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arXiv:1203.3338 · Physical Review A

Absolute absorption line-shape measurements at the shot-noise limit

Gar-Wing Truong, James D. Anstie, Eric F. May, Thomas M. Stace, Andre Nicholas Luiten

Published Sep 10, 2012• 17 citations
arXivHTMLPDF

Abstract

Here, we report a measurement scheme for determining an absorption profile with an accuracy imposed solely by photon shot noise. We demonstrate the power of this technique by measuring the absorption of cesium vapor with an uncertainty at the 2-ppm level. This extremely high signal-to-noise ratio allows us to directly observe the homogeneous line-shape component of the spectral profile, even in the presence of Doppler broadening, by measuring the spectral profile at a frequency detuning more than 200 natural linewidths from the line center. We then use this tool to discover an optically induced broadening process that is quite distinct from the well-known power broadening phenomenon.

DOI
10.1103/physreva.86.030501

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Here, we report a measurement scheme for determining an absorption profile with an accuracy imposed solely by photon shot noise. We demonstrate the power of this technique by measuring the absorption of cesium vapor with an uncertainty at the 2-ppm level. This extremely high signal-to-noise ratio allows us to directly observe the homogeneous line-shape component of the spectral profile, even in the presence of Doppler broadening, by measuring the spectral profile at a frequency detuning more than 200 natural linewidths from the line center. We then use this tool to discover an optically induced broadening process that is quite distinct from the well-known power broadening phenomenon.
The line shape and strength of two-photon absorption in an atomic vapor are studied both theoretically and experimentally for the case of absorption of unequal-frequency photons. Special attention is given to the situation in which the intermediate state is resonant or nearly resonant. It is shown that for the resonant case, maximum absorption rates and Doppler-free spectra are simultaneously obtained. Either counterpropagating or copropagating beams can be used. With counterpropagating beams the two-photon linewidths are quite insensitive to power broadening of the intermediate state. With copropagating beams the two-photon spectra can also reveal the intermediate-state structure with a resolution determined mainly by the intermediate-state lifetime (nearly as well as can be done using any spectroscopic technique). The theoretical analysis provides a closed-form solution for the line shape and strength of the two-photon spectrum. In general the line shape is composed of two features. One is Doppler broadened and predominates when the intermediate state is nonresonant. The second feature is Doppler free, and it predominates with a resonant intermediate state. Detailed comparisons of experimental measurements of the line shape and strength of two-photon absorption in Na vapor are made with the theory and found to be in excellent agreement. Signal strengths for the onresonance case are 6 \ifmmode\times\else\texttimes\fi{} 109{10}^{9}109 larger than the case of equal-frequency photons with no loss in resolution.
The Voigt profile---a convolution of a Gaussian and a Lorentzian---accurately describes the absorption lines of atomic and molecular gases at low probe powers. Fitting experimental absorption data to such a Voigt profile yields both the Lorentzian natural linewidth and the Gaussian Doppler broadening. However, as the probe power increases, saturation effects change the absorption line shape, such that it is no longer accurately described by a Voigt profile. Naively fitting a simple Voigt profile to the absorption line therefore introduces spurious power dependence into the extracted Doppler component. Using a simple atomic model, we calculate power-dependent corrections to the Voigt profile, which are parametrized by the Gaussian Doppler width, the Lorentzian natural linewidth, and the optical depth. We show numerically and experimentally that including the correction term substantially reduces the spurious power dependence in the fitted Gaussian width.
Absorption measurement is an exceptionally versatile tool for many applications in science and engineering. For absorption measurements using laser beams of light, the sensitivity is theoretically limited by the shot noise due to the fundamental Poisson distribution of the photon number in laser radiation. In practice, the shot-noise limit can only be achieved when all other sources of noise are eliminated. Here, we use seeded squeezed light to demonstrate that direct-absorption measurements can be performed with a sensitivity beyond the shot-noise limit. We present a practically realizable scheme, where intensity-squeezed beams are generated by a seeded four-wave mixing process in an atomic rubidium-vapor cell. More than 1.2 dB quantum advantage for the measurement sensitivity is obtained at faint absorption levels ($\ensuremath{\le}10\mathrm{%}$). We also present a detailed theoretical analysis to show that the observed quantum advantage when corrected for optical loss would be equivalent to 3 dB. Our experiment demonstrates a direct sub-shot-noise measurement of absorption that requires neither homodyne or lock-in nor logic coincidence-detection schemes. It is therefore very applicable in many circumstances where sub-shot-noise-level absorption measurements are highly desirable.
Absorption measurements are routinely used in science and engineering, it is an exceptionally versatile tool for most applications. For absorption measurements using laser beams of light, the sensitivity is theoretically limited by the shot noise due to the fundamental Poisson distribution of photon number in laser radiation. In practice, the shot-noise limit can only be achieved when all other sources of noise are eliminated. Here, we use bright squeezed light to demonstrate direct absorption measurement can be performed with sensitivity beyond the shot-noise limit. We present a practically realizable scheme, where the bright squeezed light is in the continuous-variable regime generated by the four-wave mixing process in an atomic rubidium vapor. This is a direct sub-shot-noise measurement of absorption, and more than 1 dB quantum advantage for the measurement sensitivity is demonstrated at faint absorption levels. A theoretical model that yields excellent agreements with experimental observations is also provided.
We determine the absolute density of a sample of laser-cooled atoms in a two-level system by recording the absorption spectrum of the 85Rb 5S1/2 (F = 3, mf = 3) → 5P3/2 (F′ = 4, m′f = 4) transition. Trapped atoms were prepared in the (F = 3, mf = 3) ground state through optical-pumping techniques. We compare our results with an independent measure of the density that relies on a direct measurement of the number of atoms and size of the atomic sample. We also study the contributions of power broadening, laser line width, and Doppler broadening to the measured absorption spectrum. Our studies suggest that the natural line width (~6 MHz) can be measured to a precision of less than ~50 kHz if the laser line width is measured in real-time with a high-finesse Fabry–Perot cavity. PACS Nos.: 32.70.Cs, 32.70.Jz, 32.80.Pj, 42.62.Fi, 32.70.–n, 32.30.–r
We calculate the two-level pump-probe absorption coefficient including both upper-to-lower-level decay and level decays to a still lower lying reservoir level. We carried out calculations of probe absorption profile for arbitrary ratios of natural width and detuning to the Doppler width associated with a given transition. This theory accounts for contributions from all velocity subclasses of atoms, not only those which are Doppler shifted into resonance with the laser field (Doppler limit).1 We observe and explain new line shape features based on dissimilar decays.