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Journal of Physics B Atomic Molecular and Optical Physics

Rydberg atoms as sensitive magnetic probes

Eugene Oks, T. Uzer

Published Jun 2, 2000• 5 citations
Publisher

Abstract

The multiphoton ionization of hydrogen in strong parallel microwave and static fields is a fundamental problem of great complexity which has been the subject of recent experimental and theoretical studies. We show that the superposition of an additional field, namely a static, relatively weak magnetic field, results in rapid oscillations of the ionization survival probability. These rapid oscillations can be used as a very sensitive method for measuring weak magnetic fields.

DOI
10.1088/0953-4075/33/12/304

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•Jan 1, 1993•1 citation
The multiphoton ionization of hydrogen in strong parallel microwave and static fields is a fundamental problem of great complexity which has been the subject of recent experimental and theoretical studies. We show that the superposition of an additional field, namely a static, relatively weak magnetic field, results in rapid oscillations of the ionization survival probability. These rapid oscillations can be used as a very sensitive method for measuring weak magnetic fields.
Experimental results of studying the spectrum of the microwave 37 P -37 S transition of Rydberg sodium atoms in a weak magnetic field (≤7 G) are reported. The populations of the Rydberg states were measured using the method of selective ionization with a pulsed electric field. When the magnetic field was parallel to the ionizing electric field, a good agreement between the calculated and experimental spectral shapes was observed, making it possible to determine the unknown polarization of the microwave radiation. In the case of the orthogonal configuration of the fields, the resonance structure was suppressed in the field ionization signals due to the strong influence of the magnetic field on the electron trajectories in the detection system.
Microwave ionization and excitation of Rydberg atoms provides a system in which quantitative experiments can be done to study single electron atoms in strong fields. In many cases microwave ionization proceeds by means of transitions through other bound states. Multiphoton transitions between two relatively isolated K Rydberg states have been examined under a variety of circumstances to establish the connection between transitions driven by quasi static fields and photon absorption and to understand the evolution during pulses of microwaves.
Although the hydrogen atom has naturally served as the basis for extensive theoretical studies of the physics of highly excited atoms in strong external fields, experiments with this fundamentally important species in magnetic fields have not been reported, except for the most recent ones carried out in our laboratory.1,2 We report new results of studies on the spectroscopy of the atom in static homogeneous magnetic fields of strength B ≲ 6 T at excitation energies from high Rydberg states (n ≳ 20) into the ionization region (E ≲ +30 cm−1).
Helium atoms in pulsed supersonic beams have been prepared in the circular Rydberg state with principal quantum number n=55n=55n=55 using the crossed-fields method. High-resolution microwave spectroscopy of the transition from this state to the n=56n=56n=56 circular state, at frequencies close to 38.5 GHz, was performed to measure static magnetic and electric fields along the axis of propagation of the beams with quantum-state-selective detection by pulsed-electric-field ionization. Magnetic fields of between 1.3 and 1.6 mT were measured to a relative precision of $\ifmmode\pm\else\textpm\fi{}900\phantom{\rule{0.28em}{0ex}}\mathrm{nT}$ by rf spectroscopy and $\ifmmode\pm\else\textpm\fi{}1.3\phantom{\rule{0.28em}{0ex}}\textmu{}\mathrm{T}$ by microwave spectroscopy, with absolute calibration, accounting for Doppler shifts and effects of weak stray electric fields to $\ifmmode\pm\else\textpm\fi{}2.0\phantom{\rule{4pt}{0ex}}\textmu{}\mathrm{T}$ and a spatial resolution of $\ifmmode\pm\else\textpm\fi{}0.87$ mm. Magnetic-field gradients could be determined to a precision of $\ifmmode\pm\else\textpm\fi{}1.49\phantom{\rule{0.28em}{0ex}}\textmu{}\mathrm{T}/\mathrm{mm}$ ($\ifmmode\pm\else\textpm\fi{}53$ nT/mm) over a baseline of 1.74 mm (35 mm). To perform these measurements, static electric fields and contributions from the motional Stark effect were minimized, and residual electric fields in each of the three spatial dimensions in the apparatus were measured to an absolute precision of between $\ifmmode\pm\else\textpm\fi{}85$ and $\ifmmode\pm\else\textpm\fi{}750\phantom{\rule{0.28em}{0ex}}\textmu{}\mathrm{V}/\mathrm{cm}$. The methods used in this work can be transferred to experiments with other atoms or molecules. They are therefore well suited for applications in minimally invasive, absolute static-field magnetometry and electrometry, for example, at hybrid interfaces between Rydberg atoms and superconducting circuits; in tests of bound-state QED or the weak equivalence principle with atomic or molecular hydrogen, antihydrogen, or positronium; and in measurements of the absolute neutrino mass by cyclotron radiation emission spectroscopy.
The behavior of Rydberg atoms in a recent experiment involving selective excitation in combined ac and dc electric fields is shown to be consistent with the predictions of a one-dimensional model incorporating only the extreme level of each Stark manifold. For low microwave powers, the excitation is resonant and is described qualitatively by multiphoton perturbation theory. For higher powers, an alternative stochastic theory predicts rapid ionization at all frequencies, as observed experimentally.
Theoretical analysis of the recently observed ionization of Rydberg atoms by ultra-short half-cycle single-polarity electromagnetic pulses is presented. It is shown that the observations are consistent with the general classical scaling for the hydrogen atom in a microwave field, but the quantitative explanation of the results is possible only within the framework of quantum mechanics. In other words, the photonic basis approach for quantum dynamics and the multiphoton ionization theory yield the measured threshold fields. This is an example of classical scaling of a non-classical effect. 1.