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Abstract
We implement a miniaturized calcium beam optical frequency standard using specially-designed fully-sealed vacuum tube, and realize the comparison with another calcium beam optical clock whose vacuum tube is sealed by flanges. The electron shelving detection method is adopted to improve the signal-to-noise ratio of the clock transition spectroscopy, and the readout laser is locked by modulation-free frequency locking technology based on Doppler effect. Injection locking is carried out to boost the power of the 657 nm master clock transition laser, thus ensuring the comparison. The fractional instability of the miniaturized calcium beam optical frequency standard using fully-sealed vacuum tube is 1.8×10−15 after 1600 s of averaging. Total volume of the system except for electronics is about 0.3 m3. To our knowledge, it’s the first time to realize the optical frequency standard using fully-sealed vacuum tube. This work will promote the miniaturization and transportability of the optical clock based on atomic beam.
© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The advancement of good-performance optical clocks promotes the application of them into the fundamental scientific research and technical innovations [1–4]. While stationary optical lattice clocks or ion clocks which are typically large in size are constrained to the laboratory, applications like optical clock networks [5], space optical clocks or commercial requirements demand the optical clocks to support the flexibility of operation sites. Such clocks generally need to care about: (i) instability which might represent the most important property of an atomic standard [6]; (ii) size which is pivotal for transportability. Hence small or transportable optical frequency standards utilizing different quantum ensembles or different experimental schemes have been under research in the last two decades [7–16], especially much progress has been achieved in recent years.
Quantum absorbers for small or transportable optical frequency standards are generally alkaline-earth elements, e.g. calcium [7–10, 13, 15, 16] and strontium [11, 12, 14], due to narrow band clock transition and available diode laser corresponding to the electronic transition. Although optical lattice clocks [11, 12, 14] or ion clocks [15] have better uncertainty, they all depend on complicated laser cooling and trapping technology [17], and need at least 5 lasers, thus the smallest volume of them except for electronics is 0.54 m3 currently [15]. Atomic beam optical frequency standards owning simpler construction have great potential to satisfy the demanding in instability and size.
Relevant works on calcium beam optical frequency standards were reported in [7–10, 13, 16]. PTB detected the clock transition directly, restricted by the collection efficiency of the spontaneously emitted photons, leading to a relatively low signal-to-noise ratio [7]. Therefore, we firstly put forward the application of the electronic shelving detection method [18] into the atomic beam optical frequency standards [8] to address that problem. Based on this idea, Mcferran et al. [9] realized a calcium beam optical frequency standard whose minimum Allan deviation is 2×10−14 at 64 s but rised to 5×10−14 at 200 s, Zhang et al. [13] showed a minimum self-estimated Allan deviation of 3×10−15 at 200 s, and Olson et al. [16] achieved an instability of 2×10−16 at 10 s averaging time.
Besides, all atomic beam optical frequency standards are realized with vacuum tubes sealed by flanges till now, this inevitably enlarges the size of the vacuum systems. Especially for optical lattice clocks or ion clocks, the flange constructions account for the main part of the physical package [11, 12, 14, 15]. Although a highly miniaturized vacuum package was designed for ion clock, the fractional instability was only [19]. Here, a small size specially-designed fully-sealed vacuum tube, which was firstly used in the cesium beam microwave atomic clock to promote the miniaturization and commercialization, is applied in our scheme.
In this paper, we experimentally implement a miniaturized calcium beam optical frequency standard using fully-sealed vacuum tube and demonstrate the comparison with another calcium beam optical clock (this optical clock uses vacuum tube sealed by flanges) reported in [13]. Only two external cavity diode lasers are used, and a compact Pound-Drever-Hall (PDH) system [20, 21] is fulfilled to narrow the linewidth of the clock transition laser whose power is boosted by injection locking [22, 23]. Besides, the properties of the systemic instability and uncertainty are investigated. To our knowledge, it’s the first time to realize the miniaturization of optical frequency standard using fully-sealed vacuum tube.
2. Experimental methods
The overall system is depicted in Fig. 1. Two vacuum tubes (vacuum tube 1 and vacuum tube 2) serve as quantum references independently, one clock transition laser and one readout laser are shared by the two systems (system I and system II). Here the vacuum tube 1 is sealed by flanges and the vacuum tube 2 is fully-sealed.
Fig. 1 Overall configuration of both small calcium optical frequency standards. The cornsilk dashed box is the PDH construction, the azure dashed box is the injection locking construction, and the chartreuse dashed boxes are the atomic interaction constructions. Polarization maintaining fiber (PMF, Thorlabs P3-630PM-FC). 657 nm ML, 657 nm maser laser. 657 nm SL, 657 nm slave laser. Isolator, optical isolator. Rotator, Faraday rotator. AOM, acousto-optic modulator. EOM, electro-optic modulator. PD, photodetector. PMT, photomultiplier tube. DDS, direct digital synthesizer. AOM3 and AOM4 are double-passed. The system I uses the vacuum tube sealed by flanges and the system II uses the fully-sealed vacuum tube. The directions of the atomic beam flow of the two vacuum tubes are all from right to the left.
In our experiments, two systems are placed on two separated platforms enclosed by boxes to reduce the influence of the air flow. Besides, we use the integrated optical mounts which can significantly reduce the dithering of the optical path. About 0.5 mW 657 nm laser is delivered to a 100 mm optical cavity whose measured finesse is ~ 250,000 to narrow the linewidth of the laser using PDH technique [20, 21]. The cavity is placed into a small vacuum chamber maintained by a 10 L/s ion pump and the temperature is set at the zero crossing temperature. The error signal acquired after demodulating the output signal of PD1 is fed back to the current high-speed feedback port and the piezoelectric transducer of the laser by commercial servo circuits (Vescent D2-125, Newfocus LB1005). The whole PDH system is placed in a 0.18 m3 airtight black box.
Given the insufficient 657 nm master laser power for system II, injection locking [22, 23] is carried out to boost the laser power and to keep the coherence of the master laser. The λ/2 plate, the Faraday rotator and the polarization beam splitter make up the discrete optical isolator to isolate the scattered light and reflected light.
Figure 2 is the photograph and computer darwing of our fully-sealed vacuum tube, the size of it is 55 cm×16 cm×15 cm. The material of the entire fully-sealed vacuum tube is mainly stainless steel, all units are assembled by argon arc welding or braze welding techniques, the sealing ports between the optical windows and the main body of the vacuum tube also adopt the welding techniques. A 5 L/s ion pump whose size is really small to maintain the vacuum pressure which is evaluated to be 10−7 Torr. The divergent angle of the calcium beam in the fully-sealed vacuum is measured as 31.2 mrad. Multi-layered heat shield is used to reduce the heat dissipation. The lifetime of the fully-sealed vacuum tube is expected to be four to five years.
Fig. 2 Photograph and computer drawing of the fully-sealed vacuum tube. There are three pairs of windows in the direction of beam flow, the first pair near to the calcium granules is 423 nm readout laser locking window, the second pair is 657 nm clock transition window surrounded by solenoid, and the third pair is the 423 nm readout transition window.
For vacuum tube 1, the temperature of the oven is sensed by a thermocouple, we heat the oven until the thermocouple indicates 923 K [13], the sensed temperature is close to the actual temperature. For vacuum tube 2, the temperature of the oven is sensed by a thermistor, we heat the oven until the thermistor indicates 798 K, whereas the actual temperature is about 893 K because the thermistor is placed away from the nozzle. The temperature of the oven of the fully-sealed vacuum tube is controlled by a high-precision servo circuit, which can ensure that the temperature fluctuation of the oven is not more than 20 mK in a few hours.
As showed in the Fig. 1, the 657 nm laser interacts with atoms perpendicularly to eliminate the linear Doppler effect, the lens and the mirror form the cat’s eye configuration. The 657 nm laser spot size is measured as 4.1 mm×3.6 mm, and the intensity of the 657 nm laser is 39.8 mW/cm2. Then a 5 G magnetic field supplied by the solenoid is applied in clock transition window to separate the magnetic sublevel of the 3P1 state (relevant energy level see the insert figure in Fig. 3), a λ/2 wave plate used to adjust the polarization direction of the 657 nm is to choose the Δm=0 transition which is chosen as the clock transition since it is almost immune to the electrical and magnetic field.
Fig. 3 Spectrometer of the clock transition. Inset figure is the relevant energy level of the calcium atom. The natural linewidth of the 3P1 state is ~400 Hz.
A 423 nm readout external cavity diode laser is introduced to monitor the population variation of the ground state 1S0 after the clock transition laser interacting with the atoms. The readout laser is locked on the center frequency of 1S0-1P1 transition using the side-lock stabilization technique [24, 25]. The 423 nm readout laser interacts with atoms perpendicularly in the readout transition window, but interacts with atoms in a slight angle deviation from the orthogonal direction in the readout laser locking window, then the fluorescence in the readout laser locking window is directly sent to the servo circuits to lock the 423 nm laser [25]. This technique can avoid introducing additional frequency noise to the readout laser and provide larger feedback bandwidth when compared with [9]. The frequency instability of the 423 nm laser is at the level of 10−12 on long timescales [25], the intensity instability of the 423 nm laser and 657 nm laser is at the level of 10−4. The intensity of the 423 nm laser in the readout transition window is 198.9 mW/cm2, the distance between the clock laser beam and the readout laser beam is about 5 cm in the fully-sealed vacuum tube setup.
Considering the Hanle effect [26, 27], a λ/2 wave plate placed before the 423 nm laser interacting with the atoms is used to adjust the polarization direction of the 423 nm laser. The fluorescence intensity varies with the polarization direction of 423 nm laser adjusted, the maximum fluorescence intensity can be detected when the polarization direction of the laser is perpendicular to the magnetic field. However, when the polarization direction of the laser is parallel to the magnetic field, the detected fluorescence intensity is minimum [27].
3. Results and discussion
The clock transition spectroscopy for system II is acquired and showed in Fig. 3. The measured linewidth of the spectrometer is 500 kHz, which involves in saturation broadening, interaction time broadening and the broadening induced by the distortion of the curvature of the Gaussian beam. The estimated contribution of the saturation broadening is about 183.3 kHz, and the contribution of the interaction time broadening is about 200 kHz. The maximum normalized excitation ratio of the 1S0-3P1 transition is approximate 0.1, it is because that the residual divergence of the atomic beam leads to wide spread of velocities distribution in the direction of the laser propagation, then atoms with relatively large transverse velocities contributing to the 423 nm readout fluorescence are unable to be excited to the 3P1 state. Therefore, we suppose that taking full advantage of the atoms radiating the readout fluorescence will further greatly enhance the excitation ratio and increase the signal-to-noise of the clock transition.
We adopt the similar method described in [6, 28, 29] to estimate the instability. Since the optical local oscillator and the AOM2 are shared by the two systems (see Fig. 1), AOM3 and AOM4 are fed back by each error signal independently, the frequency difference of them is represented as νC1 − νC2=ν3 − ν4, νC1 and νC2 are the clock frequency of system I and system II, ν3 and ν4 are the corrected frequency of DDS3 and DDS4. Then the fractional instability of the system can be written as
where σ(ν3 − ν4) denotes the Allan deviation of the frequency differences (ν3 − ν4), ν0 is the center frequency of clock transition (the Eq. (1) holds on condition that the two systems are on the same noise level). Two frequency counters, which are externally triggered by one same logic signal to ensure simultaneous data recording, are used to record corrected ν3 and ν4, the gate time is set as 100 ms.As showed in Fig. 4, we measure the instability at 1 s at different measured atomic flux (marked as Ndet) and 657 nm clock transition laser power (measured before the light interacting with atoms). The measured atomic flux in the fully-sealed vacuum tube is about 5.5×1011 atoms/s when the sensed temperature is 798 K. The best measured instability of 5.5×10−14 is acquired at 4.7 mW and 5.5×1011 atoms/s. In our system we mainly consider the atomic detection noise compromising the instability, then we derive the fractional instability as [2, 8, 9, 30]
where Q is the line quality factor, N is atomic flux contributing to the Lamb-dip, n is the number of the spontaneous radiation photons per atom, η is the collection efficiency of photons, σB is the fluctuation of the background scattered photons. In the radical sign, the first two terms denoting the quantum projection noise and photon shot noise are negligible in our system. The last two terms represent the noise induced by the background scattered photons that lead to the background direct current signal and the shot noise induced by the detected atoms (photons) that do not contribute to the Lamb-dip [9]. We design a special readout transition window structure (see Fig. 2) to greatly decrease the background direct current signal and thus reducing the background scattered photon noise. We can define that K = N/Ndet which is ~ 0.03 (see Fig. 3) [9] at 4.7 mW and 5.5×1011 atoms/s. Then simplifying Eq. (2) as based on Eq. (3), the theoretical fractional instability is showed as the form of blue-dash-dot line in the upper subfigure of Fig. 4. We anticipate that the fractional instability can achieve 2×10−16 at 1 s (when Q is 1010, K is 0.15, and Ndet is 1012 atoms/s).Fig. 4 Instability at 1 s at each measured atomic flux and clock transition laser power. The colorbar on the right indicates the Allan deviation at 1 s. In the upper subfigure, blue dash-dot line is the theoretical instability at 4.7 mW clock transition laser power, red circle points are the experimental data.
Figure 5 is the recorded frequency difference of the two systems more than 3 hours at 4.7 mW and 5.5×1011 atoms/s, the data because of servo failure caused by anthropogenic interference has been excluded. Considering that the performance of the 657 nm clock transition laser is better than the clock, the elimination of the common mode noises induced by the 657 nm clock transition laser does not affect the evaluation of the clock performance. The noises of the 423 nm readout laser are not expected to be introduced into the system, those noises can generally be suppressed by choosing better performance laser, here we can eliminate those noises by sharing of the devices.
Fig. 5 Frequency difference of the two systems recorded more than three hours. Absolute mean frequency difference | < ν3 − ν4 > | is 126 Hz.
We roughly evaluate the frequency shifts and uncertainties of the two systems when mainly considering the Doppler effect and external electromagnetic field. The linear Doppler shift results from imperfect optical path alignments, we adopt the beam-reversal technique to estimate the linear Doppler shift [7]. The measured frequency interval is within 732.2 Hz for system I and 686.9 Hz for system II before or after reversing. Thus the uncertainty of the linear Doppler shift is 732.2 Hz for system I and 686.9 Hz for system II.
The quadratic Doppler shift depends on the velocities of atoms with different transition probability, it can be expressed with −υ2ω/(2c2), here the υ2 should be revised by (∫ sin2(2Ωl/υ)I(υ)dυ)/(∫ sin2(2Ωl/υ)I(υ)/(υ2dυ), I(υ) is the Maxwell velocities distribution,Ω is the Rabi frequency, l is the width of the laser beam. Then the calculated quadratic Doppler shift is −1376.4 Hz for system I and −1316.3 Hz for system II. The relative uncertainty coming from the measurements of the temperature of the oven is 6% for system I and 11% for system II. The relative uncertainties coming from the measurements of the size of the laser beam and the theoretical calculation are 2.5% and 5% respectively. Therefore, the uncertainty of the quadratic Doppler effect is 185.8 Hz for system I and 243.5 Hz for system II.
Measurements on atomic beam show the quadratic Zeeman shift of the clock transition is (+64±1) Hz/mT2 [31, 32]. We apply 4 G magnetic field to the system I and 5 G magnetic field to the system II, the magnetic field is measured by use of the Zeeman components from the Δm=0 component. The relative uncertainty of magnetic field measurement is 2.5%, and the theoretical coefficient with an uncertainty of 1%, thus the quadratic Zeeman shift is 10.24 Hz for system I and 16.00 Hz for system II, the uncertainty of the Zeeman shift is 0.36 Hz for system I and 0.56 Hz.
The influence of quadratic Stark effect is determined to be 12.4 mHz/(V/cm)2 [33]. The dc electric fields coming from the cable wire, power supply, magnetic field coils are assumed to be less than 10 V/m, and the electric fields coming from the arbitrary electric charges are assumed to be less than 50 V/cm for system I and 80 V/cm for system II. Then the quadratic Stark shift lies between 0 Hz to 30.1 Hz for system I (between 0 Hz to 79.4 Hz for system II) [32]. Thus the average quadratic stark shift is (−15.1±8.7) Hz for system I and (−39.7±22.9) Hz for system II. Frequency corrections and uncertainties of the two systems are estimated and summarized in Table 1, the absolute mean frequency difference showed in Fig. 5 is within the uncertainty of system I or system II.
Table 1. Corrections (corr., Hz) and uncertainties (unc., Hz) of the two systems.
Figure 6 is the total Allan Deviation of the miniaturized calcium beam optical frequency standard using fully-sealed vacuum tube based on the data in Fig. 5. The instability is 5.5×10−14 at 1 s, and 1.8×10−15 after 1600 s of averaging. We give an approximate calculation about the sensitivities of this system to perturbations, since the temperature fluctuation is within 20 mK and the intensity instability of the 423 nm laser is at the level of 10−4, then the sensitivities of the instability at 1 s are 2.8×10−12/K to the temperature fluctuation and 1.7×10−14/μW to the 423 nm laser power fluctuation.
Fig. 6 Total Allan deviation of the miniaturized calcium beam optical frequency standard using fully-sealed vacuum tube. Green-solid line represents white-frequency-noise asymptote of . Error bars indicate 1σ confidence intervals.
Total volume of the system except for electronics is about 0.3 m3, the volume of the electronics is not more than 0.18 m3 currently. We estimate that the volume of the electronics can be reduced to 0.09 m3 by adopting integrated electronic devices, total volume of the system can be reduced by integrating the optical path and electronics in further work.
4. Conclusion
In summary, we implement a miniaturized calcium beam optical frequency standard using fully-sealed vacuum tube and demonstrate the comparison with another calcium beam optical clock. Instability of 1.8×10−15 is acquired after 1600 s of averaging, and total volume of the system excluding electronics is about 0.3 m3. The instability at 1 s is expected to be 2×10−16 when adopting Ramsey interferometry and taking full advantage of the atomic flux at different atomic velocities. The size can be reduced by half at least after mechanical integration. As the first realized miniaturized calcium beam optical frequency standard using fully-sealed vacuum tube, it is potential to be applied into the timekeeping, satellites navigation, coherent optical communication and commercial demanding, and at the same time promotes the research on transportable optical clocks.
Funding
National High-Tech Research and Development Projects (863); National Natural Science Foundation of China (NSFC) (91436210).
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