology, China, the optical platform and other hardware of the fountain clock did not need to be adjusted. The rubidium fountain clock maintained a stability of 4.0 × 10−13τ1/2, reaching 5.0 × 10−16 at 300 000 s. After transportation, the rubidium fountain clock and a cesium fountain clock (NIM5) were operated together against the reference frequency of a hydrogen maser. In three separate operating periods, over a total of nearly three months, the average frequency repeatability of the rubidium fountain was less than 3.8 × 10−15.

The increasing penetration of distributed energy resources on the distribution networks have brought a number of technical impacts where voltage and thermal variations have been identified as the dominant effects. Active network management in distribution networks aims to integrate distributed energy resources with flexible network management so that distributed energy resources are organized to make better use of existing capacity and infrastructure. This paper propose active solutions which aims to solve the voltage and thermal issues in a distributed manner utilizing a collaborative approach. The proposed algorithms have been fully tested on a distribution network with distributed generation units.

An ultranarrow bandwidth Faraday atomic filter is realized based on cold Rb87 atoms. The atomic filter operates at 780 nm on the 52S1/2, F=2 to 52P3/2, F′=3 transition with a bandwidth of 7.1(8) MHz, which is approaching the natural linewidth of the transition. The peak transmission achieves 2.6(3)% by the multi-pass probe method. This atomic filter based on cold atoms may find potential applications in self-stabilizing lasers in the future.

The optical microwave generation scheme with an ultra-stable Fabry–Perot cavity (USC) in a self-injection loop of laser diode (LD) is proposed and experimentally demonstrated for the first time, to the best of our knowledge, in this Letter. Using an USC as the mode selector, an injection light is obtained with coherent and equidistant comb-like modes, which are separated by integer multiples of the free spectral range (FSR) of the USC in frequency domain. After injecting back to the LD, the lasing modes are referenced to these comb-like modes, and the microwaves with frequencies of integer multiples of the USC FSR are obtained from the beating signal of detection photodiode. For the microwaves at frequencies of one FSR and two FSRs, the signal-to-noise ratios are better than 60 dB, and the 3 dB linewidths are below 16 Hz. The phase noises and the frequency stability of the generated microwave are also investigated experimentally.

The cesium fountain primary frequency standard NIM5 has been developed at the National Institute of Metrology in China. The NIM5 loads atoms in an optical molasses from the background Cs vapor directly. Atoms are then cooled to a temperature of about 2 μK and launched to a height of 81 cm. The fringes of the Ramsey pattern have a width of 0.98 Hz. The NIM5 operates for more than 300 d a year, operating nearly continuously for 15 d at a time. By stabilizing the 9.19 GHz microwave frequency to the center of the central Ramsey fringe, a typical fractional frequency instability of 3 × 10−13 (τ/s)−1/2 is obtained when running at high atom density, and a combined uncertainty, including Type A and B uncertainties, is typically 1.6 × 10−15. Comparisons of data between NIM5 and 5 other fountain clocks were carried out in May 2013 via two-way satellite time and frequency transfer (TWSTFT), and the results show good agreement within the uncertainties. Six groups of NIM5 data from January to June 2014 have been published in Circular T 319 and 320.

An ultra-stable microwave down converted from the ultra-stable laser directly by an optical frequency comb (OFC) is built at the National Institute of Metrology China. The repetition rate (f r ) of OFC is stabilized by stabilizing the sum of the carrier envelope offset frequency (f ceo ) of OFC and the beating frequency between the ultra-stable laser (USL) and OFC. A current feedback with 30 kHz bandwidth and a piezoelectric transducer with 1 kHz bandwidth are applied for the frequency stabilization. The frequency jitter of the stabilized sum frequency is about 4 Hz. Though the counting of locked f r , the shifted frequency of the USL is about 2087 Hz/day. As the frequency jitter of the mixing frequency of f ceo and the beating frequency between this OFC and another USL is about 10Hz, the short time stability of f r is calculated to be about 5e-14. This ultra-stable microwave will be applied as the local oscillator for NIM5 Cs fountain to improve its shorter term instability.

In this paper we report the recent progresses on the time and frequency primary standards at the National Institute of Metrology (NIM) China: stabilized lasers for practical realization of the length unit (meter) of the International System of Units (SI); the cesium fountain clocks to realize the SI time unit (second) with an uncertainty of 2×10-15; the femto-second optical frequency combs, establishing the coherent connection between microwave frequency and optical frequency, to calibrate the optical wavelengths traceably to the microwave standard frequency with uncertainty better than 4×10-14; and the construction of a Sr lattice optical clock as a candidate of possible future redefinition of the second. We also describe: (1) fs optical combs are serve-locking systems and the specification to characterize their performance should be their tracking precision; (2) the estimated uncertainty limitations of sample cell - atom beam - cold atom fountain - trapped atom/ion frequency reference techniques.

The second laser cooling cesium fountain clock NIM5 at the National Institute of Metrology (NIM) China adopts the (1,1,1) direct optical molasses ( OM) configuration. NIM5 has been running with a stability of 3×10−15/d and an operation ratio of 99% since 2007. Preliminary evaluations of NIM5 in 2008 showed a typical combined uncertainty of 3×10−15. The NIM5 clock is operating in parallel with NIM’s first fountain clock NIM4. NIM4 and NIM5 are used to steer the frequency of the calculated NIM atomic time TA-c(NIM) and the first set of results are promising. We are now at the stage of comparing the frequency of NIM5 with UTC to support the independent frequency shift evaluations of NIM5 and contribute to the international atomic time in the near future.

TA(NIM) is being updated now. The new TA(NIM) uses an active hydrogen maser as a reference clock, and the frequency of TA(NIM) is steered by an algorithm to keep it the same as the NIM4 fountain clock, which is NIM's primary frequency standard. This paper introduces the generation of new TA(NIM), including the equations to predict maser frequency and the steering algorithm. The time difference and the frequency difference between the new TA(NIM) and UTC are also reported.

We present a laser system design for an absolute gravimeter based on 87 Rb atom interferometer. By skillful design, lasers with 9 different frequencies are based on two diode lasers including tapered amplifier. Two electrical feedback systems are used for laser frequency stabilization and the Raman lasers generation respectively. All other lasers are based on two Raman lasers and realized with frequency shift by acoustic optical modulators. This laser system not only has the compact and simple construction, but meets all requirements for laser power and frequency controlling for the atom interferometer. It has the characteristic of reliability and integrity.

We report the design of a new cesium fountain clock NIM6, which is under construction in NIM. Besides some improvements on the vacuum system, Ramsey cavity and microwave synthesizer to reduce the Type B uncertainty. Another major improvement on NIM6 is to collect more atoms from a MOT loading optical molasses and optical pumping to get a better signal to noise ratio at the detection. The atom distribution will be more uniform compared with a 2D MOT loading optical molasses, and the diameter of the cloud can be adjusted by the intensity and detuning of lights during the post cooling to keep the collisional-induced frequency shift low. The atom numbers can be further increased by a new de-pumping - optical pumping procedure to pump atoms to the |F=3, m F =0> clock state directly. With a new cryogenic sapphire oscillator (CSO) based frequency synthesizer, NIM6 is aiming to reach the quantum projection noise, thus leading to a reduced Type A uncertainty compared with NIM5.

The triggered-phase transient analyzer (TPTA) was developed in our laboratory recently. With TPTA, the phase transient of Mach-Zehnder interferometric switch which was used to reduce the microwave leakage was studied. From the measurement results, it seemed that there were some kinds of thermal effect in our interferometric switch. The TPTA has the ability to measure the phase variations of two pulsed microwaves with a fixed interval in one cycle. Therefore, after measuring the phase discontinuity between two switching on states in one fountain clock's cycle, the frequency uncertainty induced by interferometric switch was reported in this paper.

The caesium fountain primary frequency standard NIM5 has been developed at the National Institute of Metrology (NIM) of China. The NIM5 loads atoms in an optical molasses (OM) from the background Cs vapor directly. Atoms are then cooled to a temperature of about 2 μK and launched to a height of 81 cm. The fringes of the Ramsey pattern have a width of about 1 Hz. Stabilizing the 9.19 GHz microwave frequency to the centre of the central Ramsey fringe, a typical fractional frequency stability of 3×10 -13 (τ/s) -1/2 is obtained when running at high atom density, and a combined uncertainty, including Type A and B uncertainties is typically less than 1.6×10 -15 . The NIM5 operates for more than 300 days in a year with nearly continuous operation over 15 days. Comparisons of data among the NIM5 fountain clock and other 5 fountain frequency clocks were carried out in May, 2013 through Two-Way Satellite Time and Frequency Transfer (TWSTFT), also NIM5 was compared with UTC through UTC(NIM). The results demonstrated agreement within the stated uncertainties.

We are developing a new Cs fountain frequency standard in NIM, and shooting for the frequency uncertainty of a few parts in 1016. The new fountain will run in a lab with the temperature fluctuation of 0.3K, and no active temperature control system will be added outside the flight tube. Instead, an isothermal liner will be surrounded the flight tube. It is a special type of heat pipe, made of a thin layer of vacuum tube filled with pure water. The thermal conductivity of a glass isothermal liner is about 10 times higher than that of coppers. It also works like a low pass filter reducing the temperature fluctuations of the system. The advantage of using an isothermal liner is to make the temperature of the whole interrogation region more uniform and stable. With precision standard Pt thermometers measuring the temperatures of a few locations of the flight tube, the average temperature uncertainty is less than 50 mK. The frequency shift due to the blackbody radiation can be calculated, and the relative frequency shift due to black body radiation can reach down to 7.2E-17 of this new fountain clock. Key words: Fountain clock, blackbody radiation, heat pipe.

The basic design principles for interference air refractometers with lasers as light sources are reviewed and a detailed discussion of the possible error sources is given. Quantitative analysis indicates that the design of the air cell and its configuration in the measuring arm is the focus for improving measurement uncertainty. An uncertainty of d n n = 10 −8 can be achieved by means of sophisticated design with relatively simple techniques and less critical requirements: a free running HeNe laser as the light source; 1 64 fringe subdivision; and the sum of the calibration uncertainty of the air cell length(s) plus relative instability of this length(s) should be less than 2 × 10−5.

The cesium fountain primary frequency standard NIM5 started to operate since 2008 and started to report to BIPM since 2014. The major constrains of NIM5 is a relatively large background signal at the detection and microwave leakages due to the Ramsey cavity. A new fountain clock NIM6 is under construction. Besides some improvements on the vacuum system, a new Ramsey cavity and a microwave synthesizer are made to reduce the Type B uncertainty. Another feature of NIM6 is collecting atoms from a MOT loading optical molasses to get more atoms with a more uniform density distribution. With a new frequency synthesizer based on cryogenic sapphire oscillator (CSO), NIM6 is aiming to reach the quantum projection noise, thus leading to a reduced Type A uncertainty compared with NIM5.

We report hertz level relative linewidth distributed feedback diode lasers with external optical feedback from a high finesse F-P cavity, and demonstrate the efficient phase noise suppression and laser linewidth reduction of the optical feedback technique. The laser phase noise is dramatically suppressed throughout the measurement frequency range. Especially at the Fourier frequency of 17 kHz, approximately the linewidth of the F-P reference cavity, the laser phase noise is significantly suppressed by more than 92 dB. Above this Fourier frequency, the noise maintains a white phase noise plateau as low as -124.4 dBc/Hz. The laser's FWHM linewidth is reduced from 7 MHz to 4.4 Hz, and its instantaneous linewidth is 220 mHz in the Lorentzian fitting.

We have measured the absolute frequency of a clock transition at the 10(-15) level with a single, trapped, laser-cooled Ca-40(+) ion in a miniature Paul trap. In our measurement, an optical frequency comb is referenced to a hydrogen maser, which is calibrated to the SI second through the Global Positioning System (GPS). By analyzing the experimental data obtained within 32 days of a total averaging time > 2 x 10(6) s, the absolute frequency of the Ca-40(+) 4s S-2(1/2)-3d D-2(5/2) clock transition is measured as 411 042 129 776 393.0 (1.6) Hz with a fractional uncertainty of 3.9 x 10(-15).

The ultra-stable laser can be converted to microwave signal with very high fidelity combining with the optical frequency comb, and the ultra-stable microwave down converted can be used as a local oscillator for Cs fountain clocks. To produce such a microwave source, we are developing a 1542 nm laser with a potential relative stability of 10 -15 in one second. In this paper, the ultra-stable laser system with some key parameters and the Pound-Drever-Hall (PDH) locking system are introduced. Furthermore, the method and procedure of coupling the laser into the cavity resonator is described and a coupling efficiency of better than 30% is achieved. Further experiments are carried out and final results will be reported in the future.

A general analytical form of the round trip phase shift in grating feedback diode lasers is proposed. Using the new form, it is obvious that the round trip phase shift can be independent of rotation angle in first order approximation when only one restriction condition is met. We call this the quasi synchronous tuning (QST) condition. In the QST region, a considerably large mode hopping free tuning range can be obtained. An adjustment structure with only one freedom is needed to accurately find and locate the quasi synchronous pivot, which is not strictly confined on the grating surface and its extension. It means that the external cavity diode lasers design can be easier and the laser can be more stable and reliable.