Optically pumped vapor-cell atomic frequency standards, often referred to as Rubidium clocks, combine the competitive frequency stabilities of a secondary frequency standard with the advantages of a compact size, low mass, low power consumption and relatively low unit prices, making them interesting for a variety of scientific, commercial and space-oriented applications. For example, lamp-pumped Rb clocks today also constitute one of the main foundations of the GPS satellite navigation system.
It has been demonstrated, that the short-term and – to some extend – long term stability of Rb clocks can be significantly improved when the discharge lamp implemented for optical pumping is replaced by a narrow-band laser source [1-3]. In order to exploit this advantage, our on-going activity aims to develop a compact and high-performance laser-pumped Rb clock for space applications, e.g., as a possible upgrade candidate for future generations of the GALILEO satellite navigation system. Design goal is to demonstrate a compact clock unit (<1.5 liters, < 1.5 kg) with an improved stability of 10-14 at 104 seconds.
Laser-Pumped Space Rb Standard
The implementation of laser pumping instead of the discharge lamps widely used in Rb clocks offers the possibility of improved control of the pump light spectrum, as well as reduced intrinsic linewidths (down to 500Hz) and increased signal contrast (up to 25%) of the microwave resonance, leading to improved shortterm stabilities of the clock [1-3].
In the frame of an ARTES-5 project, supported by the European Space Agency and led by “TEMEX Neuchâtel Time” (TNT), we are evaluating this implementation of laser optical pumping to Rb atomic clocks, we follow a modular approach (cf. Fig. 1): A lamp-removed, modified commercial Rubidium clock  provides the physics package of the clock unit, and the pump light is provided by an independent laser head module. This allows for easy modifications or even exchange of the pump light source, while maintaining full functionality of the clock unit. It is important to mention that before the lamp was removed, the TNT clock proved a frequency stability of 3·10-12 at 1 second and below 5·10-14 at 10’000 seconds. In this manner, we could directly benefit from all the already performed progress and focus directly on the laser-related issues. Even more important, we could be sure that any instability above these levels had to be connected with the laser and not from the rest of the frequency standard.
A Compact, Frequency-Stabilized Laser Head
We have developed a compact, frequency stabilized laser head for optical pumping of the clock, that can also be utilized in stand-alone applications. The physics package of this laser head occupies a volume of only 200 cm3 and comprises a Littrow-type external-cavity diode laser (ECDL) and a small Rb vapor cell used as atomic reference . Frequency stabilization of the laser output is achieved by stabilization to sub-Doppler saturated absorption lines of the reference cell by using a FM modulation technique. The unit delivers an optical output power of more than 2 mW with a spectral linewidth below 1.5 MHz, well sufficient for the operation of the Rb clock. To our knowledge this constitutes the smallest frequency stabilized laser head of its type realized today. For further improvements and miniaturization we envisage to replace the ECDL by more advanced diode lasers like, e.g., DBR or DFB lasers, or possibly a MEMS-based ECDL.
The short-term performance up to about 1000 seconds reproduces the stability of 3·10-12 τ-1/2 of the lampoperated clock unit. We expect to improve this shortterm stability by adapting the detection electronics to the strongly increased signal contrast of about 15% and by optimizing the quartz LO loop, which is currently degraded in order to allow a more flexible setup for experimental studies . On the medium and long-term timescales beyond 1000 seconds, the frequency drifts are mainly caused by the temperature coefficient of the clock resonance cell and light shift effects due to laser intensity fluctuations (DC effect ≈10-9, see below for details). We are currently working on the reduction of these effects.
Laser Frequency Stabilization Schemes
While the sub-Doppler stabilization scheme implemented in the laser head gives satisfactory results, in a commercial product, a simpler and more robust scheme like, e.g., based on simple Doppler-broadened absorption spectroscopy, is desirable. This approach would result in only one (broader) reference line and thus avoid the need to distinguish between several closely spaced references lines to which the laser can be locked (cf. the three narrow lines in the bottom trace of Fig. 5). We have therefore studied whether the laser frequency stability of the simpler Doppler scheme would still be sufficient for a successful operation of the envisaged high-performance Rb clock. The experimental results for the comparison of the laser frequency stability reached with the “Doppler” and “sub-Doppler” stabilization are shown in Fig. 3 . As can be seen, the “sub-Doppler” stabilization fulfills the laser frequency requirements imposed by the clock stability specifications on all timescales shown. In contrast, the “Doppler” scheme shows too large drifts on timescales larger than 100 seconds, mainly due to temperature variations of the reference cell. However, this frequency stability might still be useful for Rb clock with lower performance goals or other instruments involving a compact, stabilized laser source.
Figure 4 shows the results of clock stability measurements, where for comparison both the “Doppler” and “sub-Doppler” schemes were used. Obviously the clock performance is degraded with the “Doppler” laser stabilization already at very short integration times, and remains essentially constant at a level around 3·10-12, although the laser frequency stability from Fig. 4 should be sufficient to meet the same clock performance as with the “sub-Doppler” stabilization for up to 100 seconds. We attribute the difference in clock stability mainly to the fact that with the “Doppler” scheme the laser is stabilized at a frequency detuning of about 250 MHz from the point of zero light shift, where light shift effects due to laser intensity fluctuations is strongly increased compared to the much smaller detuning around 40 MHz for sub-Doppler stabilization to the cross-over CO 21-23 line. Furthermore, the “Doppler” stabilization scheme requires a much larger FM modulation amplitude on the laser, which can contribute to additional detection noise via conversion in the clock resonance cell.
Light Shift Effects
One mayor limitation in laser-pumped Rb clocks arises from the light shift effect, i.e. from the change of atomic level energies induced by the interacting pump light field. Figure 5 shows the resulting light shift of the clock frequency measured for our laser-pumped clock as a function of both the laser frequency and intensity, where the bottom trace also shows the absorption signal of the laser head reference cell. As can be seen, the depicted situation does not allow to stabilize the laser frequency exactly to the zero light shift point, but even for stabilization to the closest reference line (CO 21-23) a detuning of about 40 MHz persists. Accordingly, in addition to the light shift related to frequency instabilities of the laser, light shifts mediated by pump light intensity fluctuations will also degrade the clock stability. In order to reduce these limitations, the laser detuning from the zero light shift point and laser fluctuations have to be reduced, or the susceptibility of the clock to the light shift, i.e., the slopes and offsets of the curves in Fig. 5 needs to be diminished, as described in the next paragraph.
New Strategies for Light Shift Reduction
The reduction of light shift effects has been an active field of research in the past and several approaches have been developed for atomic clocks based on optical pumping  and coherent population trapping [9,10], which however often complicate the physical clock realization. We have recently developed a new and simple method to suppress the influence of the light shift on the clock transition, with respect to both frequency and intensity fluctuations . This method relies on frequency modulation of the laser pump light at a frequency around 500-600 MHz, corresponding to the width of the light shift curve of the clock transition. At suitably chosen modulation parameters, one can balance the light shift contributions from the resulting sidebands in the laser spectrum in such a way that their respective positive and negative light shift contributions cancel out. This results in a “self-correction plateau” of several hundreds MHz width (region of the dashed ellipse in Fig. 6), where the slope of the light shift curves and thus the susceptibility to laser frequency fluctuations is strongly suppressed. Furthermore, as shown in Fig. 6, the offset of the self-correction plateau can be made to coincide with the level of zero light shift, thus resulting in a simultaneous suppression of the light shift due to intensity variations as well . This technique provides an excellent possibility to relax the requirements on the frequency and intensity stability of the pump light source.
We have realized a compact, frequency stabilized laser head and demonstrated its implementation in a laser-pumped Rb atomic clock. We have studied the influence of light shift effects due to offsets and fluctuations of both frequency and intensity of the pump laser. These effects have different impact on the clock performance, depending which type of the laser stabilization schemes studied (Doppler and sub-Doppler) was used in the clock. Limitations imposed by the reduced frequency stability of the Doppler scheme could be overcome by novel techniques for light-shift reduction based on multi-frequency optical pumping using FM modulation of the pump laser. The combination and optimization of these techniques should allow to realize a compact high-performance Rb clock, reaching 10-14 at 105 seconds, for space applications.
This work was financially supported by the European Space Agency (ESA/ESTEC, contract 5280/01/NL/US), the Swiss National Science Foundation (contracts 2100-66821, R’Equip 2160-067498, SCOPES JRPBUPJ062412), Canton of Neuchâtel, and the Swiss Confederation (Art. 16). We thank Temex Neuchâtel Time – and in particular Fabien Droz and his team - for the fruitful collaboration and for providing the clock module and for its repeated modifications and improvements. We acknowledge collaborations with the Group of Prof. S. Cartaleva, Institute of Electronics, Bulgarian Academy of Sciences (Sofia, Bulgaria) and the Atomics Physics Group of Prof. Weis, University of Fribourg (Switzerland).
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