Proc. Nati. Acad. Sci. USA Vol. 88, pp. 9436-9437, November 1991 Geonium "K" experiment using spin dependency of cyclotron frequency supports g data of earlier geonium "S" work (individual trapped in vacuum/electron gyromagnetic ratio/Kaufmann-Einstein mass shift/electron nncro-synchrocyclotron accelerator) RICHARD MITTLEMAN, FRED PALMER, GERALD GABRIELSE*, AND HANS DEHMELT Department of Physics, FM-15, , Seattle, WA 98195 Contributed by Hans Dehmelt, July 26, 1991

ABSTRACT By substituting the relativistic spin state de- improved by a small auxiliary magnetic bottle that makes it pendence of the cyclotron frequency for the continuous Stern- possible to null out (5) the relativistic shift and broadening of Gerlach effect and running the geonium atom as a micro- cyclotron and anomaly resonances owing to the random synchrocyclotron accelerator we have detected spin flips of the thermal axial motion. Unfortunately this also nulls the de- individual trapped electron. In our initial efforts we have been pendence ofthe axial frequency on cyclotron excitation used able to obtain a simple symmetric spin resonance about 4-fold to detect the latter. However, with the large cyclotron narrower instead of a complex asymmetric one and also to energies feasible with postacceleration very little imbalance support but not as yet seriously test the result of the earlier in the two opposing shifts suffices to save the detection geonium "S" work, g/2 = 1. 001 159 652 185 5(40). scheme. In particular, by making the magnetic bottle larger, the asymmetric high-frequency tail (1-3) of the resonance The heart of the geonium experiments (1, 2) on the electron could be kept away from the drive frequency for the critical g factor is the monitoring of the spin state of the single negative offset values. Successful accelerations from (n) 0 permanently confined electron. The continuous Stern- to (n) 30 were easily detected via the small residual shift of Gerlach effect used for this in the past geonium "S" exper- the axial frequency due to magnetic bottle and relativistic (or iments also produced an undesirable broadening of the cru- Kaufmann-Einstein) mass increase with cyclotron motion cial spin resonance. By substituting the spin state depen- energy. A sample run showing spin flips is presented in Fig. dence of the cyclotron frequency we have obtained a 4-fold 3. As in the geonium "S" work (1, 2), spin flips have been narrower spin resonance (Fig. 1) that moreover has a nearly induced by a forced oscillatory motion of the electron at the symmetric Lorentzian line shape (3) only 0.8 Hz wide instead spin-cyclotron difference frequency v. through the magnetic of a complex asymmetric one. We were also able to support bottle, which, however, now at =10 G/cm2 is about 10 times but not as yet seriously test the result (4) weaker. By tuning the va drive through the resonance at va near 190 MHz, the sharp symmetric response shown in Fig. g/2 = 1. 001 159 652 185 5(40) 1 has been obtained allowing us to measure v. to 0.2 Hz. From va and vc the g factor was then found as in the earlier work. of the earlier geonium "S" work. Solution of the Dirac The "K" experiments show great promise, but various so far equation shows (2, 5) that in our experiment with a cyclotron uninvestigated shifts limit our error to about 10 parts in 1012, frequency near 163.5 GHz the n = 0 -- 1 cyclotron transition which is still nearly three times as large as in the geonium "S" is split into two components for the two spin states, 218 Hz work. apart at We enjoyed many informative discussions with our colleagues Bob vM= vC-(1 + ms)(218 Hz), Van Dyck and Paul Schwinberg; Bob Van Dyck also read the manuscript and offered comments. The Single Elementary Particle at with ms = ±1/2 the spin quantum number and v, the classical Rest in Free Space Project is supported by the National Science nonrelativistic cyclotron frequency. This reflects the fact that Foundation. spin state energy is kinetic energy and therefore shifts the mass of the electron. By developing the frequency-sensitive 1. Van Dyck, R. S., Jr., Schwinberg, P. B. & Dehmelt, H. G. accelerator scheme (6, 8) demon- (1978) in New Frontiers in High Energy Physics, eds. Kursuno- micro-synchrocyclotron glu, B., Perlmutter, A. & Scott, L. (Plenum, New York), pp. strated earlier at the University of Washington (7) we have 159-181. been able to electronically track the n = 0 -+ 1 cyclotron 2. Van Dyck, R. S., Jr., Schwinberg, P. B. & Dehmelt, H. G. transition with a microwave synthesizer and read out its (1986) Phys. Rev. D 34, 722-736. frequency v?" continuously. Fig. 2 shows that the success of 3. Dehmelt, H., Mittleman, R. & Liu, Y. (1988) Proc. Nati. Acad. an acceleration attempt depends sensitively on the starting Sci. USA 85, 7041-7043. cyclotron drive frequency of the acceleration sweep to lower 4. Van Dyck, R. S., Jr., Schwinberg, P. B. & Dehmelt, H. G. frequencies. The resolution attained may bejudged from this (1990) in ICAP 12-Abstracts of Contributed Papers, eds. Meh- figure. The technique obviously allows us to measure shifts ring, M., von Schutz, J. & Wolf, H. (University of Michigan in 100 Hz. An determination of which Press, Ann Arbor, MI), p. 11-8. v?' to independent vOM, 5. Dehmelt, H. (1981) in Atomic Physics 7, eds. Kleppner, D. & was obtained by detecting (6) the sharply and symmetrically Pipkin, F. (Plenum, New York), pp. 337-372. resonant preexcitation n = 0 -* 1 by a i-pulse via its effect 6. Dehmelt, H. & Gabrielse, G. (1981)Bull. Am. Phys. Soc. 26,797. on the percentage of successful subsequent accelerations, 7. Gabrielse, G., Dehmelt, H. & Kells, W. (1985) Phys. Rev. Lett. shows that zero offset in Fig. 2 corresponds to vs" + 400 Hz. 54, 537-539. The steepness of the response slope in Fig. 2 was much 8. Dehmelt, H. & Gabrielse, G. (1982) Bull. Am. Phys. Soc. 27, 481-482. The publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby marked "advertisement" *Present address: Department of Physics, , Cam- in accordance with 18 U.S.C. §1734 solely to indicate this fact. bridge, MA 02138. 9436 Downloaded by guest on September 26, 2021 Physics: Mittleman et al. Proc. Natl. Acad. Sci. USA 88 (1991) 9437

40 z2

30

0 07 zl- 20 H- T

0~ 10 FIG. 1. Anomaly (spin) reso- nance. The very nearly symmetric Lorentzian line shape of these su- perimposed (Am, = + 1, Ams + An -3 = 0) transitions is dominated by -3 -2 -1 0 1 2 3 4 the life time broadening of the FREQUENCY OFFSET (HZ) excited n levels (2, 3). z 100 0 F L 1 T 0..00 w 80 _ U 60- D: 60 e UL4Il V)

D 40r 0% 200~~~~~~~~~~~~~~~~~~ can *0 (HZ)* I %e~~~~-4 4 FIG. 2. Percentage of success- ~ ~ ~ . ful accelerations versus start fre- quency for the down-sweep of the

0 C

0 CDccm

cam U FIG. 3. Spin flips recorded via shift in the n = 0 -* 1 cyclotron a / frequency. The smooth curve is a moving average of the data. For a 4o tuning of the drive close to the center of the anomaly resonance U spin excitation pulses lasting 1 min (indicated by the trapezoidal E- C) * markers) have been applied peri- 010g*f odically every 11 min. On the av- erage, every other pulse produced a random spin flip as expected for 8.5 9 9.5 10 10.5 11 1 5 strong excitation and (artificially) TIME (HOURS) high cyclotron temperature. Downloaded by guest on September 26, 2021