Integrated physics package of a chip-scale atomic clock

The physics package of a chip-scale atomic clock （CSAC） has been successfully realized by integrating vertical cavity surface emitting laser （VCSEL）, neutral density （ND） filter, λ/4 wave plate, 87Rb vapor cell, photodiode （PD）, and magnetic coil into a cuboid metal package with a volume of about 2.8 cm3. In this physics package, the critical component, 87Rb vapor cell, is batch-fabricated based on MEMS technology and in-situ chemical reaction method. Pt heater and thermistors are integrated in the physics package. A PTFE pillar is used to support the optical elements in the physics package, in order to reduce the power dissipation. The optical absorption spectrum of 87Rb D1 line and the microwave frequency correction signal are successfully observed while connecting the package with the servo circuit system. Using the above mentioned packaging solution, a CSAC with short-term frequency stability of about 7 × 10^-10τ-1/2 has been successfully achieved, which demonstrates that this physics package would become one promising solution for the CSAC.     

Frequency Stability of Atomic Clocks Based on Coherent Population Trapping Resonance in ^85Rb

An atomic clock system based on coherent population trapping （CPT） resonance in 85Rb is reported, while most past works about the CPT clock are in ST Rb. A new modulation method （full-hyperfine-frequency-splitting modulation） is presented to reduce the effect of light shift to improve the frequency stability of the CPT clock in SSRb. The experimental results show that the short-term frequency stability of the CPT clock in SSRb is in the order of 10^-10/s and the long-term frequency stability can achieve 1.5 × 10^-11/80000s, which performs as well as 87 Rb in CPT resonance. This very good frequency stability performance associated with the low-cost and low-power properties of SSRb indicates that an atomic clock based on CPT in SSRb should be a promising candidate for making the chip scale atomic clock.     

芯片原子钟相干布居囚禁谱线特性研究

通过微型原子蒸汽室产生质量满足要求的相干布居囚禁(CPT)信号是实现芯片原子钟的关键之一.本实验通过对光源实施频率调制和对光场与⁸⁷Rb原子作用产生的信号作相敏解调获得高信噪比的CPT微分谱线, 利用CPT微分谱线研究了CPT信号随工作参数变化的规律以及信号质量对原子钟频率稳定度的影响, 所获研究结果与理论模型预期相符合, 实验结果为芯片原子钟推荐了最佳工作参数.实验所采用的方法利用芯片原子钟自身的资源就可以实施, 因此为芯片原子钟开展性能研究和实施工作参数优化提供了实用的手段.     

Atomic vapor cells for chip-scale atomic clocks with improved long-term frequency stability

A novel technique for microfabricating alkali atom vapor cells is described in which alkali atoms are evaporated into a micromachined cell cavity through a glass nozzle. A cell of interior volume 1 mm3, containing 87Rb and a buffer gas, was made in this way and integrated into an atomic clock based on coherent population trapping. A fractional frequency instability of 6 x 10(-12) at 1000 s of integration was measured. The long-term drift of the F=1, mF=0-->F=2, mF=0 hyperfine frequency of atoms in these cells is below 5 x 10(-11)/day.     

Dark resonances in 87Rb atomic vapors interacting with the field of copropagated linearly polarized waves of various frequencies

The results of theoretical and numerical analysis of resonances of coherent population trapping in ⁸⁷Rb atomic vapors, obtained using copropagated linearly polarized waves, are presented. Various schemes for exciting dark resonance are compared with a view to obtaining a new-generation small-size quantum frequency standard.     

全光学冷却与囚禁133Cs原子玻色-爱因斯坦凝聚的可能性

综述了近年来有关蒸发冷却¹³³Cs原子样品的实验进展,分析了磁囚禁¹³³Cs原子玻色爱因斯坦凝聚(BEC)的困难,并在此基础上提出了一个全光型冷却与囚禁¹³³Cs原子BEC的新方案.该方案主要由一个来自半导体激光(λ=0852μm)的倒金字塔形中空光束重力光学囚禁(pyramidal-hollow-beam gravito-optical trap,缩写为PHB GOT)和一个来自Ar⁺激光(λ=05013μm)的圆锥形中空光束重力光学囚禁(conical-hollow-beam gravito-optical trap,缩写为CHB GOT)组成.在PHB GOT中,冷原子经历了一个有效的中空光束感应的Sisyphus冷却(也即强度梯度冷却)和抽运光感应的几何冷却,原子温度将被从磁光囚禁(MOT)温度(约为60μK)冷却至几个光子反冲极限(约为2μK);而在Ar⁺中空光束囚禁(CHB GOT)中,冷原子将被Raman冷却或速度选择相干粒子数囚禁技术(velocity-selection coherent population trap,缩写为VSCPT)进一步冷却至光子反冲极限以下,并被激光频率高于原子共振频率的(也即蓝失谐的)covering光束压缩.我们就PHB冷却的动力学过程进行了Monte-Carlo模拟,并计算了Ar⁺中空光束囚禁¹³³Cs原子的光学势.研究结果表明,实现一个全光学冷却与囚禁的¹³³Cs原子BEC是可能的 关键词： 倒金字塔型中空光束重力光学囚禁 强度梯度冷却 氩离子中空光束囚禁 喇曼冷却 铯原子BEC     

High-contrast coherent population trapping resonances using four-wave mixing in 87Rb

We demonstrate very high-contrast coherent population trapping(1) (CPT) resonances by using four-wave mixing in (87)Rb atoms. In the experiment, we take advantage of the spectral overlap between F=2-->F(?) and F=3-->F(?) optical resonances on the D1 line of (87)Rb and (85)Rb atoms, respectively, to eliminate the DC-light background from the CPT resonance signal. We observe a CPT resonance with a contrast in the range of 90%, compared with a few percent achieved by alternative methods.     

Minimization of the temperature coefficient of resonance frequency shift in the coherent population trapping clock

We studied the relationship between the frequency shift of coherent population trapping resonance and the cell temperature of (85)Rb. Results show that the temperature coefficient of the frequency shift can be reduced by buffer gas pressure adjustment and light shift optimization. When the contribution of buffer gas collision to temperature coefficient of frequency shift is less than 0.3 Hz/K, the contribution of light shift to the temperature coefficient of frequency shift becomes obvious. Under this cancelling effect, we can reduce the rate of total frequency shift to near zero.     

Spectral narrowing of coherent population trapping resonance in laser-cooled and room-temperature atomic gas

We have investigated coherent population trapping (CPT) in laser-cooled as well as room-temperature (with and without buffer gas) rubidium atoms. The characteristic broad signal profile emerging from the two-photon Raman resonance for room-temperature atomic vapour is consistent with the theoretical calculation incorporating associated thermal averaging. The spectral width of the dark resonance obtained with cold atoms is found to be broadened, compared to room-temperature vapour cell, due to the feeble role played by thermal averaging, although the cold atomic sample significantly overcomes the limitation of the transit time broadening. An alternative way to improve transit time is to use a buffer gas, with which we demonstrate that the coherent population trapping signal width is reduced to < 540 Hz.     

Narrow structure in the coherent population trapping resonance in rubidium

An investigation is reported of coherent resonance in the degenerate two-level system of the (Fg = 2 --> Fe = 1) transition of the 87Rb D1 line by means of a Hanle effect configuration. In a coherent population trapping experiment, a very narrow (approximately 1-kHz) resonance superimposed upon a broader resonance (approximately 100 kHz) was observed. The dependence of the width and the amplitude of the coherent resonance on the laser power density, on additional constant magnetic fields, on the laser frequency position along the fluorescence profile, and on Rb cells with different dimensions was investigated.     

Atomic Coherent State, Entangled State and Phase Operator for Studying Interference Between Two Bose-Einstein Condensates

For studying the interference between two Bose-Einstein condensates we introduce the atomic coherentstate （ACS） in the Schwinger bosonic realization along with the phase operator to directly calculate the interference pattern with steady relative phase cos Ф. Eigenstates of the density operator of condensates are classified as ACS is also demonstrated. The entangled state representation is used in some calculations.     

Alternative Scheme for Generation of Atomic SchrSdinger Cat States and Entangled Coherent States in an Optical Cavity

We propose an alternative scheme for generation of atomic Schrodinger cat states in an optical cavity. In the scheme the atoms are always populated in the two ground states and the cavity remains in the vacuum state. Therefore, the scheme is insensitive to the atomic spontaneous emission and cavity decay. The scheme may be generalized to the deterministic generation of entangled coherent states for two atomic samples. In contrast with the previously proposed schemes of [Commun. Theor. Phys. 40 （2003） 103 and Chin. our scheme is greatly shortened and thus the deeoherence can Phys. B 18 （2009） 1045], the required interaction time in be effectively suppressed.     

function for the squeezed atomic coherent state in entangled state representation and some of its applications

Based on the Einstein, Podolsky, and Rosen (EPR) entangled state representation, this paper introduces the wave function for the squeezed atomic coherent state (SACS), which turns out to be just proportional to a single-variable ordinary Hermite polynomial of order 2j. As important applications of the wave function, the Wigner function of the SACS and its marginal distribution are obtained and the eigenproblems of some Hamiltonians for the generalized angular momentum system are solved.     

Review of chip-scale atomic clocks based on coherent population trapping

Research on chip-scale atomic clocks （CSACs） based on coherent population trapping （CPT） is reviewed. The back- ground and the inspiration for the research are described, including the important schemes proposed to improve the CPT signal quality, the selection of atoms and buffer gases, and the development of micro-cell fabrication. With regard to the re- liability, stability, and service life of the CSACs, the research regarding the sensitivity of the CPT resonance to temperature and laser power changes is also reviewed, as well as the CPT resonance＇s collision and light of frequency shifts. The first generation CSACs have already been developed but its characters are still far from our expectations. Our conclusion is that miniaturization and power reduction are the most important aspects calling for further research.     

三能级原子与少周期脉冲串作用中的相干布居捕获

研究了少周期脉冲串作用下三能级原子中的布居转移和相干布居捕获现象.在非旋波近似的情况下求解了密度矩阵方程.研究结果表明在等时间间隔的锁相脉冲作用下,系统能级的布居逐步转移并积累,系统基态相干也逐步积累.在满足脉冲重复频率为基态能级频差的整数分之一倍时,三能级系统和频率梳中两梳齿频率成分作用形成相干布居捕获现象,原子暗态布居值达到最大,介质对脉冲透明.在适当选取少周期脉冲参量的情况下,在0.5个ns的时间内三能级系统相干性演化到最大后到达稳态,相干布居捕获发生.与脉宽为100个fs的多周期脉冲相比,少周期脉冲串在介质中建立相干布居捕获的时间缩短两个数量级.由于频率梳中与三能级系统发生作用的梳频成份有相同的频移,相干布居捕获的条件双光子共振仍然满足.因而,当两基态能级频率差较大时,如果选取少周期脉冲载波频率为系统能级1至2和1至3的传输频率之和的一半ω=(ω₁+ω₂)/2,室温下原子热运动的引起的多普勒频移并不会破坏相干布居捕获.     

Experiments on trapping ytterbium atoms in optical lattices

Experiments on trapping ytterbium atoms in various optical lattices are presented. After the two-stage cooling, first in a blue magneto-optical trap and then in a green magneto-optical trap, the ultracold 171 Yb atoms are successfully loaded into one-, two-, and three-dimensional optical lattices operating at the Stark-free wavelength, respectively. The temperature, number, and lifetime of cold 171 Yb atoms in one-dimensional lattice are measured. After optimization, the one-dimensional lattice with cold 171Yb atoms is used for developing an ytterbium optical clock.     

Coherent population trapping resonances in thermal (85)Rb vapor: D(1) versus D(2) line excitation

We have compared coherent population trapping (CPT) resonances, both experimentally and theoretically, for excitation of the D(1) and D(2) transitions of thermal (85)Rb vapor. Excitation of the D(1) line results in greater resonance contrast than excitation of the D(2) line and in a reduction in the resonance width, in agreement with theoretical expectations. These results translate into a nearly tenfold improvement in performance for the application of CPT resonances to a frequency standard or a sensitive magnetometer when the D(1) line, rather than the D(2) line, is used.     

Collective Excitations and Nonlinear Dynamics of 1D BEC with Two- and Three-body Interactions in Anharmonic Traps

The collective excitations of low-dimensional Bose-Einstein condensates with two- and three-body interactions in anharmonic potentials are investigated. Using the standard variational approach, the governing equations of motions for the low-energy excitations are obtained by solving time-dependent Gross-Pitaevskii-Ginzburg equation, and the excitation spectrums are calculated in small amplitude limit. The frequency shift and nonlinear mode coupling induced by the anharmonic distortion （adding cubic, quartic, or quintic terra to a harmonic trap） are studied.     

Coherent Dicke Narrowing of Absorption Spectra,Collapse and Revival: Second-Derivative Processing

Journal of Experimental and Theoretical Physics - The coherent Dicke narrowing (CDN) of the absorption spectrum in an Rb, Cs, K, or Na atomic vapor column of thickness L = (2n + 1)λ/2 (when n...     

Nondegenerate four-wave mixing in a double-Lambda system under the influence of coherent population trapping

Nondegenerate four-wave mixing (NDFWM) in a double-L system of Rb atomic vapor was achieved for collinear pump fields. By comparison of different pump-probe configurations, direct experimental evidence of influence of coherent population trapping on the output power of the NDFWM signal was established. A maximal efficiency for generating the NDFWM signal exists for a moderate pump power in this double-L system.