Measurements of the Cotton-Mouton and Inverse Cotton-Mouton effects

Transcription

1 Measurements of the Cotton-Mouton and Inverse Cotton-Mouton effects Rémy Battesti Toulouse university LABORATOIRE NATIONAL DES CHAMPS MAGNETIQUES INTENSES - TOULOUSE

2 For atomic systems U η ηe α E β B γ B δ see eg : Rizzo et al, Int. Rev. Chem. Phys., 16, 81 (1997) P = U E P ηb 2 E M = U B M ηe 2 B n = n n (η η )B 2 Cotton Mouton effect measurement = birefringence measurement M η E 2 B M η E 2 B Inverse Cotton Mouton effect measurement = aimantation measurement

3 OUTLINE 1) Inverse Cotton-Mouton effect Introduction Experimental set up Results In collaboration with : Paul Berceau Mathilde Fouché Carlo Rizzo Geert Rikken Andrei Baranga 2) Cotton-Mouton effect of vacuum : BMV project Introduction Experimental set up Some results Conclusion

4 Inverse Cotton Mouton effect (ICME) optical magnetization induced by a high intensity laser beam crossing a transparent medium perpendicular to a magnetic field. Linearly polarized beam E M B Induced magnetization M! E 2 B

5 Measuring ICME on crystals! Medium solid, liquid, gaz, vacuum Rizzo et al, Eur. Phys. Lett., 90, (2010)! Laser high power! Magnetic field : intense perpendicular to the laser beam! The probe : sensitive magnetic probe DATA acquisition system

6 Medium : TGG crystal 2 mm TGG crystallography alignment : <100> 2 mm 2 mm High laser damage threshold (>1GW/cm 2 ). We observed no damage up to the checked laser power density of 4!GW/cm 2 (10 ns pulse of 0.5 J concentrated to a Ø1.2 mm spot)

7 Optical set up " Laser: Q switched Maximum Energy/pulse=0.5 J. " Single pulse operation. " Two high power polarizers for power change and final polarization. " Laser focused 10 cm after the crystal by an f900 lens. " Laser spot on the crystal: Ø1.2 mm. Power density=4 GW/cm 2. " Laser polarization rotated by a!/2 waveplate.

8 Constant magnetic field " CW magnetic field produced by an electromagnet. " Variable distance between the poles. Set to 9 mm for the ICME probe. " Maximum magnetic 9 mm distance between the poles: 2.6 Tesla. " Field uniformity better than 0.2% over crystal volume. " Easy measuring timing.

9 Crystal magnetization measurement 2.5 mm Bobine Pickup 1 The magnetic flux density B p measured by the probes (ICME signal) is related to crystal magnetization M by a geometric conversion factor f =2.5!10 7 A/(m"T) Only ~3% of the field produced by the magnetization is captured by a 2!2 mm probe at 2.5 mm distance. A larger probe looses signal due to returning field lines. Bobine Pickup 2 Simulation of the magnetic field produced by an 1 mm diameter cylindrical magnetization. Conclusions: the probe should be equal in size or smaller than the illuminated crystal and placed close to it.

10 Pickup coils Planar, 4 turns rectangular pickup coils 2 mm Probe : one pickup coil and one compensating coil on two sides of the crystal. Compensating coil Pickup coil Calibrated effective area of the pickup coil: 10 mm 2. 9 mm (Compensation coil for pulsed magnetic field.) Sonde de calibration sans bobine de compensation Tubular configuration for laser passage. 2 mm

11 ICME tubular probe R. Battesti, Fundamental Physics laws workshop B e e k M 9 mm compensating coil signal pickup coil

12 Data acquisition " Signal amplified by a fast amplifier (400 MHz). " 100 khz high pass filter. " Signal captured by a fast digital oscilloscope of 1GS/s and stored on computer.

13 The ICME signal V(t) is proportional to the time derivative of the magnetic flux density Bp(t) in the pick up coil V (t) = ga e db p (t) dt g : signal amplification and Ae : probe effective area and the magnetic flux density Bp(t) can be written as : db p (t) dt = bb ext dp laser (t) dt b : proportionality factor Plaser : laser power density Bext : external magnetic field V (t) = ga e bb ext dp laser (t) dt

14 Probe calibration probe " The uniform field produced by a 4 coils calibration solenoid was measured by two calibrated probes for khz. " A pickup coil identical to those of our probe monitored the field inside the solenoid for the same frequency range. Lock-in Amp. Sig. IN Sin. OUT " The direction of the field monitored by our probe was determined by the field produced by a 3 mm diameter, 35 turns coil. " The amplification g was measured up to 80MHz. 3 mm Probe calibration: Ae=10 mm 2, g 1 =12; g 2 =10

15 ICME signals V (t) = ga e bb ext dp laser (t) dt the ICME signal is proportional to the time derivative of the laser pulse intensity.

16 ICME -VS- laser intensity Magnetic flux density vs. Laser power density 3.00E E-05 B p (t) =bp laser B ext Bp (Tesla) 1.50E E-06 0E+00 Laser polarisation perpendicular to B Linear.(Laser polarisation perpendicular to B) Laser polarisation parallel to B Linear.(Laser polarisation parallel to B) -7.50E-06 0E E E E E+13 laser power density (W/m2) ICME magnetization is proportional to E 2, higher for parallel polarization

17 Bp -vs- B 2.00E-05 B p (t) =bp laser B ext Magnetic flux density Bp (Tesla) 1.50E E E-06 0E E E E-05 laser polarization perpendicular to B Linear.(laser polarization perpendicular to B) laser polarization parallel to B Linear.(laser polarization parallel to B) -2.00E Applied magnetic field B (Tesla) ICME magnetization is proportional and parallel to B

18 Bp -vs- E 2 B 4.00E E-05 y = 3.36E-19x B p (t) =bp laser B ext 2.00E-05 Bp (Tesla) 1.00E E+00 y = 2.07E-19x b =(3.36 ± 0.04) m 2 W 1 b =(2.07 ± 0.05) m 2 W E-05 laser polarization perpendicular to B -2.00E-05 laser polarization parallel to B -3.00E-05-6E+13-4E+13-2E E+13 4E+13 6E+13 8E+13 1E+14 laser power density x B (W/m 2 xtesla) ICME magnetization is proportional to E 2 B

19 Inverse Cotton Mouton constant " ICME magnetization M is proportional to laser intensity and to the external magnetic field, and parallel to the applied magnetic field. M(t) C ICM P laser (t) B ext C ICM = (A.m)(W.T ) 1 C ICM = (A.m)(W.T ) 1

20 Conclusion R. Battesti, Fundamental Physics laws workshop " The Inverse Cotton-Mouton effect (ICME) has been observed and experimentally investigated for the first time. " As theoretically predicted # the ICME magnetization is proportional to laser intensity and to the transversal applied magnetic field # the ICME magnetization is parallel to the external magnetic field. " The ICME magnetization depends on laser polarization and is higher for parallel to the magnetic field polarization. " The Inverse Cotton Mouton coefficients have been calculated.

21 Vacuum magnetic birefringence

22 1934 : Vacuum is a non linear optical medium H.Euler et K.Kochel, Naturwiss. 23 (1935); W.Heisenberg et H.Euler, Z. Phys. 38 (1936) : The value of the Vacuum magnetic birefringence is published Vacuum Cotton-Mouton effect Z.Bialynicka-Birula et I.Bialynicki-Birula, Phys. Rev. D 2 (1970) 2341 Linear polarization vacuum Elliptical polarization L From QED theory : "n = 4!10-24 B 2 = "n u!b 2 Cotton Mouton effect has been discovered in 1901, studied in details since 1904, and it exists in all media. "n for helium gas (1 atm, 1 T, 0 C) is about

23 Experimental set up B 0 optical fiber Polarizer Analyzer Photodiode!=1064 nm laser ψ = π λ n u 2F π B 2 L mag sin(2θ)

24 Experimental set up cavity mirrors (T ~ ppm) B 0 optical fiber Polarizer pulsed magnetic field Analyzer Photodiode!=1064 nm laser ψ = π λ n u 2F π B 2 L mag sin(2θ)

25 Experimental final goals Table top experiment cavity finesse : F ~ LMA (Lyon IN2P3) mirrors magnetic field : B" L mag > 600 T" m ( short L mag high B )! expected ellipticity to be measured : Ψ QED = Nd:Yag laser :! = 1064 nm Battesti et al., Eur. Phys. J. D, vol. 46, pp. 323 (2008)

26 cavity mirrors (T ~ ppm) B 0 optical fiber!=1064 nm laser Polarizer pulsed magnetic field Analyzer Photodiode

27 Experimental set up B 0 B 0 Fiber!=1064 nm Polarizer mirror #1 LMA IN2P3 mirror #2 2,2 m Analyzer 26

28 Experimental set up magnet #1 magnet #2 B 0 B 0 Fiber!=1064 nm Polarizer mirror #1 LMA IN2P3 mirror #2 2,2 m Analyzer 26

29 magnet #1 magnet #2 ψ = π λ n u 2F π B 2 L mag sin(2θ) Laser Mirror #1 LMA IN2P3 Mirror #2 Polarizer Analyzer

30 Design of the pulsed magnet : X-coil goals : transverse magnetic field B"L > 600 T"m I # 1.2 B(mT) I B 1 B 2 B X coil geometry z(m) Designed for BMV at the LNCMI in 2002 (O. Portugall, S. Batut, J. Mauchain)

31 Design of the pulsed magnet : X-coil goals : transverse magnetic field B"L > 600 T"m I B"L/I" = 2,5!10-7 T"m/A" # 1.2 B(mT) I B 1 B 2 B X coil geometry z(m) Designed for BMV at the LNCMI in 2002 (O. Portugall, S. Batut, J. Mauchain)

32 The BMV project : present magnet Xcoil Transverse field B 0.25 m Coil in its LN cryostat Laser B = 14,3 T 8300 A B#L = 28 T#m Repetition rate : 5 pulses per hour

33 Cryostat 12 mm

34 magnet #1 magnet #2 ψ = π λ n u 2F π B 2 L mag sin(2θ) Laser Mirror #1 LMA IN2P3 Mirror #2 Polarizer Analyzer

35 Clean room Decembre 2005

36 Clean room July ISO 3 10 ISO 4 95 Number of particules per ft 3 ISO ISO 5 ISO 4 90 ISO 5

37 Clean room R. Battesti Les Houches 22/10/09 BMV Magnet #1 Magnet #2 Laser Analyzer Mirror #2 Mirror #1 Polarizer The experimental setup in the clean room at LNCMI 3.6 m table top experiment

38 The BMV project : optical set up Iext M2 L M1 FI 2 T2 It Locking A Fabry-Perot Cavity error signal mixer P Iréfl # Table «cavité» Optical!/2 Fiber T1 CSP!/4 AOM!/2 P2 EOM!/2 FI1 Laser! = µm Table «source»

39 I i B(t) σ 2 I ext Γ 2 ψ(t) σ 2 mirrors ellipticity ellipticity to measure polarizers extinction 2 Γ I ext = I t σ 2 + I t (Γ + ψ(t)) 2 ψ(t) = π λ n u I t 2F π B 2 L mag sin(2θ) = αb(t) 2

40 I i B(t) σ 2 I ext Γ 2 ψ(t) σ 2 mirrors ellipticity ellipticity to measure polarizers extinction 2 Γ I ext = I t σ 2 + I t (Γ + ψ(t)) 2 ψ(t) = π λ n u I t 2F π B 2 L mag sin(2θ) = αb(t) 2 Correlation between the pulsed field B(t) 2 and the measured ellipticity ψ(t) : = 2FL mag λ n u en T -2 α gives the value of the birefringence n u of the considered medium

41 photon lifetime : τ = 650µs flight distance in the cavity = 200 km! Laser switched off F = πcτ L cav =

42 photon lifetime : τ = 650µs flight distance in the cavity = 200 km! Laser switched off F = πcτ L cav = n u = λ 2πc L c L mag α 1 τ 1 sin(2θ)

43 The BMV project : Data taking Images from a movie realized for the IYA2009

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46 Example of raw data (Helium) $ Cotton-Mouton effect of helium (1 atm, 293 K) Raw data Iext(a.u.) I ext It(a.u.) Laser locked Laser unlocked I t B 2 (T 2 )

47 Results Magnetic birefringence of nitrogen vs pressure birefringence #n u (p) (!10-15 T -2 ) n(p) =p(atm) n u (1atm) n u (1atm) =( 2.39 ± 0.08) T 2 pressure (!10-3 atm) value in agreement with the existing measurements and with theoretical calculations normalized birefringence #n u (1atm) (!10-13 T -2 )

48 Preliminary results for helium : Theory : n u (1atm) =(2.400 ± 0.005) T 2 Our preliminary measurement : n u (1atm) =(2.1 ± 0.4) T 2 normalized birefringence #n u (1atm) (!10-16 T -2 ) good agreement calibration of our ellipsometer

49 Conclusion Laser locked on a 2.3 m Fabry Perot cavity All components are working together especially the high magnetic field and the Fabry Perot cavity We are able to measure the smallest Cotton mouton effect in gases What else?... 42

50 The BMV project : What next? XXLCoil XXL Coil Designed at LNCMI 70 cm 250 Kg Ø3.6 cm 32 cm Magnetic pressure: 700 t on the screws!! B 2 L > 200 T 2 m 3 magnets! Final set up

51 The BMV project : What next? XXLCoil The structure in G20

52 The BMV project : What next? XXLCoil A screw Reinforcements Winding started the 07/07/09

53 73 cm I = A B 2 L = 300 T 2 m

54 Status and perspectives Insertion of 3 XXL-coils on a new setup increase the finesse ( ) improvement of! 2 (10-7 ) decrease " 2 (10-8 ) stabilisation of our locking system Improvement of the sensitivity Vacuum measurement QED :!n = 4"10-24 B pulses (2 months)

55 Measurements of the Cotton-Mouton and Inverse Cotton-Mouton effects Paul Berceau Mathilde Fouché Carlo Rizzo Geert Rikken Andrei Baranga all the technical staff of the lab LABORATOIRE NATIONAL DES CHAMPS MAGNETIQUES INTENSES - TOULOUSE

56 Can we reach the QED limit? R. Battesti, Fundamental Physics laws workshop we have Vacuum shots performed Experimental parameters : F = B 2 L mag = 26 T 2 m $ 2 = 10-7 $ 2 = 10-6 Sensibility reached in ellipticity : corresponding to : #nu = 2 $ T -2 / shot

57 Can we reach the QED limit? R. Battesti, Fundamental Physics laws workshop we have we need Vacuum shots performed Experimental parameters : F = B 2 L mag = 26 T 2 m $ 2 = 10-7 $ 2 = 10-6 Sensibility reached in ellipticity : corresponding to : #nu = 2 $ T -2 / shot! 10! 20 / 10 / 10 New vacuum shots to be performed New experimental parameters : F = B 2 L mag = 600 T 2 m $ 2 = 10-8 $ 2 = 10-7 corresponding to a sensibility of : #nu = 8$10-23 T -2 / shot So, the number of shots is : Ψ QED = stability of locking system = 400 shots

58 The BMV project : Final goal R. Battesti Les Houches 22/10/09 BMV Experimental challenge : Radiative corrections

59 The BMV project : Final goal R. Battesti Les Houches 22/10/09 BMV Experimental challenge : "n (vide) = B 2 (B en Tesla) Radiative corrections "n (vide) $ 10-8 "n (hélium CNTP)

60 The BMV project : Final goal R. Battesti Les Houches 22/10/09 BMV Experimental challenge : "n (vide) = B 2 (B en Tesla) Radiative corrections "n (vide) $ 10-8 "n (hélium CNTP) Fundamental constants : 2006 codata n = 2 15 α 2 h 3 m 4 ec B 2 648π α µ 0 n = (4, ± 0, ) B 1T 2 V.I.Ritus,Sov. Phys. JETP 42, 774 (1975) O(! 3 ) O(! 4 )? O(! 5 )? Theoretical challenge!

61 Molecular energy U electric dipole moment static electric polarizability static magnetic polarizability U(τ; E, B )=U 0 P i E i 1 2 α ije i E j 1 2 χ ijb i B j 1 2 ζ ijkeib j B k 1 4 η ijkle i E j B k B l + O[(E,B) 3 ]. first hypermagnetizability second hypermagnetizability

62 R. Battesti, Fundamental Physics laws workshop Heisenberg-Euler effective Lagrangian L = 1 2 F + af 2 +7aG Vacuum is Lorentz and CPT invariant where F = 0 E 2 B2 µ 0 and G = 0 µ 0 E. B 1950 Pictorial representation based on Feynman s diagrams Without external field: With external field B: 1970 : c depends on light polarization! 52