Power stabilized cryogenic sapphire oscillator

Microwave oscillators of exceptional short-term stability have been realized from cryogenic sapphire resonators with loaded Q factors in excess of 10⁹ at 11.9 GHz and 6 K. This has been achieved by a power stabilized loop oscillator with active Pound frequency stabilization. These oscillators have exhibited a fractional frequency stability of 3-4×10^-15 for integration times from 0.3 to 100 s. The relative drift of these two oscillators over one day is a few times 10^-13. To reduce the long-term drift, which is principally due to excessive room temperature sensitivity, we have added cryogenic sensors for the power and frequency stabilization servos to one of these oscillators. We have also implemented a servo to reduce the room temperature sensitivity of our phase modulators. Testing of this oscillator against a Shanghai Observatory H-maser has shown an Allan deviation of 4×10^-15 from 600 to 2000 s     

Measurement of dielectrics at 100 GHz with an open resonatorconnected to a network analyzer

A high-Q hemispherical open resonator is connected to an automatic network analyzer to enable precise and fast determination of the permittivity and loss tangent of low-loss dielectric materials at 100 GHz. Both scalar theory and vector theory with a frequency variation method are used to determine the dielectric properties of low-loss materials which are used in quasioptical components, for example in fusion reactor windows and tenses for millimeter-wave receivers. The uncertainty of the measurement is 0.02% to 0.04% for ε_r(ϵ_r⩾2) and 6-40×10^-6 for tan δ(10^-4⩽tan δ⩽10^-3 )     

Very high Q microwave spectroscopy on trapped171Yb+ ions: application as a frequency standard

A microwave frequency standard based on buffer-gas cooled ¹⁷¹ Yb⁺ ions confined in a linear Paul trap has been demonstrated in prototype form. The standard exhibits a fractional frequency instability characterized by an Allan deviation σ_y (τ)=3.7×10^-13τ^-1/2 for τ<3000 s. Microwave Ramsey fringes with a Q factor of 1.5×10¹³ have been observed     

An ultralow noise microwave oscillator based on a high-Q liquidnitrogen cooled sapphire resonator

Two liquid nitrogen-cooled sapphire loaded cavities (SLC's) operating at about 80 K have been successfully constructed, Both cavities were designed to operate on the whispering gallery (WG) E_{12, 1, δ} mode at a resonant frequency of 8.95 GHz. The first SLC was used as the frequency-determining element in a loop oscillator, while the second was used as a frequency discriminator to measure oscillator phase noise. The single sideband phase noise of a free running loop oscillator incorporating the first SLC was measured as -133 dBc/Hz at an offset frequency of 1 kHz, and was limited by the SLC Q-factor and the amplifier flicker phase noise. By using specially designed feedback electronics the oscillator phase noise was reduced to -156 dBc/Hz and -162 dBc/Hz at 1 and 10 kHz offset, respectively. This measurement was shown to be limited by the electronic flicker noise imposed by the phase detector in the feedback electronics, To our knowledge the phase noise and resonator Q-factor of 6×10⁷ represent the best results ever measured at liquid nitrogen temperatures or above     

Hg+ trapped ion standard with the superconducting cavitymaser oscillator

The frequency stability of an atomic standard based on ¹⁹⁹ Hg⁺ ions confined in a hybrid RF/DC linear trap is described. The 40.5-GHz clock transition has been measured to be 17 mHz wide, representing a quality factor greater than 2×10¹². A 160-mHz line is used to steer the output of a 5-MHz crystal oscillator to obtain a stability of 2×10^-15 for 24000-s averaging times. In a separate measurement, a 37-mHz line is used to steer the output of the superconducting cavity maser oscillator to reach 1×10^-15 stability at 10000 s     

A new low-field determination of the proton gyromagnetic ratio inwater

The proton gyromagnetic ratio in water has been measured by the low field method using atomic magnetic resonance in ⁴He, a multicurrent solenoid and an induction method for the dimensional measurement of the solenoid. The result for air and vacuum environment is γ'_p (low, air)=2.67515451×10⁸ s^-1 T^-1 (0.18×10^-6), γ'_p (low, vacuum)=2.67515418×10⁸ s^-1 T^-1 (0.18×10^-6), based on the adopted values K_J-90=483597.9 GHz/V, R_K-90=25812.807 Ω, and measured values γ(⁴ He)/γ'_p=658.200556, γ(⁴He) (air)=1760.78819×10⁸ s^-1 T^-1 (0.18×10^-6), K_J-90, R_K-90     

CO2/OsO4 lasers as frequency standards in the29 THz range

The CO₂ lasers, frequency stabilized on OsO₄ transitions around 29 THz, are successfully used as secondary references for visible frequency synthesis and also for high-accuracy spectroscopy in the infrared domain. The BNM-LPTF CO₂/OsO₄ frequency standards exhibit high metrological performances: a long term reproducibility of ±10 Hz (1σ=2×10^-13) and a stability σ_y=6.6×10^-14/√τ with a Flicker plateau of 4×10^-15 (Δν/ν=0.1) for 300 s to 10³ s averaging times. These results and a preliminary study of the main effects which can induce frequency shifts are reported     

A new small nano-Kelvin resolution thermometer for low-temperatureexperiments

A small, high-resolution paramagnetic susceptibility thermometer was developed using a GdCl₃ paramagnetic salt. The device uses a superconducting quantum interference device (SQUID) magnetometer to determine the temperature dependent magnetization of the salt in a magnetic field. The magnetic field is provided by a pair of small samarium cobalt permanent magnet disks situated inside the thermometer housing. This eliminates the need for a heavy, charging solenoid used in a conventional SQUID-based magnetic thermometer system. This thermometer can resolve approximately 10^-9 K near the liquid-gas critical point of ³He (~3.31 K). The drift rate of the thermometer was measured to be <2×10^-13 K/s. This light weight thermometer (~7 g) is a candidate for use in future low-temperature Space Shuttle and International Space Station experiments     

Experimental determination of the gyromagnetic ratio of thehelium-4 atom in terms of that of the helium-3 nucleus

The ratio R=γ_4He(2³S₁)/γ_3He (1¹S₀) has been measured using gaseous samples in low magnetic field. The result, R=864.02276±3×10 ^-8, leads to a value of γ_4He=1760.78798(3×10^-7)×10⁸ ×rad×s^-1×T^-1     

短稳标准高Q值超导腔的研究

针对频率标准用超导腔的设计,通过理论分析及编程计算得到了影响微波腔指标的参数,并对不同温度下微波腔的品质因数（Q值）进行计算得到了温度变化曲线,通过此曲线可以确定达到指标所需要的温度。所设计的微波腔参数为：工作模式为TM₀₁₀模式,直径D为60mm,高度l为50mm,频率为4.4GHz,Q值在液氦温度4.2K时达到3.9×10⁷,在减压降温到2K时达到1.9×10⁹,实验结果与计算结果吻合。     

超导稳频振荡器的研究

基于理论分析和计算机仿真,得到了超导稳频振荡器的设计方案,主要包括高Q超导腔、低温环境及锁相环电路等组件的设计。通过实验验证,超导腔的Q值达到2×10⁹,低温环境温度达到1.8 K,温度的稳定度优于0.001K。根据实验结果优化设计后进行系统联调,得到了初步实验结果,超导稳频振荡器的1s频率稳定度达到10^-13量级     

Temporal measurement of plasma density variations above asemiconductor bridge (SCB)

The plasma density variations above a semiconductor bridge (SCB) device employing a capacitor discharge firing set have been measured in vacuum (⩽10^-5 torr). A novel diagnostic technique using a microwave resonator probe was used to measure the resultant plasma density variations as a function of time. This method is superior to Langmuir probes in this application because Langmuir probe measurements are affected by sheath effects, small bridge area, and unknown fraction of multiple ions. Our experimental results indicate that the plasma density is observed to increase to a peak value of 5.5× 10¹¹ cm^-3 and decay exponentially with time, which is consistent with diffusion dominating the plasma transport. The time needed for reaching the peak plasma density is about 1.6 μs, which is the duration of the late time discharge of an SCB device     

Frequency of a methane-stabilized helium-neon laser

A phase-locked laser frequency chain was used to measure the absolute frequency of a HeNe/CH₄ laser relative to the primary Cs standard, with measurement uncertainty less than ±1 part in 10¹². The frequency depends on laser parameters; a spread of 8.3×10^-11 was observed. This was attributed to the variation of Lamb dip asymmetry resulting from the gas-lens effect and the accompanying diffraction loss variation near resonance. Means of improving laser frequency reproducibility by reducing cavity diffraction loss variation were studied experimentally. The frequency obtained with a cavity exhibiting the smallest Lamb dip asymmetry was found to be 88 376 181 599.07±0.07 kHz     

Reducing local oscillator phase noise limitations on the frequencystability of passive frequency standards: tests of a new concept

We report on the experimental test of a new concept for reducing the limitation on short-term frequency stability of passive frequency standards due to local oscillator phase noise. This concept is general and can be applied to many passive frequency standards. Systems that use sinewave modulation to interrogate a stable resonance are limited in short-term frequency stability by phase noise at the second harmonic of the modulation, f_m. This effect limits the fractional frequency stability to approximately σ_v(τ7)=0.9(f _m/ν₀) (S_φ(2f_m))^1/2τ^-1/2, where ν₀ is the carrier frequency and S_φ(2f _m) is the phase noise at twice the modulation frequency. (Contributions from higher even harmonics of the modulation generally can be neglected). This new concept uses notch filters at ±2f_m from the carrier to reduce this effect. Tests on a modified passive rubidium standard demonstrate an improvement of approximately 18 in σ_y(τ). The dual notch filters proved to be feasible and were obtained commercially. Measurements suggest that ultimate performances of less than 2×10^-14τ^-1/2 are possible if the atomic resonance has sufficient quality     

Determination of the tesla-to-ampere ratio for the KRISS/VNIIMγ'P-experiment

Tesla-to-ampere ratio giving the largest error in the γ'_P-low-field-experiment has been determined using a modified noncontacting method. The total uncertainty of 0.164×10 ^-6 has been attained. The constant of a solenoid and the γ'_P-value have been corrected for magnetic susceptibility of air. The result is γ'_P=2.675 154 18×10⁸ s^-1 T^-1 (Tesla BI-90) with the total uncertainty of 0.18×10^-6     

Precision measurement of the atomic mass of 6Li using aPenning ion trap mass spectrometer

We have used a cryogenic (4 K) Penning ion trap mass spectrometer to measure the mass ratios of ⁶Li⁺/¹²C ²⁺, ⁶Li⁺/D₃⁺, and D₂⁺/He⁺. We developed techniques to create ions outside of the cryogenic trap environment and to transport them into the trap where a small number (1-10) were confined. The ions' frequencies of oscillation were measured using a high-Q tuned circuit to detect image currents induced in the trap electrodes. The measurements involving ⁶Li⁺ result in a value for the atomic mass of ⁶Li of 6.015 122 795(16) u, with a fractional uncertainty of ±2.7×10^-9 representing a factor of 30 improvement over the published, tabulated value. A measurement of the D₂⁺/He⁺ mass ratio has an uncertainty of ±1.1×10^-9 and is within 0.6×10^-9 of the tabulated value, thus demonstrating that our techniques are reliable     

High-Q thermoelectric-stabilized sapphire microwave resonators forlow-noise applications

Two low-noise high-Q sapphire-loaded cavity (SLC) resonators, with unloaded Q values of 2×10⁵ and very low densities of spurious modes, have been constructed. They were designed to operate at 0°C with a center frequency of 10.000000 GHz. The cavity was cooled with a thermoelectric (TE) Peltier element, and in practice achieved the required center frequency near 1°C. The resonator has a measured frequency-temperature coefficient of -0.7 MHz/K, and a Q factor which is measured to be proportional to T^-2.5. An upper limit to the SLC residual phase noise of ℒ (100) Hz=-147 dBc/Hz, ℒ (1 kHz)=-155 dBc/Hz, and ℒ (10) kHz=-160 dBc/Hz has been measured. Also, we have created a free-running loop oscillator based on one of the SLC resonators, and measured a phase noise of ℒ(f)~-10-30log [f] dBc/Hz between f=10 /Hz and 25 kHz, using the other as a discriminator     

Ultrastable optical frequency reference at 1.064 μm using a C2HD molecular overtone transition

Saturated molecular overtone transitions in the visible and near infrared can be detected with record-high sensitivities using our cavity-enhanced frequency modulation technique. We have stabilized a Nd:YAG laser onto the P(5) line in (ν₂+3ν₃) overtone band of C₂HD at 1.064 μm and established its absolute frequency. Excellent signal-to-noise ratio produced an Allan variance of 3.4×10^-13 at 1 s averaging, improving to 1×10^-14 after 800 s. Selection of slow molecules with low power and gas pressure gave a linewidth 13 times below the room temperature transit time limit     

锁相环路对氢原子钟性能影响的实验分析

实验以上海天文台SOHM-4型氢原子钟脉泽信号和新研制的模拟-数字混合型锁相环路为基础,主要分析锁相环路参数对氢原子钟输出信号的短期频率稳定度和单边带相位噪声的影响。针对氢脉泽信号高Q值的特殊性,通过理论分析和实验验证寻求与其相匹配的最佳环路参数。实验结果表明,锁相环路的参数设置直接影响到氢原子钟输出信号的性能;在脉泽信号不变的情况下,改进后的锁相环路和主电子学系统可使氢原子钟的频率稳定度提高至1.7×10^-13/1s, 3.3×10^-14/10s, 9.1×10^-15/100s, 2.9×10^-15/1 000s, 1.4×10^-15/10000s,即较之原有的技术指标,在各取样时间范围内,频率稳定度的测试结果均提高了半个量级。     

The shear coefficient for quartz crystal of rectangular crosssection in Timoshenko's beam theory

In this paper, we derive the shear coefficient K for quartz crystal of rectangular cross section in Timoshenko's beam theory of three-dimensional (3-D) elasticity. The theoretical result gives K as a function of the transformed elastic stiffness constants C₂₂ ^', cˆ₄₄, C₆₆'. For an isotropic material it agrees completely with that derived by G.R. Cowper (1966). In addition, a value of K and its temperature coefficient versus cut angle is calculated so that K has a value of 0.796-0.867 and its temperature coefficient of the first order varies from -15.3×10 ^-6/°C to +13.2×10^-6/°C, when a Z-plate of quartz crystal is rotated with a cut angle &thetas; of 0-180° about the x axis. The values of K are then compared with those for isotropic materials obtained by other authors