Realization of a Rubidium Atomic Frequency Standard With Short-Term Stability in 10−14τ−1/2 Level

Lamp-pumped rubidium atomic frequency standard (RAFS) is one of the most commonly utilized atomic frequency standards. Over the past few decades, the RAFS’s frequency stability performance has improved rapidly, and the best one has been in the <inline-formula> <tex-math notation="LaTeX">$10^{-13} \tau ^{-1/2}$ </tex-math></inline-formula> level. In this article, we demonstrate an RAFS with stability in the <inline-formula> <tex-math notation="LaTeX">$10^{-14} \tau ^{-1/2}$ </tex-math></inline-formula> level for the first time. In design of the physics package (PP), a rubidium spectral lamp with Xe as the starter gas was used as the pumping light source. The light was filtered by using optical and isotope double-filtering technique. A large slotted tube microwave cavity and a rubidium absorption cell with a diameter of 40 mm were utilized to enhance the atomic discrimination signal. A sealed box was designed for the PP to isolate it from the barometric environment. A low phase noise 6.835-GHz microwave was employed to interrogate the rubidium clock transition. Based on the quantitative analysis of the signal-to-noise ratio (SNR) of the atomic discrimination signal and the phase noise of the interrogation microwave, the stability of the RAFS was predicted to be 7.6 <inline-formula> <tex-math notation="LaTeX">$\times \,\,10^{-14} \tau ^{-1/2}$ </tex-math></inline-formula>. The short-term stability of the RAFS was measured by using a hydrogen maser and an optical microwave generator (OMG) as references, and the results are 9.0 <inline-formula> <tex-math notation="LaTeX">$\times \,\,10^{-14} \tau ^{-1/2}$ </tex-math></inline-formula> (1–100 s) and 9.1 <inline-formula> <tex-math notation="LaTeX">$\times \,\,10^{-14} \tau ^{-1/2}$ </tex-math></inline-formula> (1–100 s), respectively. The measured results are in agreement with the predicted one.


Realization of a Rubidium Atomic Frequency
Standard With Short-Term Stability in 10 −14 τ −1/2 Level

I. INTRODUCTION
A S ONE of the most widely used atomic frequency standards, the lamp-pumped vapor cell rubidium atomic frequency standard (RAFS) was first developed in the 1960s [1].In the early 1980s, nearly two decades later, it was commonly recognized that the RAFS had reached its limit in frequency stability performance, the short-term stability may be not better than 1 × 10 −11 τ −1/2 , and the longterm stability, not better than 1 × 10 −13 [2].The situation changed dramatically in the 1990s when the RAFS for GPS block IIR satellites was produced, which is of short-term stability 3 × 10 −12 τ −1/2 and long-term stability in 10 −14 level [3].Furthermore, in the later 2000s, the RAFS for GPS IIM and IIF satellites was reported, its short-term stability reaches 1 × 10 −12 τ −1/2 , and long-term stability is in 10 −15 level [4].
Recently, a new prototype of RAFS was designed in our laboratory.Design work focuses on enhancing the signal-tonoise ratio (SNR) of the atomic discrimination signal, reducing the phase noise of the interrogation microwave, and depressing the environmental effect of the atomic transition.A large size slotted tube microwave cavity and a rubidium absorption cell with 40 mm diameter were designed and utilized to enhance the atomic discrimination signal.Optical and isotope double-filtering technique was used for pumping light to reduce the shot noise of the signal.A low phase noise frequency synthesizer was developed to generate the 6.835-GHz interrogate microwave.To depress the environmental effect, a sealed box was designed to isolate the physics package (PP) from barometric environment.Tests showed that the RAFS is of a short-term stability in 10 −14 τ −1/2 level.In this article, design details and main characteristics of the RAFS are presented and analyzed, and the possible applications of the RAFS are discussed.

II. STRUCTURE AND FREQUENCY STABILITY
OF THE RAFS The electronic structure of the RAFS is shown in Fig. 1.It operates as a frequency-locked loop, utilizing the PP as an atomic frequency discriminator.The reference frequency of the PP is 6.835 GHz, corresponding to the frequency of the transition between hyperfine levels F = 2 and m F = 0 and F = 1 and m F = 0 of the ground state 5S 1/2 of the 87 Rb atom.The transition is also called clock transition.Normally, a 10-MHz voltage-controlled crystal oscillator (VCXO) is used as a local oscillator (LO).The synthesizer converts the 10-MHz signal of the VCXO to a frequency-modulated 6.835-GHz microwave with modulation frequency f M .The microwave is applied to the PP to interrogate the rubidium clock transition, creating the discrimination signal.After being amplified by the preamplifier (PreAMP), the discrimination signal goes to the phase sensitive detector (PSD) for demodulation, then enters the integrator for filtering and dc amplifying, and finally is transformed into the correction voltage signal to control the frequency of the VCXO, realizing locking of the whole loop.
The SNR of the discrimination signal strongly affects frequency stability which is the key performance of the RAFS.Since the discrimination signal is stimulated by the interrogation microwave provided by the synthesizer, the frequency stability is also influenced by the noise of the microwave.Research showed that the phase noise of the interrogation microwave at 2n f M will deteriorate the frequency stability through the intermodulation effect of the locking loop [10].In addition, the frequency stability is affected by environmental effects of rubidium atoms.The effects originate from the sensitivity of the atomic transition frequency to fluctuations of various environmental parameters, such as temperature, magnetic field, microwave power, light intensity, barometric pressure, and so on.Taking all the three factors into account, Allan deviation frequency stability of an RAFS can be written as [6] where τ is the averaging time and As implied by ( 1)-( 4), three fractional stabilities contribute to the frequency stability of the RAFS.The first one σ SNR (τ ) is SNR limited stability [11], determined by the noise power spectral density S N and the discrimination slope K D that measures the signal intensity, where S N = 2eI 0 with e being the electron charge and I 0 , the shot noise current [11].The second one σ PN (τ ) is the phase noise limited stability, determined by S ϕ (2n f M ), the single sideband power spectral density of the phase noise of the interrogation microwave at 2n f M (C 2n is a constant related to the modulation frequency f M and the carrier frequency been modulated).In the calculation of σ PN (τ ) by using (3), one usually considers only the contribution of the n = 1 term, since the contributions of high-order terms are very small [10].The third one σ EE (τ ) is environmental effect limited stability.In (4), υ/ P i and σ Pi (τ ) represent the frequency shift coefficient and the stability of the ith environmental parameter P i , respectively.It should be noticed that σ SNR (τ ) and σ PN (τ ) determine the short-term stability and the limit of long-term stability of the RAFS, and σ EE (τ ) determines principally the long-term stability.Formulas (1)-( 4) also imply that, for the purpose of improving the stability performance of the RAFS, one should focus on enhancing the SNR of the discrimination signal, reducing the phase noise of interrogation microwave, and depressing the environmental effect.

III. DESIGN OF THE RAFS A. Physics Package
The atomic discrimination signal originates from a process of optical-microwave double resonance of rubidium atoms that takes place in the PP.Rubidium atoms are first optically pumped by using a rubidium spectral lamp to create population reversion between two clock transition energy levels.Interrogation microwave is then applied to rubidium atoms to stimulate the clock transition.The SNR of the discrimination signal is determined by the characteristics of the PP.
The PP used is schematically shown in Fig. 2. A 87 Rb spectral lamp with Xe as starter gas was utilized as the source of pumping light.As shown by Hao et al. [12], this kind of spectral lump could output intense rubidium D 1 and D 2 line lights with narrow linewidth.After being collimated by the lens, the light is filtered by the 85 Rb filter cell to eliminate the a components in D 1 and D 2 lines and then filtered by a bandpass optical filter with a center wavelength of 786 nm and bandwidth of 22 nm to eliminate the light emitted by starter gas.This choice of light source and the double-filtering scheme enables to enhance pumping efficiency and meanwhile to reduce the noise of atomic signal.The filtered light then goes to the absorption cell inside a slotted tube microwave cavity composed of a slotted tube, a cylinder, an entrance cap, and an end cap.The absorption cell, with a diameter of 40 mm, contains 87 Rb vapor and mixed buffer gases of Ar and N 2 .Both the filter cell and the absorption cell were heated and temperature-controlled at appropriate temperatures to create stable and useful rubidium vapors.A modulated 6.835-GHz microwave is electrically coupled into the cavity to interrogate the clock transition of rubidium vapor atoms in the absorption cell.The photocell was used to detect the intensity of the transmitted light through the absorption cell, which varies when the atomic clock transition takes place.A Helmholtz coil produces a uniform C field to define quantization axis for atomic transition.Three layers of magnetic shield were employed to reduce the disturbance of environmental magnetic field, two of which were installed on the PP.
The slotted tube cavity is a nonstandard microwave cavity we developed nearly two decades ago [13].The crucial component of the cavity is a slotted tube, whose structural parameters play main role in determining the resonance frequency and mode of the cavity [14].An obvious advantage of the cavity over the commonly used standard TE 111 and TE 011 cavities is that its size could be flexibly designed.This property enables to use large size absorption cell to enhance the atomic signal SNR.Actually, a series of cavities with different sizes have been developed in our laboratory [5], [6], [7], [8], [9].In this work, we used the cavity with an inner diameter of 40 mm, the largest one we have designed so far.The structure of the slotted tube is shown in Fig. 3. Fig. 3 also shows the structure of the entrance cap of the cavity, which is needed for a large size slotted tube cavity.The central grid structure of the cap is used to eliminate RF disturbance from outside to resonance mode of the cavity and let pumping light pass through.The entrance cap also acts as an optical aperture to collimate the pumping light into a light beam with a diameter of 32 mm, slightly smaller than that of the absorption cell.For high-performance RAFS design, the microwave distribution inside the cavity is extremely important since the clock transition can be excited only by the magnetic microwave field parallel to the quantization axis.The parallelism property is described quantitatively by ξ , the field orientation factor defined as [15] where V defines the volume of interaction region of atoms and microwave, H z is the magnetic microwave field parallel to quantization axis, and H is the total field.ξ could be obtained by measuring the Zeeman transition spectrum of 87 Rb vapor atoms.The experimentally measured spectrum for the used PP is shown in Fig. 4. Based on the spectrum, ξ could be simply calculated through the relation [16] where I 3(υ) , I 4(υ) , and I 5(υ) are the transition intensity distributions of the central three transitions.The finally obtained ξ for the used cavity is 0.82.We believe that it is much higher than those of the traditional standard cavities.The SNR limited stability σ SNR (τ ) of the PP was estimated.First, the light path and the working temperatures of the absorption cell, the filter cell, and the lamp bulb were optimized for maximum discrimination slope K d .The optimal temperatures were found to be 68 • C, 93 • C, and 109 • C, respectively.In this condition, the shot noise current I 0 , i.e., background current of the photocell, was then measured to be 211 µA, and corresponding noise power spectral density S N was calculated to be 8.2 pA/Hz 1/2 .Fig. 5 shows the measured frequency discrimination curve of the RAFS.K d , the slope of the central part of the curve, was calculated to be 18.0 nA/Hz.By using (2), σ SNR (τ ) was estimated to be 4.7 × 10 −14 τ −1/2 , implying that the PP enables to realize a stability in medium 10 −14 τ −1/2 level.

B. Frequency Synthesizer
In design of the electronics of the RAFS, main attention was paid to reduce the phase noise and stabilizing the power of the interrogation microwave produced by the synthesizer.
The structure of the synthesizer is schematically shown in Fig. 6.The interrogation microwave originates from a 10-MHz LO with a stability of 1 × 10 −12 at 1 s.The 100-MHz frequency of the oven-controlled crystal oscillator (OCXO) with near-end phase noise of −153 dBc/Hz at 2 f M (here f M = 136 Hz) is phase-locked to that of the LO through phase detector PD1.Due to the 30-Hz bandwidth of the locking loop, the locked 100-MHz signal is of stability of the LO and the near-end phase noise of the OCXO.For ensuring low phase noise and high spectral purity of the 6.835-GHz microwave, two dielectric resonator oscillators (DROs) with low far-end phase noise are employed, of which DRO1 resonates at 6.80 GHz and DRO2 resonates at 6.835 GHz.The 6.80-GHz frequency of the DRO1 is phase-locked directly to the 100 MHz through PD2.In order to lock the 6.   signal is a 136-Hz square wave.The modulated 6.835-GHz microwave is coupled to the PP to interrogate the clock transition of the rubidium atoms.
The interrogation microwave obtained this way is of high spectral purity.As shown in Fig. 7, the output microwave contains only the 6.835-GHz component, and no obvious harmonic or spurious components are observed in a 500-MHz range nearby.In this case, automatic-level control (ALC) of the microwave power will be more efficient since there is less influence of harmonic or spurious components.The stabilization of the microwave power helps to reduce the microwave power shift of the clock transition.
The phase noise of the 6.835-GHz microwave was measured, and the result is shown in Fig. 8.It can be found from Fig. 8 that the phase noise of the microwave at 2 f M (272 Hz) is about −110dBc/Hz.Based on this result and by using (4), the phase noise limited stability σ PN (τ ) of the RAFS is estimated to be 6.0 × 10 −14 τ −1/2 .

C. Environmental Effect
As a common sense, for an ordinary RAFS, the influence of environmental effect on short-term stability can be ignored.When an RAFS with 10 −14 τ −1/2 level stability is expected to be realized, however, the influence must be considered.
The first observed unacceptable influence comes from the barometric pressure effect.In our earlier frequency stability measurements of the designed RAFS, the 100-s stability Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.FREQUENCY SHIFT COEFFICIENT OF THE RAFS PHYSICAL PARAMETERS was found to be around 2.5 × 10 −14 and cannot reach the 10 −15 level.To make it clear if this is caused by barometric effect, we put the RAFS into a large sealed chamber and measured its frequency shift coefficient of the barometric pressure by changing the air pressure in the chamber and recording the output frequency of the RAFS.The coefficient was experimentally measured to be 7 × 10 −15 /Pa.The RAFS was then taken back to the open air environment and the barometric pressure fluctuation was monitored.The barometric pressure was recorded once every 10 s in a period of 50 000 s. Based on the fluctuation data and the obtained frequency shift coefficient, the influence of the barometric effect to stability of the RAFS was calculated by using (4), and the result is shown as the upper line in Fig. 9.The influence to 100-s stability is 2.2 × 10 −14 , in agreement with the measured result.To reduce the barometric effect, a sealed box was designed and used to envelop the PP to isolate it from barometric environment.The resulted influence of the barometric effect is shown as the lower line in Fig. 9.It can be seen that the influence is reduced by nearly one order of magnitude.The barometric effect originates essentially from the buffer gas pressure effect inside the absorption cell [17].Barometric pressure variation deforms slightly the cell shape, thus changes the buffer gas pressure inside the cell and finally causes a frequency shift of the rubidium atomic transition.
The effects of absorption cell temperature, pumping light intensity, 6.835-GHz microwave power, and magnetic C field were also examined in similar way.The frequency shift coefficients of the five parameters are listed in Table I, and the contributions of their fluctuations to the stability of the RAFS with averaging time 10-400 s are shown in Fig. 10.
As can be seen from Fig. 10, all the environmental effects have influences on the stability of the RAFS to some degree.The total influence has been controlled to a 10 −15 level with τ ≤ 100 s, allowing realizing a 10 −14 τ −1/2 level short-term stability.When τ > 100 s, however, the influence increases  with τ considerably, which means that the environmental effect will influence the medium-term stability of the RAFS.The influence comes mainly from the temperature shift and the barometric shift, as can be seen from Fig. 10.

IV. FREQUENCY STABILITY TEST RESULTS
Two references were employed for the frequency stability test of the RAFS.One is a high-performance active hydrogen maser (H-maser) produced by KVARZ (CH1-95), and the other, an ultrastable laser based optical microwave generator (OMG) developed by Qunfeng Chen's group [18].The test scheme is displayed in Fig. 11.
It should be noticed that, if the tested RAFS and the reference have the same magnitude order of short-term frequency stability, the test result does not reflect the real performance of the RAFS.In this case, the contribution of the reference to the test result should be deducted, and the real stability of the RAFS is then where σ test (τ ) is the test stability of the RAFS and σ R (τ ) is the stability of the used reference, which is assumed to be known.
The stability result of the RAFS by using the H-maser as the reference is shown in Fig. 12.The result was obtained based on a 5000-s-long frequency data with an averaging time of 1 s.To avoid the influence of frequency drift, the stability performance is given in drift removed Allan deviation.From the circle dot data, the test stability of the RAFS was estimated  to be 1.0 × 10 −13 τ −1/2 with averaging time τ up to 100 s.The stability goes worse when τ is larger than 100 s; we believe this is caused by the environmental effect (see Fig. 10).By using the test stability data with τ no larger than 100 s and stability data of the H-maser (square dots in Fig. 12), real stability data with τ up to 100 s was obtained (diamond dots in Fig. 12).By fitting the diamond dot data, the real stability of the RAFS was finally obtained to be 9.0 × 10 −14 τ −1/2 with τ up to 100 s (dashed line in Fig. 12).
Stability result by using the OMG as the reference is shown in Fig. 13.Considering excellent short-term stability but poor medium-term stability of the reference, we give here only the short-term stability result with τ ≤ 100 s.As shown in Fig. 13, the test stability of the RAFS is about 9.7 × 10 −14 τ −1/2 , and real stability is calculated to be 9.1 × 10 −14 τ −1/2 up to 100-s averaging time and strongly supports the result obtained with H-maser.

V. CONCLUSION
A lamp-pumped RAFS with short-term stability in 10 −14 τ −1/2 level has been realized.In design of the RAFS, the influences of the SNR of atomic discrimination signal and the phase noise of the interrogation microwave to stability of the RAFS were controlled to 4.7 × 10 −14 τ −1/2 and 6.0 × 10 −14 τ −1/2 , respectively, and the influence of the environmental effect was controlled to 10 −15 τ −1/2 level.Typical short-term stability of the RAFS reached 9.0 × 10 −14 τ −1/2 (1-100 s), and symbolizing the vapor cell atomic frequency standard, including the traditional lamp-pumped RAFS and the new generation laser-pumped RAFS, has unprecedentedly achieved a stability in 10 −14 τ −1/2 level.To the best of our knowledge, the previous best result is 1.2 × 10 −13 τ −1/2 , which is realized recently on a pulsed laserpumped RAFS [19].The current RAFS device may provide a high-quality oscillator technology, since its 1-s stability has been close to that of the existing best crystal oscillator, while its 10-and 100-s stability and drift performances are much better.If the long-term stability can be improved further, the overall stability of the RAFS will be comparable to that of an active hydrogen maser.Such a compact device can be used as a new generation space clock for satellite navigation system.

Fig. 4 .
Fig. 4. Zeeman transition spectrum of hyperfine sublevels in ground state of 87 Rb atoms.Totally, nine Zeeman transitions were observed.Peak 4 at the center is the clock transition.Peaks 3 and 5 compose of two transitions each.
835 GHz of the DRO2 to the 100 MHz also, the frequencies of DRO1 and DRO2 are mixed in the double-balanced mixer (DBM), creating a 35-MHz signal.After being filtered by the low-pass filter (LPF), the 35-MHz signal is phase compared in PD3 with the 35-MHz signal produced by the direct digital synthesizer (DDS) from the 100-MHz signal.The phase comparison signal is then used to control the 6.835-GHz frequency of the DRO2.The finally obtained 6.835-GHz microwave has near-end phase noise property determined by the OCXO, far-end phase noise property determined by the DRO2, and short-term stability property determined by the LO.The modulation of the 6.835-GHz microwave is realized by modulating the 35-MHz signal of the DDS.The modulation

Fig. 9 .
Fig. 9. Influence of the barometric effect to frequency stability of the RAFS.

Fig. 10 .
Fig. 10.Contributions of environmental effects to frequency stability of the RAFS.All the results are obtained when the PP is inside the sealed box.

Fig. 11 .
Fig. 11.Frequency stability test scheme for the RAFS.The test could be conducted by using an H-maser or an ultrastable laser based OMG.The phase noise analyzer (3120A, Symmetricom) is used for frequency comparison of the RAFS with the selected reference.

Fig. 12 .
Fig. 12. Frequency stability test result of the RAFS with the H-maser as the reference.

Fig. 13 .
Fig. 13.Frequency stability test result of the RAFS with the OMG as the reference.