Recent progress in laser-pumped rubidium gas-cell frequency standards

This paper presents the current results of our development of a laser-pumped passive rubidium frequency standard. With a vapor cell containing isotopic Rb/sup 87/ and a mixture of buffer gas we obtained a double resonance signal compatible with a short-term stability of 2.10/sup -13/ /spl tau//sup -1/2/ (shot noise limit). Measurements of the effect of the interrogating phase noise demonstrated that our microwave synthesizer did not limit this potential short-term stability. Two types of monochromatic light source lasers have been used: broad-band solitary lasers and extended cavity lasers. We found that their main limitation on the frequency stability was due to the AM noise detected by the photocell. In order to improve the S/N of the clock, an all-electronic AM noise cancellation technique has been successfully employed. Light-shift measurements allowed tuning of the laser frequency to the zero light-shift point. Presently, our clock has a short-term stability of 7.10/sup -13/ /spl tau//sup -1/2/ (2</spl tau/<40 s) with the solitary laser and 5.10/sup -13/ /spl tau//sup -1/2/ (4</spl tau/<40 s) with the extended cavity laser. These are the best reported performances for passive rubidium clocks.


Introduction
The paper is organized in the following manner. This section introduces topics related to the short-term stability of laser-pumped rubidium clocks. The second section describes the different components of the clock, outlines the experimental setup, and illustrates the laser noise cancellation and the light-shift adjustment. The third section shows our experimental results of frequency stability measurements.
A summary concludes the paper.
Laser-pumped, gascell, passive frequency standards have been the subject of many studies [l]. These studies focused not only on the development of a new type of atomic clock but also on the investigation of interesting physical effects, especially those related to the light-shift [2]. Three main directions are presently under investigation: (1) the replacement of the discharge-lamp rubidium clocks; (2) the possibility of new applications for greatly miniaturized clocks; (3) the development of a "super" local oscillator with a short-term stability at the level for use in clocks based on slow atoms and ions.
A detailed discussion of these different aspects is beyond the scope of this work. However, a short presentation of the principal ideas available in the past reports will simplify the discussion of our work towards the development of a super local oscillator. This short presentation is organized in two sections. The first section reviews the new physical processes which occuf in the cell when a laser is used instead of the lamp. The second introduces our main field of interest: the improvement of the short-term stability.

Understanding the new Dhvsics
The first microwavdoptical double resonance experiments involving a laser-pumped vapor cell evidenced a new phenomenon [3] called the light-shift saturation, which was in apparent disagreement with well known physical laws [4]. Later, it was shown that this effect was caused by the light and microwave inhomogeneities in the interrogated vapor [5]. Finally, it was demonstrated that these effects were mainly due to the transverse inhomogeneities in the laser beam 161.
Light-shift saturation is related to another interesting phenomenon called the double resonance signal saturation or peaking [7], which must be considered to optimize the clock parameters. Thanks to this more general point of view, the measured characteristics of the double resonance signal (width, amplitude and shift) can be related in a quantitative way to the theoretical predictions. Careful calculations realistically quantiQ the ultimate performance of the laser-pumped vapor gas-cell frequency standards at a level of l-2-lO-" . -l n (z is the sampling time),and relate these numbers to the magnitude of the physical quantities involved in the experiment [g].
However, the discrepancy between predicted and measured short-term stability is still not understood. In fact, the short-term fiequency stability of the laser pumped clocks was in general not better than that of the best lamppumped rubidium clocks which, is now approximately 2*10-12 zan. Explaining this discrepancy is one of our main objectives.
Toward a suwr local oscillator Two problems prevent us from reaching our desired short-term stability: the limitations due to the interaction of the atoms with the light field and those due to the interaction with the microwave field.

a. Limitations due to the atom-light interaction
The best short-term stability that can be obtain fiom a passive clock is determined by the ratio of the shot noise on the detection photocell (,/W where I is the photocurrent and q is the charge of the electron) and the discriminator slope (D), according to equation (1) [g]. this estimation corresponds to the best measured stability in today's lamppumped rubidium clocks. Using a laser, with its more efficient optical pumping, the shot noise can be reduced to 1 PA/% and the discriminator slope increased by a factor 2 or 3. This should improve the short term stability by approximately one order of magnitude. With wallcoated cells, the discriminator slope can be increased by about a factor 15 so that the improvement could in principle be two orders of magnitude.
However, these advances have never been achieved due to limitations other than shot noise. As far as the laser is concerned, these limitations are suspected to be related to the AM and FM noise, and the light shift experienced by the rubidium atoms.

b. Limitations due to the atom-microwave interaction
One important limitation to the short-term stability is related to the phase modulation (PM) noise in the 6.8347 G& synthesizer. When examined in detail, the limit on short-term frequency stability depends on the modulation index, line width, and all even harmonics of fn (Pi is the Fourier coefficient of rank i in the response of the resonance) [g] : The largest contribution is due to the noise at f 2 f, from the carrier (1st term) which can be written as a function of the spectral density of PM noise S&. The quasi-static model for the special case of square wave modulation predicts : However, the above formulas give only a first approximation on the actual limitation from the phase noise of the synthesizer since the other d c i e n t s (4th, 6th, etc.) might play a role depending on the desired level of stability. Furthermore, these formulas are based on the socalled quasi-static approximation, which is valid only for low modulation frequencies and might not be strictly correct when the modulation frequency approaches the atomic line-width.

Experimental setup andpreliminary measurements
This section presents the three main components of our clock: the physics package, the laser diode, and the microwave synthesizer. The overall experimental setup and some preliminary measurements are then discussed.

The Dhvsics package
We used the physics package of an existing l a m ppumped rubidium fresuency standard with the lamp and filter sections removed. The cylindrical absorption cell had a volume of 25 c m 3 and contained isotopic RbS7 and a mixture of buffer gas which provides efficient quenching and a lower temperature coefhcient. The microwave cavity used a mode and had a quality factor of approximately 100. The detection photocell was removed and replaced by a lens so that an external photodetector could be used. Part of the original electronic breadboard was also employed to control the temperature of the absorption cell.

The laser diodes
We used two types of laser diode sources, a broad-band solitary laser and an extendedcavity grating feedback laser. Both lasers were operated on the Dz (5Sla + 5P30, 780 nm) rubidium line. Their frequencies were servocontrolled to a saturated absorption feature in a separate evacuate cell. ~a acousto-optic modulator (AOM) was used to split the light in two beams having slightly different frequencies. These beams were sent to the saturated absorption cell and to the interrogated cell, respectively (see Figure 2). Thus, a fine optical frequency adjustment (0 C f C 50 M H z ) was possible by changing the RF frequency injected on the AOM. The coarse tuning (50 < f 500 MHz) could be done by choosing the appropriate Doppler-free line in the saturated absorption spectrum and the proper difhction order from the AOM. The solitary laser and the extended cavity laser had approximate line widths of 50 MHz and 100 kHz, respectively. We present hereafter the measurements of their direct intensity noise as well as the AM noise increase when an atomic absorption line is placed in the light path.

The microwave synthesizer
We used a fresuency synthesizer chain starting from a low PM noise 5 MHz local oscillator (the development of low-noise synthesizers at NIST has been described earlier [lo]). The phase modulation was applied to the 10 MHz carrier in the frequency synthesizer chain. To reach our goal to improve the short-term stability, we focused on two areas : (1) reducing the PM noise out of the phase modulator, and (2) reducing the PM noise of the x20 multiplier from the 5 MHz quartz oscillator to According to (4), this PM performance is compatible with a short-term stability below 3-10'13 -rela, for a modulation fkquency between 100 and 400 Hz. Preliminary measurements indicates that the contributions of the 4 t 4 6th and 8th harmonics are small enough to be neglected this level.
Laser freuuencv tuning to the zero light-shift mint It was not our intention to perform fundamental measurements of light-shift coefficients, but only to set the laser frequency at the most convenient point so that light-shift effects on the short-term and long-term stability of the clock were as small as possible. As described previously, light-shifts have to be measured in a vely accurate way since saturation effects can occur and lead to incorrect conclusions. We chose to tune the laser to one of the Doppler-free transitions at 780 nm starting from the F = 2 hyperfine level of the ground state &as7, since the optical pumping is more efficient than when the F = l level is depopulated. Figure 1 shows an example of the results of our laser fiequency fine tuning measurements.

Fiaure 1. Fine tuning of the laser frequency to the zero light-shift point. The clock transition fiequency shift is plotted as a finction of the light intensity for drflerent laser detunings with respect to the zero light-shiftfiequency.
The above figure shows that it is possible to tune the laser frequency so that the light-shift is zero within the uncertainty of our measurements. We also see that a saturation phenomenon occuls for a photocurrent above 1 p.4. This result reveals the effect of residual inhomogeneities in the interaction between the rubidium atoms and the two microwave and optical radiation fields. As a result of this technique, we could reduce the light-shift coefficient below 1.1013 /(% of light intensity). For this particular atomic transition, we found an average value of the light shift coefficient which confirmed both previous theoretical

Laser noise measurements and noise cancellation
As mentioned previously, an important limit for the short-term stability of the clock is the noise level on the photodetector, and the ultimate goal is to reach the shot This AM noise increased when the rubidium cell was placed in the path of the laser beam, and its level depended on the laser detuning in the absorption line, as well as on the temperature of the vapor. In typical conditions and at the zero light-shift frequency, we measured 32 PA/%. This value did not vary significantly within the tuning range of the RF signal on the AOM (-50 MHz). This additional noise was suspected to be the result of a conversion through the atomic absorption line of the laser FM noise into AM noise [ 131. However, the fact that the noise level was similar for the two types of lasers seems to contradict this interpretation. One possible explanation might be the fact that our present extended cavity laser is very sensitive to mechanical vibrations which results in additional FM noise.
As a first attempt to reduce this noise, we tried to optimize the parameters of the laser frequency locking. With the solitary laser, for example, the modulation frequency of the current was increased to 70 kFIz in order to increase the bandwidth of the locking system.
However, this did not significantly improve our results.
After failing to actively reduce the intrinsic Ah4 and FM noise in the laser beam, we decided to cancel it from the detection signal in a passive way. The pumping beam was separated into two beams with a beam splitter and the additional beam was used as a sample beam in a classical photacurrent subtraction scheme which cancels the AM noise out of the first amplifier of the detection system 1141. A second rubidium cell, identical to the absorption cell, was placed in the path of this beam for canceling the FM contribution to the AM noise. Figure 2 displays the overall experimental setup. As a result the total AM noise out of the detector was 3 PA/& (without rubidium cells in the path the shot noise level is reached), which was satisfactory as a first step.
As it is shown on Figure 2, a detector is placed to monitor the level of the light intensity incident on the rubidium cell. This detector can also be used for maintaining this intensity constant by automatically adjusting the RF power on the AOM.

Frequency stability measurements
we have observed that no signifcant improvement is achieved with the noise cancellation if no rubidium cell Figure 3 shows the frequency stability obtained with is Placed in the Path Of the Sample beam, we can the experimental stup described h v e , as well as the conclude that the main contribution to the AM noise perfom= without noise cancellation. ms results from the presence of the absorption line in the picture demonstrates clearly the limitation resulting Path ofthe laser beam.
from the laser AM and FM noise. Furthermore, since Sample time [S] Finure 3.

Short-term stability. The experimental points correspond to the solitary and extended cavity lasers. Typical results obtained with a lamp or lasers without noise cancellation are shown for comparison.
These results are very important, since it is the first time that a rubidium clock has demonstrated a shortterm stability better than 1-10'2 r-lD, and l.lO-" after less than 30 S. However, since the shot noise limit has not yet been reached, it is worthwhile to try to understand and reduce the laser AM and FM noise. Potentially, this might improve the short-term stability of the clock by approximately a factor of 3. Furthermore, the effect of the microwave radiation on the noise level at the photodetector has not been studied in details but might also sect the clock stability in a significant way.
Remarks on the medium and long term stability Unfortunately, the results for longer sample times (r > 40 S) depend on the environmental fluctuations. Typically, the Allan deviation starts to increase after 40 S and is approximately 8.l0-I3 at 1000 S. We are presently investigating the reasons of this high sensitivity to environmental conditions. We suspect microwave power changes and RF power fluctuations (on the AOM). We are also investigating possible laser changes due to aging processes and temperature sensitivity.

Summary
We have built a laser pumped rubidium clock and demonstrated a short-term stability of 5.10-" r-ln. The theoretical shot noise limit is 2.lO"' r-In. Our results show that the main limitation results from the AM noise on the detection photocell, increased by the transmission through the absorption cell. The origin of this additional AM noise is still not fully understood since it does not change when going from the solitary to the extended cavity laser, At the present stability level, the light-shifl does not limit the short-term stability. We also have studied the effect of synthesizer interrogation P M noise on the clock stability. These results indicate that the P M noise in our synthesizer contributes less than 2-3~10"~ T -'~ to the frzlctional instability.