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European Journal of Physics

Dispersion relations measured at the D 2 resonance of 85 Rb

H W Haag, Ernst Wilhelm Otten, M Schick, Christian Weinheimer

Published Jan 1, 1999• 2 citations
Publisher

Abstract

We describe an experiment to be carried out by advanced students as part of their laboratory practice. Its aims are (i) to measure simultaneously the frequency dependence of both the refractive index n and the extinction coefficient of an atomic gas interacting with a resonant laser beam and (ii) to examine that n and satisfy the Kramers-Kronig relations. The medium to be probed consists of a dilute 85 Rb vapour exposed to collisions with a buffer gas. The D 2 resonance line is thereby broadened to such an extent that its hyperfine components merge into single Lorentzian dispersion and absorption profiles, respectively. The main features of the apparatus are a tunable laser diode, a Mach-Zehnder interferometer at nearly zero path difference, an array of photodiodes to measure the interference pattern as a function of laser frequency and Rb density in one of the interferometer arms, an absorption monitor, computer-controlled electronics to read out and analyse the data, and a video camera for visual control and adjustment of the interference pattern.

DOI
10.1088/0143-0807/20/3/314

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We describe an experiment to be carried out by advanced students as part of their laboratory practice. Its aims are (i) to measure simultaneously the frequency dependence of both the refractive index n and the extinction coefficient of an atomic gas interacting with a resonant laser beam and (ii) to examine that n and satisfy the Kramers-Kronig relations. The medium to be probed consists of a dilute 85 Rb vapour exposed to collisions with a buffer gas. The D 2 resonance line is thereby broadened to such an extent that its hyperfine components merge into single Lorentzian dispersion and absorption profiles, respectively. The main features of the apparatus are a tunable laser diode, a Mach-Zehnder interferometer at nearly zero path difference, an array of photodiodes to measure the interference pattern as a function of laser frequency and Rb density in one of the interferometer arms, an absorption monitor, computer-controlled electronics to read out and analyse the data, and a video camera for visual control and adjustment of the interference pattern.
We present a laboratory demonstration of the Kramers-Kronig relation between the resonant absorption and refractive index in rubidium gas. Our experiment uses a rubidium vapor cell in one arm of a simple Mach-Zehnder interferometer. As the laser frequency is scanned over an atomic resonance, the interferometer output is affected by variations of both the absorption and refractive index of the gas with frequency, all of which can be calculated in a straightforward manner. Changing the vapor density and interferometer phase produces a family of different output signals. The experiment was performed using a commercially available tunable diode laser system that was designed specifically for the undergraduate physics laboratory. As a teaching tool this experiment is reliable, fun, and instructive, while it also introduces the student to some sophisticated and fundamental physical concepts.
The real and imaginary parts of the complex index of refraction have been measured in the R1 line of optically pumped ruby. The experiments, which employed a temperature-controlled, single-mode ruby laser as a variable-frequency monochromatic source, were performed near liquid-nitrogen temperature, where the R1 doublet structure is well resolved. R1 absorption profiles were measured for several optical-pumping conditions, ranging from zero up to a pump power that excited a population in the 2E state equal to about 60% of the population of the 4A2 ground state. For each pumping condition, the anomalous-dispersion curve was measured interferometrically. The spectral profiles of the absorption coefficient and the anomalous dispersion display a dependence on the optical-pumping conditions that is more complicated than simple saturation of the R1 transitions, but for given pumping conditions the two quantities are correlated as predicted by the Kramers–Kronig relations.
Continuous wave extended cavity diode lasers are used to measure the absorptive and dispersive properties of the 5 2S1/2 → 5 (^2)Рз/2 resonance, at 780 nm, in Rubidium (Rb) vapour. The Doppler-broadened hyperfine transitions are studied both with and without a pump beam. The investigation concentrates on three-level Л-systems, realized in the presence of a pump beam, exhibiting Electromagnetically Induced Transparency (EIT). Electromagnetically Induced Absorption (EIA) IS also seen. The EIT and EIA resonances can be several orders of magnitude narrower than the natural line width of the atomic transitions in the absence of the pump beam. Further, the EIT resonances are sensitive to applied magnetic fields. The narrowest resonances measured in this work have a full-width at half- maximum of 〜 80 kHz. This is limited by the transit time of the atoms through the probe and pump beams. Predictions of theoretical calculations and models are compared to experimental results. The theory of beam splitters and interferometers is developed to enable the implementation of a Sagnac interferometer in a novel "biased" alignment. This allows the dispersion of atomic resonances to be measured directly. The direct measurement of the dispersion of the narrow EIT features in a "biased" Sagnac interferometer is presented. Such a signal is ideally suited to precision measurement applications such 88 inertial sensing and magnetometry.
The goal of this experiment was to measure the hyperfine energy splittings of the ground to first excited state transitions in rubidium using saturated absorption spectroscopy. Using this technique, we measured these transition energy spectra by taking the difference of two photodiode outputs due to multiple beams of a single laser scanned over a range of frequencies and shone through a cell of Rb vapor. When the laser frequency was resonant with an atomic transition, photons of those frequencies were absorbed, leaving a dip in intensity of the beam measured at the photodiode. One of the two laser beams had its excitations saturated by a more intense, counter-propagating pump beam from the same laser. The pump beam saturated the absorption of the velocity equal zero atoms that the counter-propagating probe beam could have also interacted with due to no Doppler shift. At these frequencies the probe beam experienced less absorption that was measured by a photodiode. The photodiode output was calibrated to the change in frequency of the scanned laser using a Fabry-Pérot interferometer. The output of this interferometer served as a reference for how the laser frequency changed. Final results for the 87Rb F=1 spectrum accounted for the largest error with a maximum of 12.2% deviation from accepted energy spacing values due in part to systematic error. Other spectra measurements were in better agreement, possessing error ranging from 2.1% to 10.1% and some agreeing with accepted values to within our uncertainty.
Strong enhancement of group refractive index in a dense buffered atomic vapor is recorded using a technique of reflection from a low-finesse Fabry–Perot cavity filled with dense atomic vapor allowing the retrieval of a dispersion curve for the hyperfine structure of Rb D2 line buffered by a high-density Cs vapor. Oscillations of the recorded signal resulting from interference of beams reflected from the front and rear windows of the cell appearing with the laser frequency scanning across the resonance allow easy reconstruction of the dispersion curve. Contribution from concomitant interconnected processes, in particular, the determinative role of radiation channeling in enhancement of the resonator Q-factor, is analyzed.
We have developed a Mach-Zehnder atom interferometer which uses elastic diffraction of lithium atom on laser standing waves for the coherent manipulation of the atom wave. The interference signal is of sufficient quality to achieve a phase sensitivity near 10 milliradians/. With this apparatus, we have recently measured the index of refraction of several gases for lithium waves. The interference signals give access to the real and imaginary parts of () and we have tested the linear dependence of these two quantities with gas density. The measured values of () are in good agreement with calculations and they exhibit glory oscillations, as predicted by theory.