As one of the important circuits of the rubidium atomic clock, the C-field circuit plays a significant role in the rubidium atomic clock’s performance. Generally, a C-field circuit is used to provide a constant current to a C-field coil by forming a weak magnetic field to select two hyperfine mF = 0 energy levels and thus fine-tune the transition frequency of 87Rb. In this way, the C-field circuit has a direct influence on the frequency stability of the rubidium atomic clock. In this paper, by studying the principles and functions of the C-field in a rubidium atomic clock, we propose a modified C-field circuit, which not only provides constant current to the C-field coil but also provides a pathway to improve the performance of the rubidium atomic clock significantly by optimizing the start-up characteristics and temperature coefficient carefully. In addition, according to the theoretical analysis and test verification, the rubidium atomic clock with the proposed C-field circuit improves the temperature coefficient from −1.2 × 10−13 to 2.7 × 10−15/°C, and in addition, the stability of long-term frequency can reach 3.88 × 10−15 at 105 s.
I. INTRODUCTION
The rubidium frequency standard is widely used in global positioning systems,1,2 communication, navigation, and running survey systems owing to its excellent properties such as low weight, small volume, low power consumption, and high reliability.3,4 The lamp-pumped rubidium atomic frequency standard (RAFS) arguably affords the driving force for atomic timekeeping in space, which possesses the excellent stability of short-term and long-term frequency,5,6 longevity in space, and relative radiation insensitivity.7 Despite the attractive characteristics and ubiquity of the RAFS, system and space mission planners are constantly striving for better performance to meet more stringent systems as per the mission requirements.8
Among physical processes and circuits that could play a role in the performance of the rubidium atomic clock, the C-field gained immense importance, which is closely associated with the physics package (PP) and circuit part. Most importantly, by analyzing the principles of the C-field, it has been observed that the stability of the weak magnetic field produced by the C-field is determined by the circuit of the C-field, which is directly related to the output frequency of the rubidium atomic clock. Hence, a robust C-field circuit not only provides a constant current for the C-field coil but ultimately reduces the temperature coefficient and improves the long-term frequency stability of the rubidium atomic clock.
In this report, by analyzing the theory of the RAFS and the original C-field circuit, we propose the development of a modified C-field circuit. First, it can improve the start-up characteristic of the rubidium atomic clock by providing a greater current to the C-field coil before the rubidium atomic clock locked. Second, it can optimize the temperature coefficient, which improves the long-term frequency stability of the rubidium atomic clock. Finally, the accuracy of rubidium atomic clock’s output frequency can be fine-tuned by adjusting the current flow in the C-field circuit.
The tests indicate that the temperature coefficient of the rubidium atomic clock with the proposed C-field circuit reaches 2.5 × 10−15/°C, which is superior compared to the previous report,8 where the temperature sensitivity of the rubidium atomic clock was 4 × 10−15/°C. The stability of long-term frequency reached about 3.8 × 10−15 at 105 s. The experimental results prove that the proposed scheme is feasible both theoretically and practically, and most importantly, it can provide an applied basis for the applications of rubidium atomic clocks in aerospace.
II. THE VAPOR-CELL ATOMIC CLOCK
The vapor-cell atomic clock is an unpretentious device.9 The main process of the rubidium atomic clock is as follows: 10 MHz of the output frequency of voltage-controlled crystal oscillators (VCXOs) loads as input into the radio frequency synthesizer circuit; then, the process affords the output of the 6.834 GHz microwave excitation signal, which is known as 0–0 hyperfine transition resonance frequency.10,11 In this way, the PP produces a discriminator signal when the microwave signals of 6.834 GHz are applied to the resonance cell of the PP. Finally, the discriminator signal enters the servo circuit to produce the correct voltage of the VCXO, and further, the frequency of the VCXO becomes locked in the transition frequency of the rubidium atomic clock.
Figure 1 shows the diagram for the basic block of a passive atomic frequency standard, which consists of a circuit part and a PP. The PP is equivalent to the quantum frequency discriminator.12 The circuit part mainly consists of a servo circuit, a temperature control circuit, a power circuit, a radio frequency synthesizer circuit, and a C-field circuit. The function of the servo circuit is to amplify the alternate and direct current signal for achieving the phase detection; the power circuit functions to provide various voltages for all the circuits of the rubidium atomic clock; the radio frequency synthesizer circuit provides a microwave signal of 6.834 GHz, and the function of the C-field circuit is to provide a steady current to the C-field coil.
According to Fig. 2, the PP consists of an rf-discharge lamp with 87Rb and buffer gas, a filter cell with 85Rb, a resonance cell with 87Rb and buffer gas, a microwave cavity, a C-field coil, a magnetic shield, and a photo-detector.13 Each element plays an important role in the process of optical pumping. The PP converts the difference between the excitation signal frequency and the center frequency of the spectral line of 87Rb into a discriminator signal. The light from the rf-discharge lamp excited by the lamp exciter circuit passes through the filter cell and resonance cell. The photodetector forms the optical detection signal, which is basically the change in the intensity of transmitted light of the resonance cell; next, the optical detection signal relays into the servo circuit. Finally, the output frequency of the crystal oscillator becomes locked into the center frequency of the Rb transition line.
III. THE PRINCIPLE OF C-FIELD
The Zeeman effect14,15 of the interaction between the magnetic field and Rb atoms causes the splitting in atomic energy levels. The intensity of the energy levels’ split alters with the changes in the magnetic field, which causes the shifting of the magnetic frequency in the RAFS. Therefore, to avoid or minimize the influence of the geomagnetic field and external magnetic field on the rubidium atomic transition frequency, we adopted magnetic shielding technology in the microwave cavity. However, the atomic transition needs a quantum axis. Therefore, a weak static magnetic field in terms of the C-field is needed for the resonance cell in the microwave cavity.
The function of the C-field is to provide a quantized axis for the atomic transition and to reduce the influence of the residual stray magnetic field inside the PP. In addition, the C-field is also capable of fine-tuning the output frequency of the rubidium atomic clock by adjusting the current of the C-field coil. In general, the C-field part consists of a C-field coil and a C-field circuit, the purpose of which is to provide current for the C-field coil. The C-field coil produces a weak static magnetic field parallel to the direction of the microwave field, which further splits the ultra-fine energy levels of the ground state of 87Rb atoms, and selects two mF = 0 energy levels. At this time, the transitions between the other sub-levels of mF ≠ 0 expelled from the capture band of the loop.
As shown in Fig. 3, the C-field coil adopts a Helmholtz coil,16 which appears as a pair of rings parallel to each other, and each coil is of N-turns. The same magnitude of current flows though the two coils toward the same direction, and the distance between the coils remains exactly equal to the radius R of the circular coil. This coil is characterized by the ability to generate a wide and uniform magnetic field near the midpoint of its common axis. The magnetic field distribution of Helmholtz coil is shown in Fig. 4.
The schematic diagram of the proposed C-field circuit is shown in Fig. 5. Ports W1 and W2 connect the two ends of the C-field coil. U1 is a voltage reference source, which provides a stable voltage for the positive input port of the operational amplifier N1. The rubidium atomic clock remains unlocked at the startup and the lock signal appears to be of high level, which leads to the transistor Q1 conduction. When the rubidium atomic clock remains locked, the lock signal appears to be of low level, which leads to the transistor Q1 cutoff. Therefore, the C-field circuit preferably provides a greater current to the C-field coil before the rubidium atomic clock becomes locked. Hence, the function of this circuit is to improve starting lock’s characteristic of the rubidium atomic clock. In addition, the C-field circuit provides a constant current when the rubidium atomic clock becomes locked, which can reduce the variation of the C-field current caused by the fluctuation of the power supply.
According to the relationship between the C-field coil current, temperature, and output frequency of the rubidium atomic clock, we first propose a method to optimize the temperature coefficient of the rubidium atomic clock by introducing a thermistor (RT1) into the C-field circuit. The other important function of the C-field circuit is to use the resistance and temperature characteristics to optimize the temperature coefficient of the rubidium atomic clock. Moreover, the parameter of the RT1 can be determined from the original temperature coefficient, the function of C-field coil current, and the accuracy of the rubidium atomic clock’s output frequency.
IV. EXPERIMENTAL
In this paper, the PP of the rubidium atomic clock consists of three cells and two temperature-controlled systems. In order to reduce the light shift and the sensitivity of temperature, the temperature of the filter cell and resonance cell is controlled.17,18
In experiments, the first step is to determine the value of RT1 in the C-field circuit and then to test the temperature coefficient and long-term frequency stability of the rubidium atomic clock.
A. Determine the parameters of RT1
Since different rubidium atomic clocks have different temperature coefficients, we need to determine the parameters of RT1 in the C-field circuit. The detailed process is as follows: first, we obtain the function relationship between the C-field coil current and the accuracy of the rubidium atomic clock’s output frequency, and then we can get the original temperature coefficient of the rubidium atomic clock. Finally, we determine the parameters of RT1 in the C-field circuit.
In experiment, the rubidium atomic clock is placed in a vacuum tank, a resistance box that is used to regulate the current of the C-field placed outside. The output frequency accuracy is measured by changing the C-field coil current. The experimental results are shown in Table I. The equation of the fitting curve of the C-field coil current (I) and accuracy of the rubidium atomic clock’s output frequency (F) is written as follows:
The value of the C-field coil current and the accuracy of frequency.
| The C-field current (mA) | The accuracy of the frequency |
|---|---|
| 0.06 | 2.590 516 × 10−9 |
| 0.10 | 2.602 594 × 10−9 |
| 0.20 | 2.657 405 × 10−9 |
| 0.30 | 2.741 906 × 10−9 |
| 0.40 | 2.853 963 × 10−9 |
| 0.50 | 2.998 652 × 10−9 |
| 0.60 | 3.158 108 × 10−9 |
| 0.75 | 3.456 000 × 10−9 |
| 1.00 | 4.083 391 × 10−9 |
| 1.50 | 5.826 750 × 10−9 |
| 3.00 | 14.873 44 × 10−9 |
| The C-field current (mA) | The accuracy of the frequency |
|---|---|
| 0.06 | 2.590 516 × 10−9 |
| 0.10 | 2.602 594 × 10−9 |
| 0.20 | 2.657 405 × 10−9 |
| 0.30 | 2.741 906 × 10−9 |
| 0.40 | 2.853 963 × 10−9 |
| 0.50 | 2.998 652 × 10−9 |
| 0.60 | 3.158 108 × 10−9 |
| 0.75 | 3.456 000 × 10−9 |
| 1.00 | 4.083 391 × 10−9 |
| 1.50 | 5.826 750 × 10−9 |
| 3.00 | 14.873 44 × 10−9 |
According to the above equation and combining with the temperature coefficient with the original C-field circuit, we can determine the parameter of RT1 in the proposed C-field circuit. The equation of the resistance and temperature characteristics of RT1 is as follows:
B. Temperature coefficient test
As one of the most important factors affecting the performance of the RAFS, the temperature coefficient that refers to the change in the rubidium clock’s output frequency accuracy caused by the change of 1 °C in the baseplate temperature plays a significant role in the long-term frequency stability of the rubidium atomic clock.19
In the experiments, we test the temperature coefficient by changing the temperature of the vacuum tank from −15 to −5 °C. The temperature coefficient test curves with the original C-field circuit (a) and the proposed C-field circuit (b) are shown in Fig. 6. The experimental results are shown in Table II.
Temperature coefficient of the rubidium atomic clock. (a) The original C-field circuit. (b) The proposed C-field circuit.
Temperature coefficient of the rubidium atomic clock. (a) The original C-field circuit. (b) The proposed C-field circuit.
Test record of the temperature coefficient of the rubidium atomic clock.
| Temperature variations | |
|---|---|
| Circuit | −15 to −5 (°C) |
| Original C-field circuit | 1.285 × 10−14 |
| Proposed C-field circuit | −2.7 × 10−15 |
| Temperature variations | |
|---|---|
| Circuit | −15 to −5 (°C) |
| Original C-field circuit | 1.285 × 10−14 |
| Proposed C-field circuit | −2.7 × 10−15 |
As can be seen from Table II, compared with the original circuit, when the temperature changes from −15 to −5 °C, the temperature coefficient of the rubidium atomic clock with the proposed C-field circuit goes up from 1.285 × 10−14 to −2.7 × 10−15/°C. Most importantly, the temperature coefficient is the best ever reported for a vapor cell rubidium frequency standard.
C. Long-term frequency stability test
The long-term frequency stability is one of the important performance indicators of the rubidium atomic clock, which is mainly limited by the temperature fluctuation of the environment. The experimental results are shown in Table III, and the long-term frequency test curves of the frequency stability of the rubidium atomic clock with the original C-field circuit and the proposed C-field circuit are shown in Fig. 7.
Test record of the frequency stability of the rubidium atomic clock. Boldface denotes the best results, as explained further in the article.
| Tau(s) | The original C-field | The proposed C-field circuit | ||
|---|---|---|---|---|
| 1 | 8.36 × 10−13 | 8.36 × 10−13 | 8.36 × 10−13 | 8.38 × 10−13 |
| 10 | 2.74 × 10−13 | 2.73 × 10−13 | 2.72 × 10−13 | 2.72 × 10−13 |
| 102 | 8.64 × 10−14 | 8.58 × 10−14 | 8.59 × 10−14 | 8.67 × 10−14 |
| 103 | 2.67 × 10−14 | 2.69 × 10−14 | 2.62 × 10−14 | 2.67 × 10−14 |
| 104 | 7.71 × 10−15 | 9.49 × 10−15 | 7.35 × 10−15 | 7.66 × 10−15 |
| 105 | 8.05 × 10−15 | 3.88 × 10−15 | 4.39 × 10−15 | 5.29 × 10−15 |
| Tau(s) | The original C-field | The proposed C-field circuit | ||
|---|---|---|---|---|
| 1 | 8.36 × 10−13 | 8.36 × 10−13 | 8.36 × 10−13 | 8.38 × 10−13 |
| 10 | 2.74 × 10−13 | 2.73 × 10−13 | 2.72 × 10−13 | 2.72 × 10−13 |
| 102 | 8.64 × 10−14 | 8.58 × 10−14 | 8.59 × 10−14 | 8.67 × 10−14 |
| 103 | 2.67 × 10−14 | 2.69 × 10−14 | 2.62 × 10−14 | 2.67 × 10−14 |
| 104 | 7.71 × 10−15 | 9.49 × 10−15 | 7.35 × 10−15 | 7.66 × 10−15 |
| 105 | 8.05 × 10−15 | 3.88 × 10−15 | 4.39 × 10−15 | 5.29 × 10−15 |
Long-term frequency stability test curve. (a) Original C-field circuit. (b) The proposed C-field circuit.
Long-term frequency stability test curve. (a) Original C-field circuit. (b) The proposed C-field circuit.
As can be seen from Table III and Fig. 7, when using the proposed C-field circuit, the best long-term frequency stability of the rubidium atomic clock is 3.88 × 10−15 at 105 s, which clearly demonstrates that the proposed C-field circuit is helpful to improve the stability of long-term frequency in the rubidium atomic clock.
V. CONCLUSION
In conclusion, the stability of the C-field is one of the most important factors influencing the performance of the RAFS. Based on the theoretical aspects of the RAFS, the analysis of the function of C-field coil’s current, and the output frequency of the rubidium atomic clock, we propose a modified C-field circuit. Initially, we optimize the temperature coefficient of the rubidium atomic clock by introducing a thermistor. The results of experiments prove that the temperature coefficient of the rubidium atomic clock reaches 2.4 × 10−15/°C with the proposed C-field circuit. In addition, a long-term frequency stability of 3.88 × 10−15 has been achieved for a measurement time of τ ≈ 105 s. Therefore, the results demonstrate that the proposed C-field circuit can optimize the temperature coefficient and improve the long-term frequency stability of the rubidium clock. A close connection between technological innovation and engineering practice may certainly result in the development of new rubidium atomic clock with enhanced capabilities for deep-space missions.
DATA AVAILABILITY
The data that support the findings of this study are available from the corresponding author upon reasonable request.
