Comments on ``Optically Pumped Nuclear Magnetometer''H. G. Dehmelt Citation: Review of Scientific Instruments 35, 768 (1964); doi: 10.1063/1.1746771 View online: http://dx.doi.org/10.1063/1.1746771 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/35/6?ver=pdfcov Published by the AIP Publishing Articles you may be interested in A plateau in the sensitivity of a compact optically pumped atomic magnetometer AIP Advances 4, 057132 (2014); 10.1063/1.4880498 Optically pumped nuclear magnetic resonance of semiconductors J. Chem. Phys. 128, 052203 (2008); 10.1063/1.2823131 Comment on integrating magnetometers Am. J. Phys. 58, 104 (1990); 10.1119/1.16214 Erratum: Optically Pumped Nuclear Magnetometer Rev. Sci. Instrum. 35, 767 (1964); 10.1063/1.1746769 Optically Pumped Nuclear Magnetometer Rev. Sci. Instrum. 34, 1363 (1963); 10.1063/1.1718237

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768 LETTERS TO THE EDITOR

resonance frequency of order AW::::::='(WMT2/woT2)wo. Here T2 and T2 are the lifetimes of metastable and ground statt> atoms, respectively, against metastability exchange.

The argument above holds only when wMT2«1; using a spin density matrix formulation of the problem, Bender! obtains, as the general expression for the fractional fre­quency shift,

The effect is largest when W.'1fT2::::::=.1, in which case the fre­quency shift is a few parts in 105 (about one-quarter of the resonance linewidth) in the earth's magnetic field, using T2::::::=.1 sec.

However, it should be possible to lower the SHe pressure so that the line shift is reduced by a factor of ten or more below that estimated above. Thus a 3He magnetometer with absolute accuracy of a few parts per million or better would still appear to be quite feasible.

The line shift effect discussed above does not arise in the proposed free-precession mode of operation of the 3He mag­netometer, which was also discussed in the article.

* Present address: Rice University, Houston, Texas. I P. L. Bender (private communication). 2 H. G. Dehmelt (private communication, and following Letter).

Comments on "Optically Pumped Nuclear Magnetometer"

H. G. DEHMELT

University of Washington, Seattle, WaslJittgtolZ

(Received 16 January 1964)

IN a recent publication! describing a version of SHe plasma precession magnetometer, based on the princi­

ples2 of optical pumping and electron exchange on one hand, and of modulation of a light beam by precessing absorbing atoms on the other, the authors claim that their instrument should be inherently less subject to various shifts associ­ated with the orientation process than comparable devices. In particular, it should allow absolute field measurements based strictly on the 3He nuclear gyromagnetic ratio gl(SHe). In contrast to these claims, I should like to point out here that the correct g-factor for this system should be a properly weighted average geff for all the magnetic con­stituents of the discharge plasma. To clarify this we con­sider a simplified model which we hope may yield a rep­resentative value for gef!. We suppose a completely polarized system composed of a few mm Hg of 3He in the ISo, F=!, mF= +! ground state and of a fraction of 1 ppm 3He in the excited metastable 3.)\, F=!, mp= +! state, the two states being in (excited) electron exchange equi-

librium. If we now apply a weak magnetic field H 0 perpen­dicular to the previous axis of quantization, the atoms will begin to precess, the ones in the ground state at the rate wG='YGHO, and the metastables at the much faster rate WM='YMHo. However, before an appreciable angular de­viation between ground-state and metastable angular mo­menta can develop, exchange collisions proceeding at a rate W';»WM transfer angular momentum from the metastables to the ground-state atoms. The net effect appears to be that in order to obtain the correct geff factor for such a system, one has to divide the sum of the magnetic moments of all constituents by the respective sum of all angular momenta,

geff~----- ----(!+1O-6X!)h

[ -2.13+1<r6(-1836X2)JJL,v ~------------

[ 2X1.836 ]

~ 1+ 1<r3 gr(3He) 2.13

~ gr(3He) (1 + 1. 72X 1<r3) ,

here JLN denotes the nuclear magneton. In a fleld of 0.1 G a displacement equivalent to 172 JLG with respect to the isolated 3He value should result according to this formula. For the actual discharge plasma containing additional mag­netic constituents in the form of electrons and ions which also are in electron exchange equilibrium with the ground state, corresponding additional shifts may be expected. This may be compared with the optimum practical line­widths of 70 JLG reported by the authors. In any case, a shift of such magnitude should be easily observable since magnetometers capable of a resolution and stability of "'0.1 JLG have been available for some time."

1 L. D. Schearer, F. D. Colegrave, and G. K. Walters, Rev. Sci. lustr. 34, 1363 (1963).

2 H. G. Dehmelt, Phys. Rev. 105, 1924 (1957); 109, 381 (1958). 3 P. L. Bender, Phys. Rev. 128, 2218 (1962).

Erratum: Manufacture of Fine Wire Thermocouple Probes

[Rev. Sci. lnstr. 35,80 (1964)J

G. H. GEL]), B. D. MARCUS, AND D. DROPKIN

Cornell University, Ithaca, New York

(Received 3 March 1964)

FOOTNoTE 3 states: "Estimated at 0.115 sec for 95% recovery of step change .... " It should read:

"Estimated at 0.0115 sec for .... "

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