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Applied Optics

Optimizing modulation transfer spectroscopy signals for frequency locking in the presence of depleted saturating fields

David J. HOPPER, Esa A. Jaatinen

Published Apr 30, 2008• 7 citations
Publisher

Abstract

A theoretical model of modulation transfer spectroscopy (MTS) that includes pump beam depletion is presented and experimentally verified with data covering visible iodine transitions at 532, 543, and 612 nm. This model is used to determine the values for pressure, interaction length, and saturation intensity that yield maximum MTS signals for frequency locking to iodine transitions. The approach is demonstrated for iodine transitions at 532, 633, and 778 nm, with the results showing that theoretically the frequency instability scales inversely to the absorption coefficient.

DOI
10.1364/ao.47.002574

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A theoretical model of modulation transfer spectroscopy (MTS) that includes pump beam depletion is presented and experimentally verified with data covering visible iodine transitions at 532, 543, and 612 nm. This model is used to determine the values for pressure, interaction length, and saturation intensity that yield maximum MTS signals for frequency locking to iodine transitions. The approach is demonstrated for iodine transitions at 532, 633, and 778 nm, with the results showing that theoretically the frequency instability scales inversely to the absorption coefficient.
We make a detailed comparison of frequency modulation spectroscopy (FMS) and modulation transfer spectroscopy (MTS) and of their applications in stabilizing laser frequency. In both FMS and MTS, intensity modulations of probe beam are observed in saturated absorption spectroscopy of 87Rb atoms. However, the two modulation profiles appear different due to their distinct origins. Demodulation gives rise to frequency discrimination spectra, which can serve as error signals for frequency locking. The optimal error signal of FMS has a larger linear slope but also a slanted baseline, in contrast to that of MTS. We apply FMS and MTS to stabilize two 780 nm external cavity diode lasers to D2 lines of 87Rb atoms. We measure laser linewidth and stability using beat notes of two independently locked lasers. A laser linewidth as narrow as 12.9 kHz is achieved in FMS locking, compared to 70.8 kHz in MTS locking. A laser stability at the level of 10−12 is reached in both schemes. Nevertheless, FMS locking offers a better short-term stability, whereas MTS locking yields a smaller long-term drift. Our investigation of FMS and MTS would be valuable for making a choice of these spectroscopy techniques for laser stabilization as well as other relevant applications.
Modulation transfer spectroscopy (MTS) is widely used in an optical laboratory for laser frequency stabilization. There have been many theoretical and experimental papers on this spectroscopic method. However, most of the works focus on the cycling transitions like the D2 line of rubidium. In this paper, the MTS for noncycling transitions is investigated. We consider the D1 line of rubidium whose modulation transfer spectrum has been determined and compared to the polarization spectrum. It is found that the slope of the modulation transfer signal is sharper than the polarization spectrum. The performance of laser frequency locking based on the MTS method is better than that of the polarization spectroscopy method. The dependence of the signal amplitude on the temperature of the vapor cell was analyzed, and the high signal-to-noise-ratio spectra are achieved for D1 open transitions. The obtained results provide an effective spectroscopic method for the robust frequency locking of a laser at a wavelength of 795 nm.
The modulation transfer spectroscopy (MTS) technique used to stabilize two different transition lines of rubidium, required for laser cooling of atoms, is investigated. The laser source is based on a 1560 nm semiconductor laser diode that is amplified by an erbium doped fiber amplifier (EDFA). The laser output is frequency doubled with a fiber coupled periodically poled Lithium Niobate (PPLN) crystal to 780 nm. To address the weak spectral features of repumping laser, a theoretical study is conducted followed by experimental verification. The 87Rb D2 line F = 1 → F' = 0 transition temperature-enhanced MTS signal is observed, which provides a choice to stabilize the repumping laser frquency on the F = 1 → F ' = 2 transition using frequency shifting with acousto-optic modulators (AOMs). Compared with the orignal MTS signal, this method is shown to be more stable and accurate for laser frequency locking. Laer frequency locking is realized by controlling the driving current of the seed laser using digital PID feedback. After locking, the laser linewidth is 35.36 kHz.
In a spin-exchange relaxation-free (SERF) atomic magnetometer, the pump and probe laser frequencies are tuned to the D 1 transition line of alkali metal atoms to enhance measurement sensitivity. The D 1 line, a non-cycling transition, exhibits a low absorption coefficient. This study theoretically analyzes the influence of different parameters on the absorption coefficient of the D 1 line and proposes a polarization-dependent approach to enhance it. A frequency stabilization method based on modulation transfer spectroscopy (MTS) with an enhanced absorption coefficient is introduced. Compared with the conventional method, optimizing the probe beam’s polarization increases the absorption coefficient, raising the amplitude of the MTS signal. The results show that using a stronger MTS signal for frequency stabilization reduces the laser's frequency noise. Using heterodyne measurement, we characterize the linewidth-narrowing effect of MTS locking and evaluate the frequency stability of the locked laser. The linewidth of each laser is reduced from the free-running 2.2 MHz to 885 kHz after MTS stabilization. The Allan deviation measurements of the beat signal between two locked lasers are 2.6 × 10 −11 / τ . This work provides a stable optical frequency reference for SERF atomic magnetometers and offers potential applications in extracting spatial information from optically pumped atoms.
Active frequency stabilization of a laser to an atomic or molecular resonance underpins many modern-day AMO physics experiments. With a flat background and high signal-to-noise ratio, modulation transfer spectroscopy (MTS) offers an accurate and stable method for laser locking. Despite its benefits, however, the four-wave mixing process that is inherent to the MTS technique entails that the strongest modulation transfer signals are only observed for closed transitions, excluding MTS from numerous applications. Here, we report for the first time the observation of a magnetically tunable MTS error signal. Using a simple two-magnet arrangement, we show that the error signal for the 87Rb F = 2 → F' = 3 cooling transition can be Zeeman-shifted over a range of ~10 GHz to any arbitrary point on the rubidium D2 spectrum. Modulation transfer signals for locking to the 87Rb F = 1 → F' = 2 repumping transition as well as 1 GHz red-detuned to the cooling transition are presented to demonstrate the versatility of this technique, which can readily be extended to the locking of Raman and lattice lasers.
We present a high-performance laser frequency stabilization method using modulation transfer spectroscopy (MTS) on the rubidium 87 D 2 transition line. A substantial improvement of the laser frequency stability was achieved by searching for the optimal diameter and intensity settings of the probe and pump beam. The frequency instability measured from the beat frequency of two locked external cavity diode lasers (ECDLs) reached a short-term stability of 4.5 × 10 − 14 / τ and did not exceed 2 × 10 −12 until 10 5 s, which is the best performance reported thus far with a D 2 transition. The long-term stability is limited by the offset fluctuations of the baseline induced by the residual amplitude modulation (RAM), which can be further improved by reducing the current temperature variation of about 0.2 K by means of temperature stabilization or through a further reduction of the RAM.