Direct detection of galactic axions with Rydberg atoms in an inhibited cavity regime

Volume 263, number 3,4

PHYSICS LETTERS B

18 July 1991

Direct detection of galactic axions with Rydberg atoms in an inhibited cavity regime S. Matsuki Research Centerfor Nuclear Physics, Osaka University, Ibaraki, Osaka 567, Japan and Institutefor Chemical Research, Kyoto University, Uji, Kyoto 61 I, Japan

and K. Y a m a m o t o Department of Nuclear Engineering, Kyoto University, Kyoto 606, Japan Received 14 March 1991

A new scheme to detect galactic axions directly with Rydberg atoms is proposed and discussed. Rydberg atoms are excited from the lower to the upper fine-structure states by absorbing the axions in an inhibited (non-resonant) cavity regime. The weak transition rate in axion absorption could be enormously enhanced due to the huge occupation number of the axions if the axions constitute our galactic halo, while the transition rate in photon absorption could be strongly suppressed in a cooled, inhibited cavity regime. Thus it would be possible to get a good signal-to-noise ratio for axion hunting.

The Peccei-Quinn mechanism with a global U ( 1 ) PQ symmetry [ 1 ] provides the most elegant solution for the strong C P problem in QCD. The U ( I )pQ symmetry is assumed to be spontaneously broken at some scale f~ so that the strong CP-violating phase in the QCD lagrangian is rotated out dynamically. In the phenomenological point of view, the most remarkable prediction of the Peccei-Quinn mechanism is the existence of a light pseudoscalar particle, the "axion" [ 2 ]. The axion acquires a mass m a ~ f ~ m J f a ~ 10 -5 eV (1012 GeV/f~) through the QCD instanton effects, and its couplings to the ordinary matter are suppressed by f~. After the experimental ruling out of the original axion model with the weak scale f~ ~ 250 GeV, the so-called "invisible axions" were proposed with much largerfa [ 3 ]. This kind of axion could make up the dark matter of the universe, which remains one of the most challenging problems in cosmology [4]. No positive indication of the existence of the axion, however, has been obtained so far. At present, the axion is constrained by laboratory searches, and by astrophysical and cosmological considerations [ 5 ]. The axion windows still

open a r e 10 - 3 e V > m a > 10 - 6 eV and 5 e V > m a > 2 eV (this window is only for the hadronic axions). In spite of the extremely weak couplings of the axions to ordinary matter, a number of intriguing methods to produce and/or detect the axions have been proposed [6]. In the first proposal by Sikivie [ 7 ], the galactic axions are converted to microwave photons in a resonant cavity under a strong magnetic field via the Primakoff effect, and the converted photons are detected with a cryogenic low-noise microwave receiver. Along this proposal, a RochesterBNL-Fermilab group has performed the first experiment [ 8 ], and has reported null results covering the mass range ma= (0.45-1.0) × 10 -5 eV. The sensitivity of their experiment is, however, 300 times smaller than that necessary to reach the theoretical coupling strength for the mass range searched. Subsequent experiments [ 9 ] have been performed to cover wider ranges of the axion mass with sensitivities still not enough to reach the above theoretical coupling strength. It could also be possible to produce axions directly from an intense laser beam under a strong magnetic

0370-2693/91/$ 03.50 © 1991 - Elsevier Science Publishers B.V. ( North-Holland )

523

Volume 263, number 3,4

PHYSICSLETTERSB

field due to the axion-photon coupling [ 10 ]. However, no trial has yet been reported along this line of proposal. Related to this scheme, Maiani et al. [ 11 ] proposed to measure the changes in polarization state of the laser light travelling through a magnetic field due to the axion-photon coupling. The first experiment [ 12 ] along this idea has somewhat improved the laboratory limit on the axion-photon coupling. In view of these situations in the axion hunting, it is clear that the development of more efficient and sensitive detection schemes is crucial for further progress in the study of axion cosmology and related areas of research. We have recently suggested [13 ] that Rydberg atoms in a resonant cavity can be used to detect individually the converted microwave photons from the axions in Sikivie's regime. As demonstrated by a number of groups [ 14], the Rydberg atom, which is a highly excited atom near to the threshold of ionization, has quite a high probability to absorb microwave photons, and thus is a quite sensitive low-noise detector of microwave photons. In passing through a cooled resonant cavity, the Rydberg atoms absorb the converted microwave photons, thereby being excited to an upper state. Only the Rydberg atoms thus excited are ionized with an applied electric field (field ionization [ 15 ] ) and detected. In the cavity cooled down to about 10 m K with an appropriate refrigeration system, the background due to the black-body radiations could be appreciably reduced, and thus the axions could be searched for under quite low-noise circumstances. With this scheme it would be possible within a reasonable measuring time to reach the theoretical limit given by the relation between the axion mass and the axion-photon coupling under the assumption that the axions dominate the dark halo of our galaxy.

In this note, we propose another scheme to search for the cosmic axions directly ~Lwith the Rydberg atoms via the coupling of the axion to the electron. The schematic experimental system of our approach is shown in fig. 1. An alkaline atomic beam (Rb or Cs beam, for example) prepared at an oven source is passed through a cavity which is cooled down to liquid He temperature. Just before entering the cooled cavity, the atoms in the beam are excited to a lower partner of the spin-orbit splitting components (n 2s+ ~Lj_ s state) in a Rydberg state with its principal effective quantum number n by the absorption of multi-photons (one-three photons) from lasers (multistep laser excitation). In the cavity the cosmic axions are absorbed by the Rydberg atoms, thereby causing M 1-type transitions between the partners of the spin-orbit splitting components in the Rydberg states. The relevant coupling is given by L~ee -- ige ~75 ~gCa,

ov[•enl "1 beam

source

>

~aee = -- ( g e / m e )

(ff*~"O~"VCa

~ A related idea based on resonant atomic excitation has been suggestedby Zioutas and Semertzidis [ 16] in a contextdifferent from our approach.

etectron multiptier

I__;__ I

Rydl~erg atom

field ionization electrode

Laser Fig. 1. Schematicexperimentalsystemto search for cosmicaxions directly with Rydbergatoms in an inhibited cavity regime. 524

(2)

for the upper-half two-component spinor ~ of the Dirac field ~,, where 6e ( = ½a) is the spin operator. The transition rate from the state with the total angular momentum J~=J- 1 to that with Jf=J of the

[

I

(1)

where Ca refers to the axion field, and the coupling constant of the axion to the electron g~ is related to the Peccei-Quinn symmetry mass scale fa and the electron mass me by ge~ rnJfa. Hereafter we use h = c = 1. In the non-relativistic approximation, this interaction lagrangian is reduced to

cooled, nonresonant cavity "--,axion I atomic beam

18 July 1991

Volume 263, number 3,4

PHYSICS LETTERSB na ~ 1025( 10 -5 eV/m~) 4 ,

. I12S+ILj

axion

• n 2S+lLj.1

Rydberg atom Fig. 2. Transition due to the axion absorption between the finestructure splitting components of the Rydbergatom. Rydberg atom (see fig. 2) due to the axion absorption is then calculated as eVa

2 3 /247tree) 2 Fn, = (gek

(3)

for an axion bath with an occupation number n, for each quantum state. The axion m o m e n t u m is given by k = (o92 _ m 2 ) j/2 with the transition energy o9. The factor F is determined by taking absolute squares of the matrix elements of ~ between the initial and final states, and by averaging them over Jz of the initial state:

F=J -t ( 2 J - 1 ) - t (L + S+ J+ 1)(L + S - J + 1) × (J+S-L) (J+L-S),

(4)

where the orbital angular m o m e n t u m L and the spin S are conserved in the transition. This transition should be compared to the similar transition due to the absorption of a photon bath with an occupation number n~ through the magnetic coupling (e/me)V× (~*Se~0) .A, whose rate is given by Wv= (ao~3/12m~2) Fnv ,

18 July 1991

(5)

where c~= e 2/4n and the photon energy is taken equal to the atomic transition energy o). In the above rate, the sum is taken over the two polarization states of the photon. In spite of the small axion-photon coupling g~ ~ m~/f~, the transition due to the axion absorption would be enormously enhanced due to the occupation number n~ if the axions dominate our galaxy halo. As noted first by Sikivie [ 7 ], the axion number density nort - 3 / 2 e x p ( - x 2) 4nx2dx [x=k/ko and no= ( 4 × 108 eV/ma) cm -3] divided by the density of states (2n)-3k34rcx2 (ix gives the occupation number of the axions:

(6)

for the typical galactic velocity fl~ ko/m, ~ 10-3. This suggests that the strong stimulated emission and absorption occur due to this enormous occupation number na. Since the broadening of frequency in a single mode laser ( < 30 MHz) is much smaller than the energy difference ( > GHz from our present purpose) between the spin-orbit splitting components, we could populate only the lower-component n 2s+ ~Lj_ ~state selectively by multistep laser excitation. The enhancement of the transition could thus be fully utilized without any cancellation between the emission and absorption processes. Then, only the Rydberg atoms excited to the upper state are detected with the method of field ionization. The total number of Rydberg atoms excited due to the axion absorption within the measuring time t is then given by N a

=NRytWa~, 2

( g e l =0.77 1×10_8

NRyIO-SeVt~t 1013 ma 103S 1 ms '

(7)

where NRy is the number of incident Rydberg atoms per unit time by multistep laser excitation, ~t is the transit time of the Rydberg atoms through the cavity, and k -~/~m, is taken for/~--- 10 -3. In the above estimation, we have neglected the effect of F because its magnitude is of order of unity. In view of the small probabilities of the transitions, it is quite essential to suppress the normal transitions due to the photons in the cavity, in order to see clearly the desired signals. This can be done with a non-resonant cavity, that is, inhibited cavity regime: there are several important effects in the inhibited cavity on the suppression of the transition due to the photons. A cavity of finite quality factor Q exhibits some losses which yield a cavity line width A~o=coc/Q, where o9¢ is the resonant angular frequency of the fundamental cavity mode. For a lorentzian line shape, the density of modes per unit volume around the frequency O)c with the cavity volume Vc ~23 (2c~ 2n/ e)c is the wavelength of the fundamental cavity mode) is given by

1

o)c/2Q

(8)

pc(O))- rtv~ (o9-~o~)2+ (eo¢/2Q) 2" 525

Volume 263, number 3,4

PHYSICSLETTERSB

Thus at the resonance, (0= o9c, the spontaneous emission/absorption rate in the resonator, We, is expressed with that in the vacuum, Wv [eq. (5) ], as Wc=

[Pc((0c)/Pf((0~)] Wv= Wv(Q/4n 2) ,

(9)

where pf((0) = (02/•2 is the mode density in the vacuum (two polarization states included), and V¢is set equal to 23 for simplicity. This clearly shows that the strong enhancement of the emission rate can be obtained in a high-Q resonant cavity, if the resonant frequency is tuned to the atomic transition frequency, as demonstrated by a number of investigations [ 17 ]. Opposite to this situation, if the resonant frequency (0c is suitably larger than the atomic transition frequency (0, e.g. (0c=n(0, the emission/absorption rate is substantially suppressed as given by

Wc = Wrn4/16~z2(n - 1 )2Q.

(10)

The suppression is thus most effective for n = 2 , at which W~ is given by

Wc = Wv/zt2Q.

( 11 )

In addition to this suppression, the background photons due to the black-body radiation in the cavity can be appreciably reduced by cooling the cavity down to the liquid He temperature. The thermal average number nv of black-body photons per mode at the temperature T in the cavity is 1 / [ e x p ( ( 0 / k T ) - 1]. From this, we find, for example, for (0 = 10- 5 eV ( 2.4 GHz) nv=0.46 and 34.0 at T=0.1 K and 4 K, respectively. By taking into account the two suppression factors discussed above, the number of Rydberg atoms excited due to the absorption of the background blackbody photons is then given by Nbg ~, • ]WRyt W~,~t

= 1 . 2 × 1 0 - 7 l~Rl~

t 106( (0 )2T ~, 103S 0 \ 10---g~-~ 4 - -K l -m- s ' (12)

where we approximate nv~kT/(0 since kT>> m for T~ 4 K. Then the signal-to-noise ratio for (0 ~ ma is obtained from eqs. (7) and (12):

S/N=6.4×106(

g_~_8~2(10-SeV~3 Q 4 K \1 × 10- ] \ ~ / 106 T

(13) 526

18 July 1991

It should be noted, however, that at low temperatures the residual gas in the cavity may seriously cause the spurious transition to the upper fine-structure state due to the collision with the Rydberg atoms. As clarified by a number of theoretical and experimental investigations [ 18-21 ], angular-momentum-mixing (/-mixing) collisions of the Rydberg atoms with rare gas atoms are important processes for the quenching of the Rydberg states. To our knowledge, however, no detailed studies have been done for the collisions of the Rydberg atoms with the residual gas. By extrapolating the results for the case of rare gas collisions, we can thus only estimate roughly the cross section leading to a particular excited state. The cross section leading to the partner of the fine-structure splitting components is estimated to be about 10 -22 cm 2 as in the following. According to the approximate formula by Hickman [ 19 ], the total cross section of the/-mixing process has an n dependence, n--I O'l-mix= E 0 " ( 1 ~ / ' ) ~ n - 2 " 7 3 l'

(14)

The cross section o'/.mix for Rb (nf ) + He at n = 20, for example, was experimentally found to be about 10 -Is cm 2 [21 ]. Since the cross section leading to each/-state a(l~l' ) appears to be about the same order [20], we may have roughly a(l-'l')~~oal-mix ~ 10- 16 c m 2, for n = 20. Then, for the Rydberg atoms with higher n (n >/50), the cross section is estimated to be a(l~l') 10 -17 c m 2, by considering the n dependence of the above approximate formula eq. (14). It should be noted, however, that in these estimations, no spin-dependent interactions are taken into account, so that the above arguments cannot be directly applied to the case of the transition to the partner of the fine-structure splitting components. Since the M 1-type transition strength, which is the case here concerned (fig. 2 ), is normally more suppressed by a factor 10- 5 than the E 1-type transition [ 22 ], the cross section of the Rydberg atom-residual-gas collision leading to the partner of the fine-structure splitting components is thus estimated to be about 10- 22 cm 2. In this situation, the estimated background due to the collision within a measuring time t is given by ~

Volume 263, number 3,4

PHYSICS LETTERS B

18 July 1991

from an ultra-low background germanium detector Nbgc = 2.5 NRy t P 4 K 1013s 1 0 3 s 1 0 - 1 3 T o r r T

(15)

In this estimation, we take into account the following terms: (1) the flux of Rydberg atoms is given by N R y / A , where A represents the cross section of the Rydberg-atom beam, (2) the number of residual-gas target molecules relevant to the collision is determined by ( 1/R ) (P/T)AL from the equation of state, where 1/R~_ 1.0× 1019 ( K / T o r r c m 3 ) , and P and L are the pressure of the residual gas and the length of the cavity, respectively. L is typically taken to be 10 cm. This background contribution is apparently proportional to T - l . At the present stage of vacuum technology, however, the best vacuum condition of P ~ 10 -13 Torr will be available only under a quite low-temperature environment of the relevant area. Thus to get the optimum situation for the background due to both the black-body photons and the collisions, the favorable temperature would be somewhat between 1 to 4 K. By taking into account these background contributions, an experimental limit on ge at 95% confidence level, ge < 2 . 0 × 10-8 (

(

ma 1 trns)'/2 10_5 eV

P 4 K 1013 1Q~ S) × 10- ~ T o r r T NRy

1/4

(16)

is thus expected to be obtained from this kind of measurement. In a practical experiment, the fine-structure splitting energy 09 will be varied by applying a weak external magnetic field. Then, the axion absorption signal would be significant at the specific energy 09= rna/ (1 -fl2)~/2 with fl~ 10 -3, while the background due to the collision is almost insensitive to the variation of to. Thus the actual background due to the collision will be determined through the experiment. In conclusion, we have shown that the direct detection of galactic axions with Rydberg atoms in an inhibited cavity regime would be a useful scheme to obtain a bound on the coupling of the axion to electron ge down to less than 10 -s. Although it would not be easy to reach the limits obtained from astrophysical arguments [23], this is more restrictive than those obtained from the previous laboratory experiments [ 5 ] except the one recently reporting on solar axions

[24]. The authors would like to thank A. Masaike and M. Matsuzawa for stimulating discussions.

References [1] R.D. Peccei and H.R. Quinn, Phys. Rev. Lett. 38 (1977) 1440; Phys. Rev. D 16 (1977) 1791. [2] S. Weinberg, Phys. Rev. Lett. 40 (1977) 223; F. Wilczek, Phys. Rev. Len. 40 (1977) 279. [3] M. Dine, W. Fischler and M. Srednicki, Phys. Lett. B 104 (1981) 199; A.P. Zhitnitskii, Yad. Fiz. 31 (1980) 497 [Sov. J. Nucl. Phys. 31 (1980) 260]; J. Kim, Phys. Rev. Len. 43 (1979) 103; M.A. Shifman, A.I. Vainshtein and V.I. Zakharov, Nucl. Phys. B 166 (1980)493. [4] See the relevant papers compiled in M. Srednicki, ed., Particle physics and cosmology: dark matter (NorthHolland, Amsterdam, 1990). [ 5 ] Recent reviews include J.E. Kim, Phys. Rep. 150 ( 1987 ) 1; H.Y. Chen, Phys. Rep. 158 (1988) 1; M.S. Turner, Phys. Rep. 197 (1990) 67. [6 ] Recent reviews include P.F. Smith and J.D. Lewin, Phys. Rep. 187 (1990)203. [7] P. Sikivie, Phys. Rev. Len. 51 (1983) 1415; Phys. Rev. D 32 (1985) 2988; L. Krauss et al., Phys. Rev. Lett. 55 ( 1985 ) 1797. [81 S. DePanfilis et al., Phys. Rev. Lett. 59 (1987) 839. [9] W.U. Wuensch et al., Phys. Rev. D 40 (1989) 3153; C. Hagmann et al., Phys. Rev. D 42 (1990) 1297. [101 K. Van Bibber et al., Phys. Rev. Lett. 59 (1987) 759; M. Gasperini, Phys. Rev. Lett. 59 (1987) 396. [11] L. Maiani, R. Petronzio and E. Zavattini, Phys. Lett. B 175 (1986) 359; G. Raffelt and L. Stodolsky, Phys. Rev. D 37 (1988) 1237. [12l Y. Semertzidis et al., Phys. Rev. Lett. 64 (1990) 2988. [131 S. Matsuki and Y. Fukuda, RCNP preprint 020 (December 1990). [14] T.W. Ducas et al., Phys. Rev. Lett. 35 (1975) 366; C. Fabre, D. Goy and S. Harosche, J. Phys. B 10 (1977) L183. [15] T.W. Ducas et al., Appl. Phys. Lett. 35 (1979) 382; C. Fabre, D. Goy and S. Harosche, in: S. Matsuki and Y. Fukuda, RCNP preprint 020 (December 1990); H. Figger et al., Opt. Commun. 33 (1980) 37. [16] K. Zioutas and Y. Semertzidis, Phys. Lett. A 130 (1988) 94. [17] See the recent review S. Haroche and D. Kleppner, Phys. Today (January 24, 1989). [181 T.F. Gallagher, S.A. Edelstein and R.M. Hill, Phys. Rev. Lett. 35 (1975) 644.

527

Volume 263, number 3,4

PHYSICS LETTERS B

[ 19] A.P. Hickman, Phys. Rev. A 23 ( 1981 ) 87, and references therein. [20] K. Sasano, Y. Sato and M. Matzuzawa, Phys. Rev. A 27 (1983) 2421; Y. Sato and M. Matsuzawa, Phys. Rev. A 31 (1985) 1366, and references therein. [21 ] M. Hugon et al., J. Phys. B 12 (1979) 2707. [22] See e.g.R.D. Cowan, The theory of atomic structure and spectra (University of California Press, Berkeley, 1981 ) ch. 15.

528

18 July 1991

[23] M. Fukugita, S. Watamura and M. Yoshimura, Phys. Rev. Lett. 48 (1982) 1522; Phys. Rev. D 26 (1982) 1840; D.S.P. Dearborn, D.N. Schramm and G, Steigman, Phys. Rev. Lett. 56 (1986) 26; G. Raffelt, Phys. Rev. D 33 (1986) 897; Phys. Lett. B 166 (1986) 402; Phys. Rep. 198 (1990) 1; G. Raffelt and D.S.P. Dearborn, Phys. Rev. D 36 (1987) 2211. [24] F.T. Avignone et al., Phys. Rev. D 35 (1987) 2752.