Resonantly Enhanced Axion-Photon Regeneration

0.21 MB·English

by  P. Sikivie

Resonantly Enhanced Axion-Photon Regeneration
P. Sikivie,a,b D.B. Tanner,a and Karl van Bibberc
a Department of Physics, University of Florida, Gainesville, FL 32611, USA
b Theoretical Physics Division, CERN, CH-1211 Gen`eve 23, Switzerland
c Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
Wepointoutthatphotonregeneration-experimentsthatsearchfortheaxion,oraxion-likeparti-
cles,mayberesonantlyenhancedbyemployingmatchedFabry-Perotopticalcavitiesencompassing
both the axion production and conversion magnetic field regions. Compared to a simple photon
regeneration experiment, which uses the laser in a single-pass geometry, this technique can result
in a gain in rate of order F2, where F is the finesse of the cavities. This gain could feasibly
be 10(10−12), corresponding to an improvement in sensitivity in the axion-photon coupling, g ,
aγγ
of order F1/2 ∼ 10(2.5−3), permitting a practical purely laboratory search to probe axion-photon
couplings not previously excluded by stellar evolution limits, or solar axion searches.
7
0
PACSnumbers: PACSnumbers: 12.38.-t,12.38.Qk,14.80.Mz,29.90.+r,95.35.+d
0
2

n The axion remains the most attractive solution to the The action density for the dynamics of photons and
a
strong-CPproblemandisoneoftwoleadingdark-matter axions is
J
candidates[1]. Recently,ithasbeenrealizedthattheax-
23 ionrepresentsafundamentalunderlyingfeatureofstring L= 21(ǫE2−B2)+12(∂ta)2−12(∇~a)2−21m2aa2−gaE~·B~
theories;therecouldbeseveralorevenagreatnumberof (1)

1 axionsoraxion-likeparticleswithinanyparticularstring where E~, B~ and a are respectively the electric, magnetic
v theory [2]. From the experimental viewpoint, there are
and axion fields. The electromagnetic fields are given
8
9 now several photon regeneration experiments in various in terms of scalar and vector potentials, E~ = ~Φ
1 stagesofpreparation[3],motivatedinpartbythereport ∂ A~, B~ = ~ A~, as usual. The coupling g −∇g −
t aγγ
1 of the PVLAS collaboration of a non-zero magnetically- is written w∇ith×out subscripts here, for simplicit≡y. ǫ is
0 induced dichroism of the vacuum [4], which may be in-
assumedconstantinbothspaceandtime. Inthepresence
7 terpreted as the production of a light boson with a two- of a large static magnetic field B~ (~x), the equations of
0 0
photoncoupling[5]. Althoughtheparticleinterpretation
/ motion are
h ofthe PVLASexperimentisinprinciple excludedbythe
p much more stringent limit set by the CAST solar ax- ǫ~ E~ = gB~ ~a
0
- ∇· ·∇
p ion search [6], it is important to check this result by a ~ B~ ǫ∂ E~ = gB~ ∂ a
t 0 t
e purely laboratory experiment, particularly if one could ∇× − −
∂2a ~2a+m2a = gE~ B~ . (2)
h ultimately improve such a measurement to reach previ- t −∇ a − · 0
:
v ously unexplored regions of (ma,gaγγ). B~ nowrepresentsthemagneticfieldminusB~ ,andterms
i 0
X Thesimplestandmostunambiguouspurelylaboratory of order gE and gB are neglected. Eqs. (2) describe the
r experiment to look for light pseudoscalars is photon re- conversionof axions to photons and vice-versa.
a generation (“shining light through walls”) [7]. A laser Using these equations, it can be shown [5, 7, 8] that
beam traverses a dipole magnet, wherein a small frac- the axion-to-photon conversion probability in a region
tion of the photons are converted into axions with the of length L, permeated by a constant magnetic field B
0
same energy. An opticalbarrierblocksthe primary laser transversetothedirectionofpropagationandadielectric
beam, whereas the axioncomponent of the beam travels constant ǫ, is given by (h¯ =c=1)
through the wall unimpeded and enters a second dipole
magnet,whereitisreconvertedtophotonswiththesame 1 2 qL 2
p= (gB L)2 sin , (3)
probability (we will assume magnets of identical length 4β √ǫ 0 (cid:18)qL 2 (cid:19)
a
LandfieldstrengthB withoutlossofgenerality). How-
0
ever, because the photon-regeneration rate goes as g4 , with βa the axionspeed and q =ka kγ the momentum
aγγ −
the sensitivity of the experiment to small values of g transfer. In terms of the energy ω, which is the same for
aγγ
is poor in its basic form, improved appreciably only by the axionandthe photon,ka = ω2−m2a,βa = kωa and
increasing B0 or L. kγ = √ǫω. The photon to axiopn conversion probability
in this same region is also equal to p. Everything else
In this Letter, we point outthat matchedFabry-Perot
beingthesame,theconversionprobabilityislargestwhen
cavities incorporated into the production and detection
q 0. For m <<ω, and propagation in a vacuum
magnets canimprove the sensitivity in the axion-photon ≈ a
coupling, gaγγ by the square root of the cavities’ finesse, m2
1/2. This factor may be 10(2.5 3). q = a +(1 √ǫ)ω . (4)
F − −2ω −
2
(a) Photon date,byRuosoetal. utilizedan“opticaldelayline,”i.e.,
B Wall B
0 0 Detector
an incoherent cavity encompassing the production mag-
! a
Laser net, causing the laser beam to traverse the magnet 200
Magnet Magnet times before exiting. With relatively modest magnets
L L (4.4 m, 3.7 T each), a limit of gaγγ <7.7×10−7 GeV−1
was set [9].
Photon
(b) Detectors There is substantial gain from building up the laser
power in the axion production magnet; however, it is
IO immaterial whether one “recycles” the photons incoher-
Laser
ently, as in an optical delay line, or coherently, as in a
Magnet Magnet Fabry-Perot (FP) cavity. In contrast, the coherent case
alonecanprovidealargeadditionalgaininsensitivityfor
Matched Fabry-Perots
photonregeneration. Thus,thesecondimprovementisto
FIG.1: (color)(a)Simplephotonregeneration. (b)Resonant alsoinstallaFabry-Perotcavityonthe regenerationside
photon regeneration, employing matched Fabry-Perot cavi- of the experiment, making a symmetric arrangement, as
ties. The overall envelope schematically shown by the thin illustrated in Fig. 1b. When the second FP cavity is
dashedlinesindicatestheimportantconditionthattheaxion
locked to the first, the probability of axion to photon
wave,andthustheFabry-Perotmode,intheconversionmag-
conversion in the second FP cavity is 2 p = 2 p
netmustfollow thatofthehypotheticallyunimpededphoton η′ ′ π F′ ′
wave from the Fabry-Perot mode in the production magnet. where ′ is the finesse of the cavity, and p′ is the axion-
F
Between the laser and the cavity is the injection optics (IO) to-photon conversion probability in the absence of the
which manages modematchingofthelaser tothecavity,im- cavity. The calculation which yields this result is out-
poses RF sidebands for reflection locking of the laser to the lined in the next paragraph.
cavity,andprovidesisolationforthelaser. Thephotondetec-
The cavity modes are described by
torsarealsoprecededbymatchingandbeam-steeringoptics.
Notshownatallistheelectro-opticalsystemrequiredtolock nπ
A~ =A (t)yˆsin( z) (6)
thetwo cavities together in frequency. n n L
wherezˆisinthedirectionoflightpropagationandyˆisa
Fig. 1a shows the axion-photon regeneration exper- transverse direction. The dependence of the mode func-
iment as usually conceived. If P0 is the power of the tion on the transversecoordinates (x and y) is neglected
laser, the power of the axion beam traversingthe wall is here, but will be discussed later. Using Eqs (2) one can
p P0 where p is the conversionprobabilityin the magnet show that, in the presence of an axion beam travelling
ontheLHSofFig. 1a. Letp′ betheconversionprobabil- through the cavity in the z-direction
ity inthe magnetonthe RHS. The powerinregenerated
photons is P =p′ p P0. a(z,t)=Asin(kaz−ωt) , (7)
Fig. 1b shows the two improvements we propose for
the coefficients A (t) satisfy
theexperiment. Thefirstimprovementistobuildupthe n
power on the photon-to-axion conversion side of the ex-
d2 d qL
perimentusingaFabry-Perotcavity,asillustrated. Pho- ( +γ +ω2)A (t)=Csin(ωt ) , (8)
dt2 dt n n − 2
tons in the production cavity will then convert to ax-
ions with probability p for each pass through the cavity. where ω = nπ and
n √ǫL
Thestandingwaveintheproductioncavityisthesumof
left-moving and right-moving components of equal am- 1 2 qL
C = gωB sin( ) . (9)
plitude. If the reflectivity of the cavity mirrors is given ǫ 0ALq 2
by
As before,q =k k = ω2 m2 nπ is the momen-
R=1 η (5) a− n − a− L
− tumtransfer. Whenthepproductioncavityandtheregen-
and the power of the laser is P0, the power of the right- eration cavity are tuned to the same frequency, ωn = ω
movingwaveinthe productioncavityis 1 P . Therefore for some n. Then
η 0
the axionpower throughthe wallin the setup of Fig. 1b C nπ qL π
is η1 p P0. Assuming the lasers in Fig. 1a and Fig. 1b A~n =yˆωγ sin( L z)sin(ωt− 2 − 2) , (10)
have the same power, the axion flux is increased by the
factor 1. up to transients. The energy stored in the cavity is
η
Increasingtheaxionproductionrate,andthusthepho- E = 1SLA2ǫω2 where A = C and S is the cross-
4 ωγ
tonregenerationrate,bybuildinguptheopticalpowerin sectional area of the cavity mode. The power emitted
the firstmagnetis nota new idea. In fact, the only pho- by the cavity is P = γE, assuming that there are no
tonregenerationexperimentperformedandpublishedto losses other than by transmission through the mirrors.
3
The power of the axion beam is P = 1S 2ωk , assum- µm light, and for 130 m between end mirrors, the beam
a 2 A a
ing it has the same cross-sectional area S as the cavity is everywheresmallerthan 36mm, and is notclipped by
mode. Theaxiontophotonconversionprobabilityinthe the sagitta of the LHC dipoles [11].
FP cavity is therefore Another limit is that the intracavity power density at
themirrorsbebelowthedamagethreshold,whichforthe
p = P = 1g2B02QL 2 sin(qL) 2 , (11) bestmultilayerdielectricmirrorsapproaches1GW/cm2.
FP
Pa 2ǫβaω (cid:18)qL 2 (cid:19) Puttingthe waistofthe modeatthe barrierimplies that
the limitation on power density will be first encountered
where Q= ω is the quality factorofthe cavity. In terms
γ for the slightly convex inboard mirrors. The total circu-
oftheconversionprobabilityp inthesameregion(length
′ lating power in the production magnet is 1 MW.
L, magnetic field B , and dielectric constant ǫ) without ∼
0 The best Fabry-Perot resonators have achieved a fi-
thecavity,wehavep = 2Q p = 2 ′p asannounced.
FP √ǫLω ′ Fπ ′ nesse of a few million; here, we take for the finesse,
Including both improvements, the regenerated photon 3.1 105, an order of magnitude lower, which is
F ∼ ×
power emitted from the cavity is still ambitious, but feasible. For the line-width implied
by this finesse, 7.3 Hz, the vibration tolerance for the
2
P = η η p′ p P0 . (12) cavitymirrorsis of order10−3 nm, well within the expe-
′ rience of LIGO detectors [10]. Also for this finesse, we
Half of the power P is right-moving and half is left- can design the cavity to ensure that transmission domi-
moving. To detect all the regenerated photons, detec- nates loss (scattering and diffraction), and this has been
torsareinstalledonbothsidesoftheFabry-Perotcavity, assumed.
as illustrated. The combined improvements yield an in- Intrinsic to resonantly enhanced photon regeneration
crease by a factor 2/ηη in signal power. With present is the requirement that the production and regeneration
′
technology, this factor may be as large as 1012. cavities remained locked in frequency together, within
In general, the loss of power from the cavity will have their bandwidth, ∆ν = 2ν/Q, where the quality factor,
other contributions, η =η +η +η , where the Q =n of the cavity, and n its mode index. The 10 W
′ t′rans a′bs s′catt F
latter two terms representabsorptionandscattering(in- laser is reflection locked to one of the cavity modes of
cluding diffraction) losses. If transmissionis not entirely the production cavity using the Pound-Dreever-Hall re-
dominant, then Eq. (12) should be modified by a mul- flection locking scheme [12]. Then, the challenge is to
tiplicative factor f = η /η . There is no such factor implement the locking of the regeneration cavity in a
t′rans ′
correspondingto the productionside, asthe transmitted way that does not introduce any spurious photons into
power is irrelevant, and the laser power can always be the detectors. The scheme we envision is to use a low
brought up to the limit established by optical damage. power Nd:YAG laser, offset locked by (integer) FSR of
×
There are practical limitations to the optics which es- theproductioncavity(say,50MHz)fromthemainlaser,
tablish the achievable sensitivity of a resonant photon and use the same Pound-Dreever-Hall reflection locking
regeneration experiment. Here, we present a plausible method to control the length of the regeneration cavity.
experimental realization, utilizing a 10 W CW Nd:YAG Foradditionalrejection,thelockingcouldbedoneinthe
(λ=1.064µm)laser,similartothe LIGOlaser[10], and orthogonal polarization state, i.e. perpendicular to the
a total of eight LHC dipole magnets (8.75 T, 14.3 m, 50 dipole magnetic field B~0.
mm ), which are well-suited to the experiment. There areseveralpossible schemesfor detection ofthe
⊘
With the magnets set end-to-end, four for the pro- weak signal from the regeneration cavity. The simplest
duction leg and four for the regenerationleg, the overall is to focus the cavityoutput ona cooledInGaAs charge-
length of each cavity will exceed 60 m. We use 66 m in coupled devices (CCDs), with pixels of the order of 15
this estimate, giving a cavity free spectral range (FSR) µm. Modern CCDs developed for astronomy have very
of2.3MHz. Wewillrefertothisasa4+4configuration lowdarkcurrentrates,oforder1-2emin−1pixel−1. How-
of LHC dipole magnets. The magnet diameter deter- ever, the best scheme seems to be heterodyne detection,
mines the maximum size of the TEM Gaussian mode mixing the generation cavity output with the locking
00
ofthecavities. Furthermore,thespatio-temporalprofiles laser at an RF photodiode and detecting both in-phase
oftheaxionandphotonmodesareidentical,i.e., theax- and quadrature signals at the difference frequency be-
ion mode follows that of a hypothetically unobstructed tween the laser in the generating cavity and the locking
photon beam. Thus the cavities should be symmetric, beam, especially as the frequencies of both lasers (and
with the beam waistatthe opticalbarrier,suchthatthe their difference) are well known.
two end mirrors would support the optical mode if the Definingadiscoverytobe5σ,whereσisassumedtobe
barrier and inboard mirrors were removed (Figure 1b). dominated by the square-root counting statistics of the
Thereis no constraintthatthe lengthofthe twocavities dark-current background, we find that the experiment
be exactly equal, nor that their relative separationequal is sensitive to axions or generalized pseudoscalars with
a multiple number of wavelengths. For the case of 1.064 g =2.7 10 11 GeV 1,after10dayscumulativerun-
aγγ − −
×
4
10-4 sensitivitying stillonlygains(orloses)as 1/2. Thus
aγγ
F
in the example above, the experiment would still reach
10-6 Laserexperiments PVLAS a limit of g = 8.5 10 11 GeV 1 even if the Fabry-
aγγ − −
×
Perot only achieved a finesse of 30,000. As it will
10-8 likely be easier to attain higher Fval≃ues of for shorter
-1V) baselines,wefurthernotethatasg (BFL) 1,alimit
(Ge!!a10-10 RSeoslaornsaenatrlychenhanced HBStars oHfograizγoγn∼tal10B−r1a0ncGheVSt−a1r,lii.me.ite,qsuhaoluatlγodγts∝hteillCbAeS−aTchainedvatbhlee
g
10-12 photonregeneration Axionmodels even with only one LHC dipole in each leg.
10-14 Microwavecavity A fully-detailed derivation of the central result Eq.
darkmattersearches (12), and a detailed discussion of the experimental de-
10-16 signworkedout as an example in this Letter will appear
10-6 10-5 10-4 10-3 10-2
in a future publication.
ma(eV)
We thank Frank Nezrick, Stan Whitcomb, Tom Car-
FIG. 2: (color) Current exclusion plot of mass and photon
ruthers,KemCook,BruceMacintosh,GeorgRaffeltand
coupling (m ,g ) for the axion, and the 5 σ discovery po-
a aγγ Guido Mueller for useful conversations during the de-
tential for the resonantly enhanced photon regeneration ex-
velopment of the concept. This work was supported in
periment calculated for a configuration of 4 + 4 LHC dipole
magnets. The existing exclusion limits indicated on the plot part by the U.S. Department of Energy under contracts
include the cavity microwave experiments assuming axions W-7405-ENG-48 and DE-FG02-97ER41029. P.S. grate-
saturatethedarkmatterhalodensity[1],thebestdirectsolar fullyacknowledgesthehospitalityoftheAspenCenterof
axionsearch(CASTcollaboration)[6],theHorizontalBranch Physics while working on this project.
Star limit [13], and previous laser experiments [9]. The red
errorellipseindicatesthepositiveresultofthePVLAScollab-
oration, if interpreted as a light pseudoscalar, based on mea-
surements of magnetically-induced dichroism of the vacuum
[4]. For the estimated limits of resonantly enhanced photon
[1] R. Bradley et al.,Rev. Mod. Phys. 75, 777 (2003).
regeneration presented here, the solid curve corresponds to
[2] P. Svrˇcek and E. Witten, hep-th/0605206
the↑↑↑↑ configuration of theindividualLHCdipole magnets
[3] See, for example, R. Rabad´an, A. Ringwald and K. Sig-
in both the production and regeneration strings; the dotted
urdson,Phys.Rev.Lett.96,110407(2006);A.Afanasev,
curve indicates the extension of the mass reach by addition-
JeffersonLaboratoryproposal,March25,2006;L.Duvil-
ally runningin the↑↑↓↓, and ↑↓↑↓ configurations.
laret et al.,CERN-SPSC-2005-034
[4] E. Zavattini et al. (PVLAS Collaboration), Phys. Rev.
Lett. 96, 110406 (2006).
ning, up to an axion mass of ma ∼2×10−4 eV (Figure [5] P. Sikivie, Phys. Rev. Lett. 51, 1415 (1983); Phys. Rev
2). Notetheexperiment’sreachingaγγ degradessharply D32, 2988 (1985).
withincreasingmassbeyondthatvalue. Thisupperlimit [6] K.Zioutasetal.(CASTCollaboration),Phys.Rev.Lett.
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∼ − (1988).
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gler” to cover higher regions of mass, up to values corre- theorbitof 2804-m mean radius; thecold masscould be
flexed to take thesagitta out if necessary.
spondingto the oscillationlengthdeterminedby asingle
[12] R.W.P.Drever,J.L.Hall,F.V.Kowalski,J.Hough,G.M.
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↑↑↑↑ ↑↑↓↓ ↑↓↑↓
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∼ ×
While resonant photon regeneration marks a signifi- tal Physics, University of Chicago Press 1996; and
cantimprovementoverthesimpleexperiment,infactthe hep-ph/0611350.