We present an evaluation of the long-term frequency instability and environmental sensitivity of a chip-scale atomic clock based on coherent population trapping (CPT), particularly as affected by the light source subassembly. The long-term frequency stability of this type of device can be dramatically improved by judicious choice of operating parameters of the light source subassembly. We find that the clock frequency is influenced by the laser injection current, laser temperature and RF modulation index. The sensitivity of the clock frequency to changes in laser injection current or substrate temperature can be significantly reduced through adjustment of the RF modulation index. This makes the requirements imposed on the laser temperature stabilization, in order to achieve a given frequency stability, less severe. The clock frequency instability due to variations in local oscillator power is shown to be reduced through the choice of an appropriate light intensity inside the cell. While this work is intended to improve the performance of a chip-scale device, it is applicable to similar compact atomic clocks based on coherent population trapping.

There are several aspects that make a chip-scale atomic clock (CSAC) different from a conventional lamp-pumped compact atomic clock system. A typical CSAC architecture is shown in the figure above. First, the light source in a CSAC device is a laser as opposed to a lamp; the wavelength of the laser light depends strongly on the injection current and temperature of the laser. These two dependencies are especially high in vertical cavity surface emitting lasers (VCSEL) which are the lasers of choice in CSAC structures due to their low power consumption and high modulation efficiency. The change of laser wavelength with temperature and laser injection current makes the clock frequency dependent on laser operating parameters through the AC Stark shift. Second, coherent population trapping rather than a microwave field is used to excite the hyperfine resonance. The multiplicity of optical field frequencies required for CPT complicate the way in which the AC Stark shift plays a role. If the optical fields are generated by a modulated diode laser, the spectrum depends sensitively on the FM and AM modulation indices. Since the output power of a small, low power local oscillator is more unstable than that of their counterpart in a compact atomic reference, the dependence of the frequency of the CSAC on the LO output power increases in importance. Therefore, through the AC Stark effect, the external control parameters of the optics assembly (laser current, laser temperature and RF power) all influence the clock frequency, as shown schematically in (b) above.

Ambient temperature change is one of the major contributions to the long term frequency instability of the small clocks. While the sensitivity of the clock frequency to cell temperature can be largely compensated by use of buffer gas mixtures, the sensitivity of the clock frequency to temperature induced changes in the parameters of the optics subassembly (which includes the laser) remains an unaddressed difficulty. In this work it is shown that this sensitivity can be significantly reduced. We also show that the sensitivity of the clock frequency to power fluctuations of the local oscillator can be reduced simultaneously, which is of importance when the size and power consumption of the LO are restricted. The fractional frequency deviation as a function of the substrate temperature for etched mesa structure (left) and oxide-confined structure (right) lasers at different RF power levels is shown in the figure below.

In (b) above, the shaded area represents the region where the change in the clock frequency versus laser substrate temperature is minimized. From (a) it is clear that choosing a proper modulation index can make the clock frequency largely insensitive to changes in laser temperature (and therefore intensity). Unfortunately, (b) shows that for some lasers this reduced sensitivity is only achieved over a limited temperature range.

The CPT clock frequency versus RF power at different light intensities is shown in the figure below.

As can be seen from the selected region, it is possible to reduce the drift of the clock frequency caused by RF power changes to 1.4 × 10-12 (%)-2 (fractional frequency deviation per RF power change, in percent squared) by choosing an appropriate light intensity inside the cell. The frequency variation (solid triangles) is 7 × 10-10 per 2 dB change of the RF power around the selected region in the figure. The short-term stability of the clock is not degraded by more than a factor of two at any of the light intensities and laser RF modulation levels shown in the figure above. A comparison of the frequency stability at two RF power levels, one corresponding to best short-term stability and the other corresponding to the best long-term stability, is shown in the figure below.

Therefore, we conclude that by properly choosing the laser operating parameters, the clock frequency drifts can be reduced to below the 10-9 K-1 level. The impact RF power instabilities have on the clock frequency can also be minimized by adjusting the laser intensity inside the alkali cell. Reducing the small clock sensitivity to these external parameters will lead to a better long-term stability of the clock frequency.

References:

V. Gerginov, S. Knappe, P. Schwindt, V. Shah, L.W. Hollberg and J. Kitching, Long-term frequency instability of CPT clocks with microfabricated vapor cells, J. Opt. Soc. Am. B 23, 593-597 (2006).

V. Gerginov, V. Shah, S. Knappe, L.W. Hollberg and J. Kitching, Atom-based stabilization for laser-pumped atomic clocks, Opt. Lett. 31, 1851-1853 (2006).

S. Knappe, V. Gerginov, P. D. D. Schwindt, V. Shah, H. G. Robinson, L. Hollberg, and J. Kitching, "Atomic vapor cells for chip-scale atomic clocks with improved long-term frequency stability," Opt. Lett., 30, 2351, 2005.

S. Knappe, L. Liew, V. Shah, P. Schwindt, J. Moreland, L. Hollberg and J. Kitching, "A microfabricated atomic clock," Appl. Phys. Lett., 85, 1460, 2004.