VCSELs in nonlinear spectroscopy: making optical magnetometers and atomic clocks practical

Institute for Applied Physics, Bonn University, D-53115 Bonn, Germany

* National Institute of Standards and Technology, Boulder, CO 80303, USA

Tel +49-228-733483, Fax +49-228-733474, E-mail: wynands@iap.uni-bonn.de

Abstract

We describe the use of VCSELs in optical magnetometry at the picotesla level and in miniaturized atomic clocks. The performance is limited by VCSEL noise.

We have experimentally investigated the potential of narrow coherent population trapping (CPT) resonances [1] for precision applications like magnetometry [2, 3], miniaturized atomic frequency standards [4,5], and the determination of atomic g-factors [6] using the D lines in thermal Cs or Rb vapor. These narrow resonances (widths smaller than 100 Hz are routinely achieved) are probed by a bichromatic laser light field with a frequency difference in the GHz range (9.2 GHz, 6.7 GHz, and 3.0 GHz for Cs, Rb-87, and Rb-85, respectively). This light field can conveniently be derived from a current-modulated single-mode VCSEL, using the carrier and one of the modulation sidebands [7]. This allows for the construction of extremely compact setups with not more than a few 100 mW of electrical power consumption.

When a small magnetic offset field is applied the CPT resonance splits into several Zeeman components. The magnetometer works by monitoring the position of the Zeeman-shifted outermost resonance component. The central Zeeman component is well suited for frequency standard applications because its position is shifted by magnetic fields only in second order. Certain other components lend themselves readily for a determination of the ratio of electronic and nuclear magnetic moments in the atom (g-factor ratio). Picotesla sensitivity for a magnetometer and 10^{-12} relative instability for a finger-sized clock have been achieved in this way (Fig. 1), and a relative inaccuracy of the g-factor ratio of better than 10^{-6} is envisioned for the near future.

## Fig. 1. (a) Magnetometric sensitivity of the Cs dark resonance magnetometer [3]. (b) Allan standard deviation of a compact Cs dark resonance clock [5]. |

## Fig. 2: Detector noise power spectral density as a function of detuning of the laser frequencies from optical resonance (dots: experimental data, dashed line: calculation using the FM and AM noise of the laser, solid line: frequency-dependent optical pumping included) [5]. |

The common problem for all such precision measurements is to gain a thorough understanding of possible systematic effects and of the noise processes limiting the precision. Apart from “the usual suspects” in that context we have identified a new noise source connected to optical hyperfine pumping [8]. Fig. 2 shows the measured detection noise power spectral density (dots) as a function of laser detuning from resonance with the optical transitions. The dashed line is a calculation based on the measured frequency (FM) and amplitude (AM) noise of the laser. The peculiar shape reflects the absolute value of the slope of the Doppler-broadened optical absorption line: laser FM noise is converted at this slope into AM noise behind the vapor cell. Surprisingly, the whole curve is shifted by about 40 MHz from the center of the optical absorption spectrum. When this shift is included the calculation agrees very well with the experimental data (solid line in Fig. 2).

## Table. A very optimistic estimate of the anticipated improvements in signal and noise level if advanced VCSELs were available. |

The shift can be explained and modeled by considering the dependence of the optical hyperfine pumping on the Fourier frequency of the noise. This model further predicts the presence of an additional noise term that is also responsible for the fact that the noise minimum lies somewhat higher than the shot and laser AM noise level. This excess noise should also occur in other types of atomic clocks that involve optical pumping. Furthermore, the shift of the noise minimum with respect to the optical absorption maximum implies a similar shift of the optimum operating point of the dark resonance magnetometer or clock.

The newly-discovered excess noise as well as the general performance of the devices is mainly limited by the FM noise of the VCSEL. The table shows a very optimistic estimate of the improvements in signal-to-noise ratio one can hope for when VCSELs with certain improved characteristics were available. The development of VCSELs with lower 1/f noise, smaller linewidths but still large modulation bandwidth is therefore highly desirable for these applications.

References

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*Europhys. Lett.*44, 31 (1998). - M. Staehler et al., “Picotesla magnetometry with coherent dark states”, Europhys. Lett. 53, 323 (2001).
- J. Kitching et al., “A microwave frequency reference based on VCSEL-driven
dark line resonances in Cs vapor”,
*IEEE Trans. Instrum. Meas.*49, 1313 (2000). - S. Knappe et al., “Characterization of coherent population trapping resonances
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*J. Opt. Soc. Am. B*, in the press. - A. Nagel et al., “Influence of excited state hyperfine structure on ground
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