1. Nonlinear Magneto-Optical Rotation with Frequency-Modulated Light Derek Kimball Dmitry Budker Simon Rochester Valeriy Yashchuk Max Zolotorev and many others...

2. Some of the many others: D. English K. Kerner C.-H. Li T. Millet A.-T. Nguyen J. Stalnaker A. Sushkov E. B. Alexandrov M. V. Balabas W. Gawlik Yu. P. Malakyan A. B. Matsko I. Novikova A. I. Okunevich H. G. Robinson A. Weis G. R. Welch Budker Group: Non-Berkeley Folks: Technical Support: M. Solarz A. Vaynberg G. Weber J. Davis Funding: ONR

3. Plan: Linear Magneto-Optical (Faraday) Rotation Nonlinear Magneto-Optical Rotation (NMOR) –Coherence effects –Paraffin-coated cells –Experiments NMOR with Frequency-Modulated light (FM NMOR) –Motivation –Experimental setup –Data: B-field dependence, spectrum, etc. A little mystery... Applications –Sensitive magnetometry –EDM search? Review: Budker, Gawlik, Kimball, Rochester, Yashchuk, Weis (2002). Rev. Mod. Phys. 74(4), 1153-1201.

4. Linear Magneto-Optical (Faraday) Rotation  Medium Linear Polarization Circular Components Magnetic Field  = (n + -n - ) 0l0l 2c2c = (n + -n - ) ll 1846-1855: Faraday discovers magneto-optical rotation 1898,1899: Macaluso and Corbino discover resonant character of Faraday rotation

5. Linear Magneto-Optical (Faraday) Rotation 1898: Voigt connects Faraday rotation to the Zeeman effect

6. Linear Magneto-Optical (Faraday) Rotation

7.  B ~ 400 G

8. Nonlinear Magneto-Optical Rotation Faraday rotation is a linear effect because rotation is independent of light intensity. Nonlinear magneto-optical rotation possible when light modifies the properties of the medium: B = 0  Spectral hole-burning: Number of atoms Atomic velocity Light detuning Index of refraction Re[n + -n - ] B  0 Small field NMOR enhanced!

9. Coherence Effects in NMOR 1.Resonant light polarizes atomic sample via optical pumping. 2.Polarized atoms precess in the magnetic field. 3.This changes the optical properties of the medium  rotation of light polarization. Three-stage process: x-polarized light interacts with coherent superposition of ground state Zeeman sublevels

10. Coherence Effects in NMOR Optical pumping:  Polarizes atoms  Aligns magnetic dipole moments  Creates optical anisotropy (linear dichroism)

11. Coherence Effects in NMOR Visualization of atomic polarization: Draw 3D surface where distance from origin equals the probability to be found in a stretched state ( M=F ) along this direction. Rochester and Budker (2001). Am. J. Phys. 69, 450-4.

12. Coherence Effects in NMOR torque causes atomic polarization to precess:. B

13. Coherence Effects in NMOR torque causes atomic polarization to precess:

14. Coherence Effects in NMOR Relaxation of atomic polarization: Plane of light polarization is rotated, just as if light had propagated through a set of “polaroid” films. Equilibrium conditions result in net atomic polarization at an angle to initial light polarization. (polarized atoms only)

15. Coherence Effects in NMOR Magnetic-field dependence of NMOR due to coherence effects can be described by the same formula we used for linear Faraday rotation, but    rel : How can we get slowest possible  rel ?

16. Paraffin-coated cells Academician Alexandrov has brought us some beautiful “holiday ornaments”... Magical!

17. Paraffin-coated cells Alkali atoms work best with paraffin coating... Most of our work involves Rb: 87 Rb (I = 3/2)

18. Paraffin-coated cells Polarized atoms can bounce off the walls of a paraffin-coated cell ~10,000 times before depolarizing! This can be seen using the method of “relaxation in the dark.”

19. Paraffin-coated cells

20. DC polarimeter calibration polarizer magnetic shield magnetic coil Rb-cell lock-in reference pre-amplifier analyzer polarization- modulator polarization- rotator PD1 PD2 attenuator spectrum analyzer diode laser P uncoated Rb cell in magnetic field /4 BS PD Dichroic Atomic Vapor Laser Lock differential amplifier PD light-pipe feedback laser frequency control fluorescence control and data acquisition absorption magnetic field current first harmonic Experimental Setup

21. Magnetic Shielding Four-layer ferromagnetic magnetic shielding with nearly spherical geometry reduces fields in all directions by a factor of 10 6 !

22. Magnetic Shielding

23. 3-D coils allow control and cancellation of fields and gradients inside shields.

24. NMOR Coherence Effect in Paraffin-coated Cell 85 Rb D2 Line, I = 50  W/cm 2, F=3  F’=4 component  rel = 2   0.9 Hz Kanorsky, Weis, Skalla (1995). Appl. Phys. B 60, 165. Budker, Yashchuk, Zolotorev (1998). PRL 81, 5788. Budker, Kimball, Rochester, Yashchuk, Zolotorev (2000). PRA 62, 043403.

25. Sensitive measurement of magnetic fields 85 Rb D2 line, F=3  F’ component, I = 4.5 mW/cm 2

26. The dynamic range of an NMOR-based magnetometer is limited by the width of the resonance:  B ~ 2  G How can we increase the dynamic range?

27. NMOR with Frequency-Modulated Light Magnetic field modulates optical properties of medium at 2  L. There should be a resonance when the frequency of light is modulated at the same rate! Experimental Setup: Inspired by: Barkov, Zolotorev (1978). JETP Lett. 28, 503. Barkov, Zolotorev, Melik-Pashaev (1988). JETP Lett. 48, 134.

28. NMOR with Frequency-Modulated Light In-phase component Out-of-phase (quadrature) component  m = 2  1 kHz  = 2  220 MHz P  15  W 87 Rb D1 Line F = 2  1 Budker, Kimball, Yashchuk, Zolotorev (2002). PRA 65, 055403.

29. NMOR with Frequency-Modulated Light Low-field FM NMOR resonance is analogous to that seen in conventional NMOR. Low field resonance:  L   rel

30. NMOR with Frequency-Modulated Light Laser frequency modulation  modulation of optical pumping. If periodicity of pumping is synchronized with Larmor precession, atoms are pumped into aligned states rotating at  L. High field resonances:  L >>  rel

31. NMOR with Frequency-Modulated Light Optical properties of the atomic medium are modulated at 2  L. Resonances occur for n  m = 2  L. Largest amplitude for n = 1.

32. NMOR with Frequency-Modulated Light Quadrature signals arise due to difference in phase between rotating medium and probe light. Second harmonic signals appear for  m =  L.

33. NMOR with Frequency-Modulated Light Low field resonance High field resonance Note that spectrum of FM NMOR First Harmonic is related to NMOR spectrum: For 2nd harmonic (not shown):

34. NMOR with Frequency-Modulated Light Demonstrated sensitivity ~ 10 -9

35. A mystery...  m = 4  L See new resonances at for high light power!  m = 200 Hz

36. Hexadecapole Resonance Arises due to creation and probing of hexadecapole moment (  = 4). Yashchuk, Budker, Gawlik, Kimball, Malakyan, Rochester (2003). PRL 90, 253001.

37. Hexadecapole Resonance Highest moment possible:  = 2F No resonance for F=1

38. Hexadecapole Resonance At low light powers: Quadrupole signal  I 2 Hexadecapole signal  I 4

39. Applications Measurement of decay of hyperpolarized Xe: (In collaboration with Pines Group)

40. EDM search? Permanent EDM violates parity and time-reversal invariance! Best limit on electron EDM: Regan, Commins, Schmidt, DeMille (2002). PRL 88, 071805.

41. EDM search? E = 5 kV/cm  60 ms

42. EDM search? Use nonlinear induced ellipticity to measure electric field: Enhanced by Bennett structures in the atomic velocity distribution!

43. EDM search? Comparison of experiment to density matrix calculation indicates atoms see full 5 kV/cm electric field!

44. EDM search?

45. Future directions... Reduce technical sources of noise in system. Demonstrate projected sensitivity at Earth field. Investigate application of electric field to cells. Investigate causes of spin-relaxation in paraffin-coated cells. Apply FM NMOR to magnetic field measurements! Apply FM NMOR to fundamental symmetry tests?