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Optics Letters

Dark-state imaging for two-dimensional mapping of a magnetic field

Hitoshi Asahi, Koji Motomura, Ken-ichi Harada, Masaharu Mitsunaga

Published Jul 1, 2003• 15 citations
Publisher

Abstract

By imaging the dark states that are due to coherent population trapping in Na atomic vapor, we have succeeded in depicting a spatially inhomogeneous magnetic field. Highly resolved dark lines represent cross sections of the surfaces of constant magnetic fields, and they agree well with the predicted hyperfine Zeeman splitting and the two-photon selection rules of the Na atom. Mapping was made two dimensionally in real time, but extension to three dimensions is straightforward. Furthermore, unlike the previous techniques based on optical pumping, this method can be used for any magnetic-field directions.

DOI
10.1364/ol.28.001153

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By imaging the dark states that are due to coherent population trapping in Na atomic vapor, we have succeeded in depicting a spatially inhomogeneous magnetic field. Highly resolved dark lines represent cross sections of the surfaces of constant magnetic fields, and they agree well with the predicted hyperfine Zeeman splitting and the two-photon selection rules of the Na atom. Mapping was made two dimensionally in real time, but extension to three dimensions is straightforward. Furthermore, unlike the previous techniques based on optical pumping, this method can be used for any magnetic-field directions.
24 In recent years interest has been growing into the fascinating properties of dark resonances. Most of the experiments have been carried out in alkali atoms due to their favourable level structure and the commercially available diode lasers, resulting in numerous applications. Teams from Siena and Sofia developed an all-optical magnetometer based on such dark resonances. The dark-state effect was discovered in 1976 by G. Alzetta, A. Gozzini, L. Moi and G. Orriols [1], while they were working on optical-pumping experiments with a multimode dye laser. They wanted to make the observation of multi-photon radio-frequency resonances in sodium atoms easy, i.e., observable by the naked eye. To this end, they introduced a magnetic field (MF) that was constant in time but spatially inhomogeneous along the laser beam, so as to produce Zeeman splitting of groundstate hyperfine levels (Fig.1a, left). In this way, an applied radio-frequency field was resonant only if it matched the Zeeman splitting. As a result, a bright radio-frequency resonance appeared (Fig.1a, right). During these experiments, besides the bright resonances, a new “dark” resonance was observed, which does not require any radio-frequency field. In the introductory illustration only the dark resonance is shown. The new dark state (DS) effect appears in a position along the laser beam where the frequency difference (ω10-ω20) between two optical frequencies is equal to the frequency splitting ω12 between two Zeeman sublevels (Fig.1b, left). This is the resonant condition for the stimulated Raman transitions between the two longliving ground levels. Theoretical studies described the dark resonance as a coherent superposition of two long-living ground levels prepared by the bi-chromatic laser field, and ‘atomic population trapping’ was introduced, leading to the term Coherent Population Trapping (CPT) [2]. l Luigi Moi1, Stefka Cartaleva2 DOI: 10.1051/epn/2012603
Neutral atoms may be trapped via the interaction of their magnetic dipole moment with magnetic field gradients. One of the possible schemes is the cloverleaf trap. It is often desirable to have at hand a fast and precise technique for measuring the magnetic field distribution. We introduce a novel diagnostic tool for instantaneous imaging the equipotential lines of a magnetic field within a region of space (the vacuum recipient) that is not accessible to massive probes. Our technique is based on spatially resolved observation of the fluorescence emitted by a hot beam of sodium atoms crossing a thin slice of resonant laser light within the magnetic field region to be investigated. The inhomogeneous magnetic field spatially modulates the resonance condition between the Zeeman-shifted hyperfine sublevels and the laser light and therefore the amount of scattered photons. We demonstrate this technique by mapping the field of our cloverleaf trap in three dimensions under various conditions. 1
We consider the coherent-population-trapping (CPT) phenomenon in a sodium atomic vapor. The experiment leading to the first observation of CPT is revisited with an improved experimental setup and a larger range of magnetic-field strengths. From the analysis of the ground-state hyperfine splitting as a function of the applied magnetic field, we conclude that we have observed the whole spectrum of dark resonances within the D1 line corresponding to the nonabsorbing coherent superposition of two Zeeman sublevels of two different components of the 32S1/2 level. This was not obvious a priori because the transition probabilities at high magnetic-field strengths, as applied in the experiment, have to be taken into account. The differences in the contrast of the various black lines are explained in terms of pumpings outside the interaction scheme preparing the nonabsorbing state. Possible applications of CPT in high magnetic fields are discussed.
We present a spectroscopic method for mapping two-dimensional distributions of magnetic field strengths (magnetic scalar potential lines) using CCD recordings of the fluorescence patterns emitted by spin-polarized Cs vapor in a buffer gas exposed to inhomogeneous magnetic fields. The method relies on the position-selective destruction of spin polarization by magnetic resonances induced by multi-component oscillating magnetic fields, such that magnetic potential lines can directly be detected by the CCD camera. We also present a generic algebraic model allowing the calculation of the fluorescence patterns and find excellent agreement with the experimental observations for three distinct inhomogeneous field topologies. The spatial resolution obtained with these proof-of-principle experiments is on the order of 1 mm. A substantial increase of spatial and magnetic field resolution is expected by deploying the method in a magnetically shielded environment.
In a weak magnetic field coherent dark resonances in cesium vapor are split into up to 15 resolved components, depending on field direction and laser polarizations. We find that the selection rules are different for vapor cells with and without buffer gas due to a change in multipolarity of the two-photon coupling. At low laser intensities or sufficiently high buffer-gas pressure optical pumping between different dark resonances can be neglected so that a simple model allows one to calculate the relative line strengths, giving complete agreement with the experimental spectra.
A new method has been designed for obtaining the hyperfine optical pumping of Na vapor. The pumping lamp is placed in a magnetic field and the light emitted in the field direction is used for excitation after crossing a circular polarizer selecting one of the Zeeman lines. This method has two interesting features: (i) The atoms can be pumped either in the lower or in the upper hyperfine sublevel by simply rotating a polarizer by an angle of $\frac{1}{2}\ensuremath{\pi}$; (ii) the hyperfine pumping is obtained using both the D1{D}_{1}D1​ and D2{D}_{2}D2​ resonance lines without filtering losses. The pumping efficiency is good and it has been possible to measure the spin-exchange cross section between sodium atoms by studying the hyperfine relaxation rates as a function of the sodium density. The result is ${\ensuremath{\sigma}}_{\mathrm{ex}}=(1.109\ifmmode\pm\else\textpm\fi{}0.005)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ cm2{\mathrm{cm}}^{2}cm2.