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Journal of Optics B Quantum and Semiclassical Optics

FM spectroscopy in recoil-induced resonances

Martin C. Fischer, Artem M. Dudarev, Braulio Gutiérrez–Medina, Mark G. Raizen

Published Aug 1, 2001• 16 citations
Publisher

Abstract

We report on an experimental study of recoil-induced resonances as a method of velocimetry for cold atomic samples. We present a refined experimental method that greatly improves the sensitivity of the measurement over previous experiments. Using frequency-modulation (FM) spectroscopy techniques we achieve a sensitivity that approaches the shot noise limit. In addition, we present a novel approach to deriving the line shape of the observed signal, based on the concept of quantum transport and tunnelling in motional Bloch bands.

DOI
10.1088/1464-4266/3/4/313

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We report on an experimental study of recoil-induced resonances as a method of velocimetry for cold atomic samples. We present a refined experimental method that greatly improves the sensitivity of the measurement over previous experiments. Using frequency-modulation (FM) spectroscopy techniques we achieve a sensitivity that approaches the shot noise limit. In addition, we present a novel approach to deriving the line shape of the observed signal, based on the concept of quantum transport and tunnelling in motional Bloch bands.
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.
Resonant frequency modulation spectroscopy has been previously used as a highly sensitive method for measuring the output of cold atom interferometers. Using a detailed model that accounts for optical saturation, laser intensities and atomic densities that vary spatially, and radiation pressure on the atoms, we theoretically investigate under what parameter regimes the optimum signal-to-noise ratio is found under experimentally realistic conditions. We compare this technique to the standard method of fluorescence imaging and find that it outperforms fluorescence imaging for compact interferometers using condensed atomic sources or where the photon collection efficiency is limited. However, we find that fluorescence imaging is likely to be the preferred method when using squeezed atomic sources due to limited atom number.
It is shown that, as a result of the atomic recoil associated with the absorption and emission of radiation, resonances can appear in nonlinear spectroscopy. The theory is illustrated by calculating the line shapes associated with nearly degenerate four-wave mixing and pump-probe spectroscopy when laser fields interact with an ensemble of two-level atoms. The recoil-induced resonances should be observable for atoms cooled below the Doppler limit of laser cooling, and the line shapes may provide a means for measuring the velocity distribution of these cooled atoms.
In this paper we report on the first purely ``pump-probe'' nonlinear laser spectroscopy results in a slow atomic beam. We have observed Raman, Rayleigh, and recoil-induced resonances (RIR) in a continuous beam of slow and cold cesium atoms extracted from a two-dimensional (2D) magneto-optical-trap (MOT) with the moving molasses technique. The RIR enabled us to measure the velocity distribution, therefore the average speed (0.6--4 m/s) and temperature (50--500 \ensuremath{\mu}K) of the atomic beam. Compared to time of flight, this technique has the advantage of being local, more sensitive in the low-velocity regime (v<1m/s),(v<1 \mathrm{m}/\mathrm{s}),(v<1m/s), and it gives access to transverse velocities and temperatures. Moreover, it may be extended to measure atomic velocities in the 2D MOT source of the atomic beam.
Widely frequency-tunable quantum-correlated twin beams have been experimentally demonstrated. The noise of the intensity difference between the signal and idler beams of the twin beams is reduced to more than 3 dB below the shot noise limit (SNL) throughout a wavelength-tuning range of 5.6 nm. A continuously frequency-tuning range of 2.8 GHz appears around the center wavelength of 1041.506 nm, where the maximum noise reduction of about 5.3 dB is observed. The tunable twin beams are used in frequency modulation (FM) spectroscopy of Cs 2 molecules and a spectrum with a sensitivity of about 4 dB beyond that of the SNL is obtained.