We describe the principle and status of the PVLAS experiment

being prepared at the Department of Physics and INFN section in Ferrara, Italy. The goal of the experiment is to measure the magnetic birefringence of vacuum. This effect is directly connected to the vacuum QED structure and can be detected by measuring the ellipticity acquired by a linearly polarized laser beam traversing a strong magnetic field. Vacuum magnetic birefringence is predicted by the Euler-Heisenberg effective Lagrangian. The experimental method is also sensitive to new physics and could place new laboratory limits to hypothetical particles coupling to two photons, such as axion like particles, or millicharged particles

Della Valle, F.

Gastaldi, U.

Messineo, G.

Milotti, E.

Pengo, R.

Piemontese, L.

Ruoso, G.

Zavattini, Guido

English

Scientific Open-access Literature Archive and Repository

DOI 10.1393/ncc/i2013-11403-0Colloquia: IFAE 2012IL NUOVO CIMENTO Vol. 36 C, N. 1 Gennaio-Febbraio 2013The PVLAS experiment for measuring the magnetic birefringenceof vacuumG. Zavattini(1)(∗), F. Della Valle(2), U. Gastaldi(1), E. Milotti(2),G. Messineo(1), R. Pengo(3), L. Piemontese(1) and G. Ruoso(3)(1) Dipartimento di Fisica, Universita` di Ferrara and INFN, Sezione di Ferrara - Ferrara, Italy(2) Dipartimento di Fisica, Universita` di Trieste and INFN, Sezione di Trieste - Trieste, Italy(3) INFN - Laboratori Nazionali di Legnaro - Legnaro (PD), Italyricevuto il 31 Agosto 2012Summary. — We describe the principle and status of the PVLAS experimentbeing prepared at the Department of Physics and INFN section in Ferrara, Italy.The goal of the experiment is to measure the magnetic birefringence of vacuum.This effect is directly connected to the vacuum QED structure and can be detectedby measuring the ellipticity acquired by a linearly polarized laser beam traversinga strong magnetic field. Vacuum magnetic birefringence is predicted by the Euler-Heisenberg effective Lagrangian. The experimental method is also sensitive to newphysics and could place new laboratory limits to hypothetical particles coupling totwo photons, such as axion like particles, or millicharged particles.PACS 12.20.-m – Quantum electrodynamics.PACS 42.25.Lc – Birefringence.PACS 78.20.Ls – Magneto-optical effects.1. – IntroductionIt is well known that Maxwell’s equations in vacuum are linear: the superpositionprinciple is valid for electromagnetic fields. Heisenberg’s principle, though, allows vacuumto fluctuate producing virtual pairs of particles which, if charged, lead to non-linear effectsin vacuum such as light-light scattering through the box diagram where four photons caninteract. For energies well below the electron mass and fields well below their criticalvalues B  Bcrit = m2ec2/eh¯ = 4.4 · 109 T, E  Ecrit = m2ec3/eh¯ = 1.3 · 1018 V/m, suchnon-linear electrodynamic effects, can be described by the Euler-Heisenberg effective(∗) E-mail: guido.zavattini@unife.itc© Societa` Italiana di Fisica 4142 G. ZAVATTINI, F. DELLA VALLE, U. GASTALDI, ETC.Lagrangian correction first derived in 1936 [1] (in S.I. units)(1) LEH= Aeμ0⎡⎣(E2c2−B2)2+7(Ec· B)2⎤⎦ with Ae = 245μ0α2λ¯3emec2= 1.32 · 10−24 T−2,where μ0 is the magnetic permeability of vacuum, λ¯e being the Compton wavelength ofthe electron, α = e2/(h¯c4π0) the fine structure constant, me the electron mass, c thespeed of light in vacuum.As shown by Adler [2] the magnetic birefringence of vacuum can be calculated bydetermining the electric displacement vector D and magnetic intensity vector H fromthe total Lagrangian density L = LCl + LEH by using the constitutive relations(2) D =∂L∂ Eand H = − ∂L∂ B.Light propagation in an external field can now be described using Maxwell’s equationsin media. By assuming a linearly polarized beam of light propagating perpendicularly toan external magnetic field Bext there are two possible configurations: light polarizationparallel to Bext and light polarization perpendicular to Bext. If we denote the electricand magnetic fields of the laser beam with the subscript γ, and we substitute E = Eγand B = Bγ + Bext in the expressions obtained from (2) one finds the following relationsfor the relative dielectric constants, magnetic permeabilities and index of refraction:(3)⎧⎪⎨⎪⎩‖ = 1 + 10AeB2ext,μ‖ = 1 + 4AeB2ext,n‖ = 1 + 7AeB2ext,⎧⎪⎨⎪⎩⊥ = 1− 4AeB2ext,μ⊥ = 1 + 12AeB2ext,n⊥ = 1 + 4AeB2ext.From these sets of equations two important consequences arise: the velocity of lightin the presence of an external magnetic field is no longer c and vacuum is birefringent:(4) Δn = 3AeB2ext.With BExt = 2.5T numerically this leads to a birefringence of(5) Δn = 3AeB2ext = 2.5 · 10−23.Furthermore, hypothetical neutral particles coupling to two photons may also allowthe interaction between two photons. These effects also result in v = c, birefringence,and dichroism in the presence of an external field (magnetic or electric). The Lagrangiandensities describing the interaction of either pseudoscalar fields φa or scalar fields φs withtwo photons can be expressed as (written in natural Heavyside-Lorentz units)(6) La = 1Maφa E · B and Ls = 1Msφs(E2 −B2),where Ma and Ms are the inverse coupling constants.Depending on the mass of the hypothetical particle with respect to the photon energy,both birefringence and dichroism will be induced [3]. Here we will only report the inducedTHE PVLAS EXPERIMENT FOR MEASURING THE MAGNETIC BIREFRINGENCE OF VACUUM 43birefringence. The induced birefringence in the pseudoscalar case, where na‖ > 1 andna⊥ = 1, and in the scalar case, where ns⊥ > 1 and ns‖ = 1, will be(7) |Δn| = na‖ − 1 = ns⊥ − 1 =B2ext2M2a,sm2a,s(1− sin 2x2x),where, in vacuum, x = Lm2a,s4ω , ω is the photon energy and L is the magnetic field length.The above expressions are in natural Heavyside-Lorentz units whereby 1T =√h¯3c3e4μ0=195 eV2 and 1m = eh¯c = 5.06 · 106 eV−1.Finally particles with millicharge e will also induce birefringence through the Feyn-man box diagram [4-6]. In this case one must distinguish between fermions and spin0 bosons. Defining a mass parameter χ ≡ 32 h¯ωmc2 eBexth¯m2c2 (S.I. units) for fermions thebirefringence isΔnDf =⎧⎨⎩3AB2ext, for χ  1,− 97 452π1/221/3(Γ( 23 ))2Γ( 16 )χ−4/3AB2ext, for χ  1,whereas for spin 0 bosons the birefringence isΔns0 =⎧⎨⎩− 64AB2ext, for χ  1,914452π1/221/3(Γ( 23 ))2Γ( 16 )χ−4/3AB2ext, for χ  1.The best limit set today on magnetic induced vacuum birefringence at 95% c.l. [7] is(8) Δn(PVLAS) < 4.6 · 10−20.2. – MethodThe PVLAS experiment, with a new setup being currently mounted at the PhysicsDepartment of the University of Ferrara and INFN section, Ferrara, Italy, has the goalof detecting for the first time magnetic vacuum birefringence by measuring the elliptic-ity Ψ acquired by a linearly polarized beam of light when traversing a magnetic fieldperpendicular to the propagation direction:(9) Ψ = πLeffΔnλsin 2ϑ,where Leff is the effective path length within the birefringent region with birefringenceΔn, λ is the wavelength of the light traversing it and ϑ is the angle between the magneticfield and the light polarization.To maximize the induced ellipticity the magnetic field region must be as long aspossible, the magnetic field as intense as possible and the wavelength small. Finallythe expected ellipticity must be compared to the different noise sources present and tothe maximum available integration time. Experimentally Leff can be made very long byusing a very high-finesse Fabry-Perot cavity. Given a birefringent region of length L theeffective path length is Leff = 2Fπ L. Today finesses F > 400000 can be obtained.44 G. ZAVATTINI, F. DELLA VALLE, U. GASTALDI, ETC.Fig. 1. – Scheme of the PVLAS ellipsometer.Very high magnetic fields can be obtained with superconducting magnets but it isdesirable to have a time-dependent induced ellipticity at a frequency as high as possibleso as to stay away from DC and reduce 1/f noise. This can be done by either rampingthe magnet, thereby changing Δn or by rotating the field direction, thereby changing ϑ.This makes superconducting magnets far less appealing than permanent magnets which,today, can reach fields of 2.5T over volumes as those needed for PVLAS. Furthermorepermanent magnets are relatively inexpensive, have no running costs and have 100%duty cycle allowing in principle very long integration times. Pulsed fields are anotheroption for very intense and quickly varying fields [8] but duty cycle may be an issue.The laser we are working with is a Nd:YAG laser emitting radiation at 1064 nm.Frequency doubled versions exist and could double the induced ellipticity but at themoment higher finesses have been obtained at 1064 nm.A scheme of the ellipsometer is shown in fig. 1. The input polarizer linearly polarizesthe laser beam of intensity I0 which then enters the sensitive region defined by theFabry-Perot cavity mirrors. The laser is phase locked to this cavity thus increasing theoptical path length within the magnetic field by a factor 2F/π. After the cavity, to allowheterodyne detection the laser beam passes through a photo-elastic ellipticity modulator(PEM) which adds a known time dependent ellipticity η(t) = η0 cos(ωModt + φMod)to the beam. After the PEM the beam passes through the analyzer which selects thepolarization perpendicular to the input polarization. A photodiode detects ITr and itsFourier spectrum is then analyzed. The intensity detected at the photodiode is therefore(10) ITr(t) = Iout∣∣∣∣ıα(t) + ıη(t) + ı(2Fπ)ψ sin (2ΩMagt + 2φMag)∣∣∣∣2,where we have also introduced α(t) which represents slowly varying spurious ellipticitiesdue to the optical elements in the apparatus [9]. Therefore small ellipticities add upalgebraically and the Fabry-Perot multiplies the single pass ellipticity ψ sin 2ϑ, generatedwithin the cavity, by a factor 2F/π.The presence of the beat frequency between η(t) and Ψ(t) generates a component atωMod ± 2ΩMag and identifies an induced ellipticity within the Fabry-Perot cavity.The apparatus being assembled in Ferrara has two 92 cm long permanent dipolemagnets characterized by∫B2dl = 11T2m which will rotate at an angular velocityof ΩMag = 10π rad/s and a cavity with finesse F > 400000. The reason for having twomagnets instead of a single longer one is to be able to make zero measurements. Byorienting the magnetic fields perpendicularly to each other the ellipticity induced by onemagnet is cancelled by the second. One of the important characteristics is that the entireoptical setup will be on one single optical bench thus strongly reducing seismic noise.A test setup was built with two small 20 cm long, 2.3T rotating magnets to understandand verify our design and understand whether it was possible to reach the requiredsensitivity necessary to detect for the first time vacuum magnetic birefringence with areasonable integration time. A picture of the smaller test setup is shown in fig. 2. ResultsTHE PVLAS EXPERIMENT FOR MEASURING THE MAGNETIC BIREFRINGENCE OF VACUUM 45Fig. 2. – Photograph of the small test ellipsometer.have been promising [7]. Furthermore the subtraction of the effects of the two magnetswas also demonstrated using the Cotton-Mouton effect.With this small apparatus we were able to improve by a factor ∼ 2 the previouslimits [10] on magnetic-induced vacuum birefringence reported in eq. (8) and a limit onAe at 95% c.l. [7](11) A(PVLAS)e < 2.9 · 10−21 T−2.With our new experimental parameters the induced ellipticity ΨQED will be(12) ΨQED =2Fππ3AeB2ExtLλ= 3.2 · 10−11We hope to achieve an ellipticity sensitivity of Ψsens = 2·10−8 1/√Hz [11]. This wouldlead to a first measurement of vacuum magnetic birefringence in (Ψsens/ΨQED)2 = 103hours.REFERENCES[1] Euler H. and Kochel B., Naturwiss., 23 (1935) 246. Heisenberg W. and Euler H.,Z. Phys., 98 (1936) 718. Weisskopf V. S., Kgl. Danske Vid. Sels., Math.-fys. Medd., 14(1936) 6.[2] Adler S. L., Ann. Phys. (N.Y.), 67 (1971) 559. Bialynicka-Birula Z. and Bialynicki-Birula I., Phys. Rev. D, 2 (1970) 2341.[3] Maiani L. et al., Phys. Lett. B, 175 (1986) 359. Raffelt G. and Stodolsky L., Phys.Rev. D, 37 (1988) 1237.[4] Tsai W. y. and Erber T., Phys. Rev. D, 12 (1975) 1132.[5] Ahlers M. et al., Phys. Rev. D, 75 (2007) 035011. Gies H. et al., Phys. Rev. Lett., 97(2006) 140402.[6] Schubert C., Nucl. Phys. B, 585 (2000) 407.[7] Zavattini G. et al., Int. J. Mod. Phys. A, 27 (2012) 1260017.[8] Berceau P. et al., Phys. Rev. A, 85 (2012) 013837.[9] Zavattini G. et al., Appl. Phys. B, 83 (2006) 571.[10] Bregant M. et al., Phys. Rev. D, 78 (2008) 032006.[11] Della Valle F. et al., Optics Commun., 293 (2010) 4194.

The PVLAS experiment for measuring the magnetic birefringence of vacuum

We describe the principle and status of the PVLAS experiment being prepared at the Department of Physics and INFN section in Ferrara, Italy. The goal of the experiment is to measure the· magnetic birefringence of vacuum. This effect is directly connected to the vacuum QED structure and can be detected by measuring the ellipticity acquired by a linearly polarized laser beam traversing a strong magnetic field. Vacuum magnetic birefringence is predicted by the Euler-Heisenberg effective Lagrangian. The experimental method is also sensitive to new physics and could place new laboratory limits to hypothetical particles coupling to two photons, such as axion-like particles, to millicharged particles

The PVLAS experiment for measuring the magnetic birefringence of vacuum

Abstract

Similar works

Full text

Available Versions

Scientific Open-access Literature Archive and Repository

Archivio della Ricerca - Università degli Studi di Siena