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Journal of Physics B Atomic and Molecular Physics

Aligned atoms in strong oscillating RF fields. II. Modulation signals

E Jacobson

Published Sep 28, 1980• 1 citation
Publisher

Abstract

For pt.I see ibid., vol.13, p.3577 (1980). In a radio frequency (RF) experiment on aligned atoms modulation signals have been observed containing high-order harmonics of the fundamental RF (up to the 13th). The amplitudes of these harmonics have been investigated as a function of the static magnetic field over a wide range. Resonance structures have been found which are related to single- and (odd) multi-quanta transitions as well. The measurements are in good agreement with numerical calculations based on the semiclassical approach.

DOI
10.1088/0022-3700/13/18/011

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For pt.I see ibid., vol.13, p.3577 (1980). In a radio frequency (RF) experiment on aligned atoms modulation signals have been observed containing high-order harmonics of the fundamental RF (up to the 13th). The amplitudes of these harmonics have been investigated as a function of the static magnetic field over a wide range. Resonance structures have been found which are related to single- and (odd) multi-quanta transitions as well. The measurements are in good agreement with numerical calculations based on the semiclassical approach.
In radio frequency (RF) experiments on aligned atoms (e.g. optical double resonance) new phenomena can be found in the case of longitudinal excitation if a strong oscillating RF field is used: both the positions of the RF resonances (RF shift) and the widths (power broadening) depend on the direction of the light observed and on the state of its (linear) polarisation. This applies to the main (single-quantum) transitions as well as the (odd) multi-quanta transitions. These effects have been observed in an experiment on aligned mercury atoms in the metastable 6 3 P 2 state and have been confirmed by numerical calculations based on the semiclassical approach.
A longitudinal radio-frequency (rf) magnetic field resonating at the Larmor frequency along the $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{z}$ direction in the presence of a static transverse magnetic field s investigated. Optical-radio-frequency double resonance in 85Rb^{85}\mathrm{Rb}85Rb characterizes the strength of an external magnetic field through the precession frequency of 85Rb^{85}\mathrm{Rb}85Rb atoms. The measurements are carried out in a paraffin-coated 85Rb^{85}\mathrm{Rb}85Rb cell with a spin alignment configuration. An intriguing discovery of magnetic resonance peaks is observed at subharmonics of the Larmor frequency, accompanied by the emergence of nonlinear effects in the vicinity of the resonance. Notably, when the Larmor frequency reaches zero, the optical rotation signals induced by the rf magnetic field demonstrate a superposition of high-order harmonics of the rf frequency. Based on the simplified density matrix formalism and perturbation treatment, analytical expressions for the optical rotation are consistent with experimental outcomes. These findings hold the potential of extending our understanding on unveiling the dynamics of population and coherence among Zeeman sublevels, thereby advancing our knowledge in the field of alignment magnetometry.
For pt.I see ibid., vol.17, p.29-52 (1984). Wavelengths, dipole strengths, oscillator strengths and transition probabilities for electromagnetic transitions between low-lying states of the hydrogen atom embedded in a magnetic field of arbitrary strength (0<B<or=4.70*10 8 T) are calculated with high numerical accuracy for a sufficiently dense mesh of B values using the wavefunctions and energy values determined in paper I by expanding the wavefunctions in terms of spherical harmonics (weak and moderate fields), or in terms of Landau states (strong and very strong fields). Effects caused by the finiteness of the proton mass are taken into account, and the scaling laws are quoted by the aid of which the results presented can be utilised to cover quantitatively the whole hydrogenic sequence in intense magnetic fields; finally, the quality of the results of previous calculations is checked.
The coupling between microwave fields and atoms (or atomlike systems) is inherently weaker than for optical fields, making microwave signal manipulation for applications like quantum information processing technically challenging. In order to better understand this coupling and to develop tools for measuring it, we explore the microwave coupling to atoms using the ``atomic candle'' technique, and push it beyond the bounds of the small-signal regime in order to deliver a larger signal. In familiar two-level systems, responses beyond the usual Rabi oscillations can arise when a single-tone drive is phase modulated, causing the steady-state populations to oscillate at integer harmonics of the modulation frequency. Resonant behavior of the first two harmonics for frequencies near the Rabi frequency, known as $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ Rabi resonances, is widely used for microwave-field magnetometry and as a power standard known as the atomic candle. Here, we explore Rabi resonances beyond the small-signal approximation and report upon experimental observations of higher-order-harmonic population response for microwave hyperfine transitions in cold 87Rb^{87}\mathrm{Rb}87Rb atoms, which we compare to numerical simulations.
We study Rydberg atoms modulated by strong radio-frequency (rf) fields with a frequency of 70 MHz. The Rydberg atoms are prepared in a room-temperature cesium cell, and their level structure is probed using electromagnetically induced transparency (EIT). As the rf field increases from the weak- into the strong-field regime, the range of observed rf-induced phenomena progresses from ac level shifts through increasingly pronounced and numerous rf modulation sidebands to complex state mixing and level crossings with $\mathrm{high}\ensuremath{-}l$ hydrogenlike states. Weak anharmonic admixtures in the rf field generate clearly visible modifications in the Rydberg EIT spectra. A Floquet analysis is employed to model the Rydberg spectra, and good agreement with the experimental observations is found. Our results show that all-optical spectroscopy of Rydberg atoms in vapor cells can serve as an antenna-free, atom-based, and calibration-free technique to measure rf electric fields and to analyze their higher-harmonic contents.