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arXiv:1310.6465

Frequency Modulation Spectroscopy at High Modulation Depth in an Indium Atomic Beam

Nathan Schine, Gambhir Ranjit, Protik Majumder

Published Oct 24, 2013• 0 citations
arXivHTMLPDF

Abstract

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 $5p_{1/2}\rightarrow 6s_{1/2}$ 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 $\sim 10^{-3}$. 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.

DOI
10.48550/arxiv.1310.6465

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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.
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We discuss experimental observations of an induced phase shift of the rf signal produced in FM saturated absorption measurements under the conditions of large probe beam intensities. This phase shift can be understood in terms of the phase difference between the phase modulation of the optical driving field and the steady state macroscopic polarization of the medium. This phase difference is relatively insensitive to detuning of the laser from the atomic resonance, such that essentially the same spectrum can be observed by changing the rf detection phase. We also present theoretically calculated spectra which are based on the optical Bloch equations, and which are in excellent agreement with the experimental results.
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