We discuss the prospects for enhancing absorption and scattering of light from a weakly coupled atom in a high-finesse optical cavity by adding a medium with large, positive group index of refraction. The slow-light effect is known to narrow the cavity transmission spectrum and increase the photon lifetime, but the quality factor of the cavity may not be increased in a metrologically useful sense. Specifically, detection of the weakly coupled atom through either cavity ringdown measurements or the Purcell effect fails to improve with the addition of material slow light. A single-atom model of the dispersive medium helps elucidate why this is the case.
We discuss the prospects for enhancing absorption and scattering of light from a weakly coupled atom in a high-finesse optical cavity by adding a medium with large, positive group index of refraction. The slow-light effect is known to narrow the cavity transmission spectrum and increase the photon lifetime, but the quality factor of the cavity may not be increased in a metrologically useful sense. Specifically, detection of the weakly coupled atom through either cavity ringdown measurements or the Purcell effect fails to improve with the addition of material slow light. A single-atom model of the dispersive medium helps elucidate why this is the case.
We discuss the prospects for enhancing absorption and scattering of light from a weakly coupled atom in a high-finesse optical cavity by adding a medium with large, positive group index of refraction. The slow-light effect is known to narrow the cavity transmission spectrum and increase the photon lifetime, but the quality factor of the cavity is not increased in a metrologically useful sense. Specifically, detection of the weakly coupled atom through either cavity ringdown measurements or the Purcell effect fails to improve with the addition of material slow light. A single-atom model of the dispersive medium helps elucidate why this is the case.
Summary form only given. Optical microcavities with high quality factors Q are of great interest in integrated micro- and nanophotonics. Their narrow resonance and long photon lifetime (τcav) can be used in fundamental physics, sensing applications, microwave signal optical processing or for optical delay line and memory miniaturization [1]. Considering a Lorentzian resonance profile, the quality factor and the photon lifetime of a microcavity with a resonant angular frequency ωο = 2·πε/λ0reads: Q = ω0τcab= nG(ω0)LF/λ0, (1) where ngis the group index of the material constituting the microcavity, F is the finesse and L is the cavity round-trip length. The usual method to obtain ultra-high quality factors consists in optimizing the manufacturing process to reach high finesse values. Following this approach record quality factors up to 1011have been measured in millimetric CaF2 whispering gallery mode (WGM) resonators [2]. Otherwise, Eq. (1) shows that for a given finesse, the use of resonators made with slow-light materials displaying high group indices can also increase the quality factor. This method has already been successfully implemented in bulky resonators including a highly dispersive slow-light medium [3]. We have recently demonstrated that this approach can be applied to solid-state optical micro-resonators [4]. The slow-light effect was introduced thanks to population oscillations in an Er3+doped WGM fluoride glass microsphere (diameter 100 μm). Since the lifetime of the4I13/2level is very long (T ≈ 10 ms) strong group index up to 106can be obtained. Using a cavity-ring-down method (see Fig. 1) in a pump probe configuration, we have measured a photon lifetime of 2.5 ms at 1530 nm corresponding to a quality factor of 3 × 1012[4].
We have measured mode pushing by the dispersion of a rubidium vapor in a Fabry-Perot cavity and have shown that the scale factor and sensitivity of a passive cavity can be strongly enhanced by the presence of such an anomalous dispersion medium. The enhancement is the result of the atom-cavity coupling, which provides a positive feedback to the cavity response. The cavity sensitivity can also be controlled and tuned through a pole by a second, optical pumping, beam applied transverse to the cavity. Alternatively, the sensitivity can be controlled by the introduction of a second counter-propagating input beam that interferes with the first beam, coherently increasing the cavity absorptance. We show that the pole in the sensitivity occurs when the sum of the effective group index and an additional cavity delay factor that accounts for mode reshaping goes to zero, and is an example of an exceptional point, commonly associated with coupled non- Hermitian Hamiltonian systems. Additionally we show that a normal dispersion feature can decrease the cavity scale factor and can be generated through velocity selective optical pumping.
When a coherently prepared atomic medium is confined in an optical cavity, the atomic coherence and interference manifested by electromagnetically induced transparency (EIT) can be manipulated and enhanced by the collective atom–cavity coupling and the cavity feedback. We present an experimental study of the light transmission through an optical cavity coupled with coherently prepared cold Rb atoms. In the frequency domain, the cavity transmission spectrum exhibits spectral peaks representing the cavity normal modes associated with the multi-atom vacuum Rabi splitting and the intra-cavity dark state manifested by the combined EIT effects of the absorption suppression and the steep normal dispersion. In the time domain, a light pulse coupled into the cavity mode propagates with a slow group velocity and the propagation time delay is significantly increased by the cavity feedback.
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.
We investigate how the use of slow-light methods can enhance the performance of various types of spectroscopic interferometers under practical conditions. We show that, while in ideal cases the enhancement of the spectral resolution is equal to the magnitude of the group index of the slow-light medium, the ratio between the associated gain or loss and the group index of the slow-light medium actually determines the spectral resolution under more-general conditions. Moreover, the dispersion of this ratio leads to frequency-dependent spectral resolution, which limits the useful working bandwidth of the interferometer. We also evaluate the performance of interferometers using three specific slow-light processes in terms of the achievable spectral resolution and the effective working finesse. We show that the spectral resolution is typically limited by the characteristic linewidth of each slow-light process and that there is no fundamental upper limit for the effective working finesse.