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arXiv:0810.4209 · Physical Review A

Quantum limits and robustness of nonlinear intracavity absorption spectroscopy

John K. Stockton, Ari K. Tuchman

Published Jan 27, 2009• 2 citations
arXivHTMLPDF

Abstract

We investigate the limits of intracavity absorption spectroscopy with nonlinear media. Using a common theoretical framework, we compare the detection of a trace gas within (i) an undriven cavity with gain near and above threshold; (ii) a driven cavity with gain kept just below threshold; and (iii) a cavity driven close to the saturation point of a saturable absorber. These phase-transition-based metrology methods are typically quantum limited by spontaneous emission, and we compare them to the empty-cavity shot-noise-limited case. Although the fundamental limits achievable with nonlinear media do not surpass the empty-cavity limits, we show that nonlinear methods are more robust against certain technical noise models. This recognition may have applications in spectrometer design for devices operating in nonideal field environments.

DOI
10.1103/physreva.79.013822

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We investigate the limits of intracavity absorption spectroscopy with nonlinear media. Using a common theoretical framework, we compare the detection of a trace gas within (i) an undriven cavity with gain near and above threshold; (ii) a driven cavity with gain kept just below threshold; and (iii) a cavity driven close to the saturation point of a saturable absorber. These phase-transition-based metrology methods are typically quantum limited by spontaneous emission, and we compare them to the empty-cavity shot-noise-limited case. Although the fundamental limits achievable with nonlinear media do not surpass the empty-cavity limits, we show that nonlinear methods are more robust against certain technical noise models. This recognition may have applications in spectrometer design for devices operating in nonideal field environments.
This paper presents a theoretical analysis of the optical properties of an optical cavity with both one- and two-photon intracavity absorption loss, without saturation. The cavity two-photon absorption loss per pass is assumed to be small, but otherwise the analysis is general. Analytical results for the cavity transmission as a function of cavity parameters, linear and two-photon intracavity loss, and detuning from resonance are derived and limiting cases discussed. Extraction of the two-photon loss from both cavity ring-down and cavity-enhanced absorption spectroscopy methods is analyzed and the predicted shot-noise limited sensitivities derived and compared. Numerical results are computed using the parameters of a recent experimental intracavity measurement of two-photon absorption of nitrous oxide. The results will be useful in the design and interpretation of cavity-enhanced, two-photon absorption spectroscopy.
We have carried out a linearized quantum analysis of the steady-state operation of an optical parametric oscillator (OPO) without cavity detunings; our analysis emphasizes the effects of pump quantum noise and pump excess noise. We show that pump excess noise reduces the observable signal/idler intensity correlation at low frequencies only in the presence of a cavity-loss mismatch between these subharmonic waves. This effect is so strong that the combination of pump excess noise and cavity-loss mismatch explains the rapid low-frequency noise increase well above the shot-noise level that has been seen in recent signal/idler correlation measurements. Moreover, the critical dependence of intensity correlation on cavity-loss mismatch opens a new possibility for ultrasensitive intracavity absorption spectroscopy. Specifically, sinusoidal amplitude modulation of the OPO pump beam with lock-in amplification of the signal/idler photocurrent affords a sensitive probe of subharmonic cavity-loss mismatch. Although this robust measurement capability exploits the strong intracavity correlation between the signal and idler waves, it does not require that nonclassical correlation be externally observable, nor is it limited to near-threshold OPO operation.
Cavity-enhanced absorption spectroscopy is now widely used as an ultrasensitive technique in observing weak spectroscopic absorptions. Photons inside the cavity are reflected back and forth between the mirrors with reflectivities R close to one and thus (on average) exploit an absorption pathlength L that is 1/(1 − R ) longer than a single pass measurement. As suggested by the Beer-Lambert law, this increase in L results in enhanced absorbance A (given by αL with α being the absorption coefficient) which in turn favours the detection of weak absorptions. At the same time, however, only (1 − R ) of the incident light can enter the cavity [assuming that mirror transmission T is equal to (1 − R )], so that the reduction in transmitted light intensity Δ I caused by molecular absorption equates to that would be obtained if in fact no cavity were present . The enhancement in A = Δ I / I , where I is the total transmitted light intensity, achievable from CEAS therefore comes not from an increase in Δ I , but a sharp decrease in I. In this paper, we calculate the magnitudes of these two terms before and after a cavity is introduced, and aim at interpreting the sensitivity improvement offered by cavity-enhanced absorption spectroscopy from this observable-oriented (i.e. Δ I and I ) perspective. It is first shown that photon energy stored in the cavity is at best as intense as the input light source, implying that any absorbing sample within the cavity is exposed to the same or even lower light intensity after the cavity is formed. As a consequence, the intensity of the light absorbed or scattered by the sample, which corresponds to the Δ I term aforementioned, is never greater than would be the case in a single pass measurement. It is then shown that while this “numerator” term is not improved, the “denominator” term, I , is reduced considerably; therefore, the increase in contrast ratio Δ I / I is solely contributed by the attenuation of transmitted background light I and is ultimately down to the suppression of any measurement noise that is associated with it. The noise component that is most effectively suppressed is the type whose magnitude scales linearly with light intensity I , as is typical of noise caused by environmental instabilities, followed by the shot noise which scales as square root of I . No suppression is achievable for noise sources that are independent of I , a notable example being the thermal noise of a detector or of detection electronics. The usefulness of this “noise suppression” argument is that it links the sensitivity gain offered by a cavity with the property of measurement noise present in the system, and clearly suggests that the achievable sensitivity is dependent on how efficient the various noise components are “suppressed” by the cavity.
Within the framework of quantum electrodynamics in dispersing and absorbing media, we have studied the quantum state of the radiation emitted from an initially in the upper state prepared two-level atom in a high-Q cavity, including the regime where the emitted photon belongs to a wave packet that simultaneously covers areas inside and outside the cavity. Furthermore, we have compared the results with those of quantum noise theory where the intracavity field and the field outside the cavity are regarded as approximately representing independent degrees of freedom such that two separate Hilbert spaces can be introduced.
We present an ac heterodyne technique in cavity ringdown spectroscopy that permits $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ absorption sensitivity with microwatt-level light power. Two cavity modes, one probing the empty cavity and the other probing intracavity absorption, are excited simultaneously but with their intensities temporally out of phase, with one mode decaying and the other rising. Heterodyne detection between the two modes reveals the dynamic time constants associated with the empty cavity and the additional intracavity gas absorption. The method offers a quick comparison between the on- and off-resonance information, a prerequisite to reaching the fundamental shot-noise limit. This simple and yet important improvement of cavity ringdown spectroscopy should lead to the enhanced performance of a wide range of applications.