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Temperature Sensitivity of an Atomic Vapor Cell-Based Dispersion-Enhanced Optical Cavity

Krishna Myneni, H. Chang, D. D. Smith, H. A. Luckay

Published Jan 1, 2015• 0 citations
OpenAlex

Abstract

Enhancement of the response of an optical cavity to a change in optical path length, through the use of an intracavity fast-light medium, has previously been demonstrated experimentally and described theoretically for an atomic vapor cell as the intracavity resonant absorber. This phenomenon may be used to enhance both the scale factor and sensitivity of an optical cavity mode to the change in path length, e.g. in gyroscopic applications. We study the temperature sensitivity of the on-resonant scale factor enhancement, S(sub o), due to the thermal sensitivity of the lower-level atom density in an atomic vapor cell, specifically for the case of the Rb-87 D(sub 2) transition. A semi-empirical model of the temperature-dependence of the absorption profile, characterized by two parameters, a(sub o)(T) and gamma(sub a)(T) allows the temperature-dependence of the cavity response, S(sub o)(T) and dS(sub o)/dT to be predicted over a range of temperature. We compare the predictions to experiment. Our model will be useful in determining the useful range for S(sub o), given the practical constraints on temperature stability for an atomic vapor cell.

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•Jul 28, 2014•0 citations
Enhancement of the response of an optical cavity to a change in optical path length, through the use of an intracavity fast-light medium, has previously been demonstrated experimentally and described theoretically for an atomic vapor cell as the intracavity resonant absorber. This phenomenon may be used to enhance both the scale factor and sensitivity of an optical cavity mode to the change in path length, e.g. in gyroscopic applications. We study the temperature sensitivity of the on-resonant scale factor enhancement, S(sub o), due to the thermal sensitivity of the lower-level atom density in an atomic vapor cell, specifically for the case of the Rb-87 D(sub 2) transition. A semi-empirical model of the temperature-dependence of the absorption profile, characterized by two parameters, a(sub o)(T) and gamma(sub a)(T) allows the temperature-dependence of the cavity response, S(sub o)(T) and dS(sub o)/dT to be predicted over a range of temperature. We compare the predictions to experiment. Our model will be useful in determining the useful range for S(sub o), given the practical constraints on temperature stability for an atomic vapor cell.
We derive analytic expressions for the on-resonant cavity scale factor enhancement dependence on temperature, S0(T){S}_{0}(T)S0​(T), for an intracavity medium with a Gaussian absorption resonance. Results are expressed as functions of the cavity parameters and the two resonance parameters: ${\ensuremath{\alpha}}_{0}(T)$, the peak absorption coefficient, and ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\alpha}}^{R}(T)$, the resonance width. A semiempirical model is developed for the temperature-dependent absorption coefficient, ${\ensuremath{\alpha}}_{F}(\mathrm{\ensuremath{\Delta}},T)$, in an alkali-metal-atom vapor cell, and is used to compare the predicted behavior of ${\ensuremath{\alpha}}_{0}(T)$ and ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\alpha}}^{R}(T)$ with the measured values for the $D{}_{2}\phantom{\rule{0.28em}{0ex}}F=2\ensuremath{\rightarrow}{F}^{\ensuremath{'}}$ resonance in 87Rb^{87}\mathrm{Rb}87Rb, over the temperature range 298--325 K. Measurements of S0(T){S}_{0}(T)S0​(T) in a low-finesse ring cavity, using the same vapor cell as the intracavity dispersive medium, were performed and found to be in agreement with the temperature-dependent behavior predicted by our theory, with quantitative agreement to 2 K for the critical temperature. The practical range of S0{S}_{0}S0​ is found to be limited by the achievable temperature stability of the resonance parameters of the dispersive medium.
We demonstrate the operation of a closed-loop fast-light cavity that allows rapid (~10 ms) measurements of the cavity mode frequency and its uncertainty. We vary the scale factor by temperature tuning the atomic density of an intracavity vapor cell. The cavity remains locked even as the system passes through the critical anomalous dispersion where a pole is observed in the scale factor. Positive and negative scale-factor enhancements as large as |S| ≈70 were obtained. To our knowledge, these are the first experiments that demonstrate a scale-factor enhancement in a closed-loop fast-light device by changing the optical path length, laying the groundwork for the improvement of cavity-based metrology instruments such as optical gyroscopes.
The pushing of the modes of a Fabry-Perot cavity by an intracavity rubidium cell is measured. The scale factor of the modes is increased by the anomalous dispersion and is inversely proportional to the sum of the effective group index and an additional cavity delay factor that arises from the variation of the Rb absorption over a free spectral range. This additional positive feedback further increases the effect of the anomalous dispersion and goes to zero at the lasing threshold. The mode width does not grow as fast as the scale factor as the intracavity absorption is increased resulting in enhanced measurement sensitivities. For absorptions larger than the scale factor pole, the atom-cavity response is multivalued and mode splitting occurs.
We demonstrate for a passive optical cavity containing a dispersive atomic medium, the increase in scale factor near the critical anomalous dispersion is not cancelled by mode broadening or attenuation, resulting in an overall increase in the predicted quantum-noise-limited sensitivity. Enhancements of over two orders of magnitude are measured in the scale factor, which translates to greater than an order-of-magnitude enhancement in the predicted quantum-noise-limited measurement precision, by temperature tuning a low-pressure vapor of non-interacting atoms in a low-finesse cavity close to the critical anomalous dispersion condition. The predicted enhancement in sensitivity is confirmed through Monte-Carlo numerical simulations.
In this work we investigate the transmission in an optical cell containing an atomic vapor, when a laser is tuned to the wings of the Doppler line, presenting inhomogeneous broadening. The experiment is designed to detect the transmission of a laser beam through a an atomic cesium vapor within a quartz cell. Due to the high atomic density in the 1 mm cell, the laser beam is totally absorbed at resonance. On the other hand, when the detuning by few GHz from the center of the line an oscillatory signal is observed as a function of the laser frequency. The amplitude of the transmission signal varies linearly with the laser intensity. These oscillations exhibit diferent behavior as we change some parameters of the system, and the rate of the oscillations vary with laser detuning and on the atomic density. The phase of the transmited field is also sensitive to the angle of incidence of the laser beam in the cell, which allows to vary the lineshape of the signal without changing the parameters of the laser (intensity, frequency, ...) or atomic vapor. Out of resonance with the atomic vapor, the parallel windows of commercial optical cell cavity works as a low finesse Fabry-Pérot with a free spectral range of 150 GHz. However, in resonance, the optical path of the cavity changes varies with frequency due to the dispersive response of the atomic vapor. This study experimentally characterized the transmission signal through a cavity containing resonant vapor as a function of intensity and frequency of the laser, as well as its dependence on the angle of incidence of the beam. A numerical model that allows to determine the collisional broadening of the atomic vapor adjusting the spectral curves of the transmission signal was developed. As an application, exploring the oscillations in the wings of the resonance, we can lock the laser frequency at a few GHz off the center of the atomic resonance. The lock was performed in the frequency range between 0,8 GHz and 2,4 GHz from the center of the D2 line of cesium. To characterize the locking stability we measure the optical beat signal between two similar experiments, using the same locking technique.