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arXiv:1902.06926 · Optics Express

Large optical depth frequency modulation spectroscopy

Chang Chi Kwong, E. A. Chan, S. A. Aljunid, R. Shakhmuratov, David Wilkowski

Published Oct 23, 2019• 3 citations
arXivHTMLPDF

Abstract

Band-resolved frequency modulation spectroscopy is a common method to measure weak signals of radiative ensembles. When the optical depth of the medium is large, the signal drops exponentially and the technique becomes ineffective. In this situation, we show that a signal can be recovered when a larger modulation index is applied. Noticeably, this signal can be dominated by the natural linewidth of the resonance, regardless of the presence of inhomogeneous line broadening. We implement this technique on a cesium vapor, and then explore its main spectroscopic features. This work opens the road towards measurement of cooperative emission effects in bulk atomic ensemble.

DOI
10.1364/oe.27.032323

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Band-resolved frequency modulation spectroscopy is a common method to measure weak signals of radiative ensembles. When the optical depth of the medium is large, the signal drops exponentially and the technique becomes ineffective. In this situation, we show that a signal can be recovered when a larger modulation index is applied. Noticeably, this signal can be dominated by the natural linewidth of the resonance, regardless of the presence of inhomogeneous line broadening. We implement this technique on a cesium vapor, and then explore its main spectroscopic features. This work opens the road towards measurement of cooperative emission effects in bulk atomic ensemble.
We present a detailed analysis of an application of frequency modulation (FM) spectroscopy in the high modulation depth limit. We have recently completed and reported a measurement of the Stark shift in the indium 5p1/2→6s1/25p_{1/2}\rightarrow 6s_{1/2}5p1/2​→6s1/2​ 410 nm transition using this spectroscopy method [Ranjit, et al. Phys. Rev. A 87, 032506 (2013)]. FM spectroscopy proved essential to resolve spectroscopic features in an atomic beam where the optical depth was ∼10−3\sim 10^{-3}∼10−3. A dual-modulation scheme is described which ensures truly background-free FM signals even in the low-density limit. Lock-in detection of the FM signal was accomplished using both the fundamental (1f) and second-harmonic (2f) modulation frequencies. A derivation of both the 1f and 2f signal line shapes in the high-modulation-depth limit is presented. These line shapes form the basis for quantitative fits to a wide variety of experimental FM spectra.
The advent of lasers has revolutionized the methods and possibilities of spectroscopy. Their monochromaticity permits the study of extremely narrow spectral features which would not have been resolved using classical techniques. Moreover, their extreme spectral power density, in giving rise to the field of nonlinear optics, which will be studied in Chapter 7, has resulted in the development of new and powerful spectroscopic techniques. These techniques, of which we describe briefly some examples in this complement, have as their basis the fact that an atom does not respond linearly when subjected to a very intense light field. First of all we shall describe the broadening mechanisms that explain the fact that the experimentally measured widths of atomic or molecular resonances are larger than those that would be observed if the atoms were isolated and at rest. We shall introduce in Section 3G.1 the concept of homogeneous width, which can be considered as the intrinsic width of a transition, and inhomogeneous width which concerns the variation of the frequency of a given transition that occurs because of the state of motion of the atom, or because of factors in its environment. We shall explain why it is possible, using nonlinear optical techniques to eliminate the effects of inhomogeneous broadening on recorded spectra, resulting in an improvement over the resolution of conventional techniques. We shall then concentrate more specifically on Doppler broadening , which is the most commonly encountered source of inhomogeneous broadening, describing two nonlinear optical techniques, saturated absorption spectroscopy (in Section 3G.2) and two-photon spectroscopy (in Section 3G.3), which enable it to be overcome.
Spectroscopic properties of coherently prepared, optically dense atomic media are studied experimentally and analyzed theoretically. It is shown that in such media the power broadening of the resonances can be substantially reduced. A density-dependent spectral narrowing of the electromagnetically induced transparency (EIT) window and novel, even narrower, resonances superimposed on the EIT line are observed in dense Rb vapor. A nonlinear two-photon spectroscopic technique based on coherent atomic media and combining high resolution with a large signal-to-noise ratio seems feasible.
Ramsey resonance is a high-resolution technique used in spectroscopy, precise measurement of time and frequency, and the creation of modern clocks. The Ramsey experiments are typically done in optically dilute samples of atoms to improve homogeneity and avoid backaction of atoms on excitation pulses. In contrast to latter belief, we predict and experimentally show that in optically thick resonant media, the backaction can lead to the highly enhanced narrowing of Ramsey resonance. The linewidth narrowing and corresponding precision of the frequency measurement scale exponentially with an increase in optical depth of a sample and can reach the limits set by homogeneous broadening. We show that this effect is caused by a nonlinear interference of multiple echoes formed inside the atomic medium, which is experimentally confirmed with ^{167}Er^{3+} ions in Y_{2}SiO_{5} crystal. Our findings open new opportunities for sensitivity enhancement of the Ramsey technique, as well as providing researchers with an additional method to investigate fundamental issues of coherent nonlinear interaction of light pulses with resonant atomic ensembles and numerous applications.
Recently, we reported the first observation of the statistical fine structure (SFS) on an inhomogeneously broadened optical absorption line, the 0-0 origin transition of pentacene molecules in p-terphenyl crystals at liquid helium temperatures.1 SFS is a time-independent spectral structure resulting from number fluctuations in the spectral density of absorbers that we have detected directly using laser frequency modulation (FM) techniques. In our samples where the number of molecules per homogeneous linewidth N¯ H is large, a zero-background technique such as FM spectroscopy is optimal for detection of SFS because only the deviations of the absorption coefficient from the background value produce FM signals. In addition, for extremely low signal levels, we use double modulation with a Stark field to remove the effects of residual amplitude modulation in the modulator. Our goal is to describe the systematics and analysis of SFS spectra at a fixed low temperature, 1.6 K. For example, we show that the rms value of the SFS grows as the square root of N¯ H . More important, by computing the autocorrelation of the measured frozen noise spectra, the homogeneous linewidth can be determined to good accuracy without requiring spectral hole-burning or coherent transients. Since the source for SFS is fundamental statistical fluctuations in the absorber spectral density, SFS should occur for all inhomogeneously broadened lines; furthermore, the effect imposes a fundamental limit on the detectability of shallow spectral features in solids.