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Nonlinear Magneto-Optical Rotation with Frequency-Modulated Light

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

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Nonlinear Magneto-Optical Rotation with Frequency-Modulated Light

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

  2. 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 S. Pustelny A. Weis G. R. Welch Some of the many others: Budker Group: Non-Berkeley Folks: Technical Support: M. Solarz A. Vaynberg G. Weber J. Davis Funding:ONR, NSF

  3. Plan: • Linear Magneto-Optical (Faraday) Rotation • Nonlinear Magneto-Optical Rotation (NMOR) • Polarized atoms • Paraffin-coated cells • Experiments • NMOR with Frequency-Modulated light (FM NMOR) • Motivation • Experimental setup • Data: B-field dependence, spectrum, etc. • A little mystery... • Magnetometry Review: Budker, Gawlik, Kimball, Rochester, Yashchuk, Weis (2002). Rev. Mod. Phys.74(4), 1153-1201.

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

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

  6. Linear Magneto-Optical (Faraday) Rotation

  7. B ~ 400G Linear Magneto-Optical (Faraday) Rotation

  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:  Spectral hole-burning: B 0 B = 0 Index of refraction Number of atoms Re[n+-n-] Light detuning Atomic velocity Small field NMOR enhanced!

  9. Nonlinear Magneto-optical Rotation due to atomic polarization Three stage process: Optical pumping Probing via optical rotation Precession in B-field

  10. Fluorescence has random direction and polarization. M = 1 Circularly polarized light consists of photons with angular momentum = 1 ħ along z. Optical pumping Circularly polarized light propagating in z direction can create orientation along z. z F’ = 0 F = 1 MF = -1 MF = 0 MF = 1

  11. Optical pumping Circularly polarized light propagating in z direction can create orientation along z. z F’ = 0 F = 1 MF = -1 MF = 0 MF = 1 Medium is now transparent to light with right circular polarization in z direction!

  12. Optical pumping Light linearly polarized along z can create alignment along z-axis. z F’ = 0 F = 1 MF = -1 MF = 0 MF = 1

  13. Optical pumping Light linearly polarized along z can create alignment along z-axis. z F’ = 0 F = 1 MF = -1 MF = 0 MF = 1 Medium is now transparent to light with linear polarization along z!

  14. . Optical pumping Light linearly polarized along z can create alignment along z-axis. z F’ = 0 F = 1 MF = -1 MF = 0 MF = 1 Medium strongly absorbs light polarized in orthogonal direction!

  15. z z z y y y x x x Unpolarized Sphere centered at origin, equal probability in all directions. Oriented “Pumpkin” pointing in z-direction  preferred direction. Aligned “Peanut” with axis along z  preferred axis. 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.

  16. Optical pumping Optical pumping process polarizes atoms. Optical pumping is most efficient when laser frequency (l) is tuned to atomic resonance frequency (0).

  17.       =   B  =   B  dF   = dt     dF  =   B = gFB F  B dt Precession in Magnetic Field Interaction of the magnetic dipole moment with a magnetic field causes the angular momentum to precess – just like a gyroscope!  B   , F   L = gF B B

  18. Precession in Magnetic Field     B torque causes polarized atoms to precess:

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

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

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

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

  23. 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.”

  24. Relaxation in the Dark Light can be used to probe ground state atomic polarization: Photodiode F’ = 0 z F = 1 MF = -1 MF = 0 MF = 1 No absorption of right circularly polarized light.

  25. Relaxation in the Dark Light can be used to probe ground state atomic polarization: Photodiode F’ = 0 z F = 1 MF = -1 MF = 0 MF = 1 Significant absorptionof left circularly polarized light.

  26. Paraffin-coated cells

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

  28. Magnetic Shielding Four-layer ferromagnetic magnetic shielding with nearly spherical geometry reduces fields in all directions by a factor of 106!

  29. Magnetic Shielding

  30. 3-D coils allow control and cancellation of fields and gradients inside shields.

  31. NMOR Coherence Effect in Paraffin-coated Cell 85Rb D2 Line, I = 50 W/cm2, F=3  F’=4 component Kanorsky, Weis, Skalla (1995). Appl. Phys. B 60, 165. Budker, Yashchuk, Zolotorev (1998). PRL 81, 5788. Budker, Kimball, Rochester, Yashchuk, Zolotorev (2000). PRA62, 043403. rel = 2 0.9 Hz

  32. Sensitive measurement of magnetic fields 85Rb D2 line, F=3  F’ component, I = 4.5 mW/cm2

  33. 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?

  34. 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.

  35. Nonlinear Magneto-optical Rotation In-phase component 87Rb D1 Line F = 2  1 m = 21 kHz  = 2220 MHz Out-of-phase (quadrature) component P 15 W Budker, Kimball, Yashchuk, Zolotorev (2002). PRA65, 055403.

  36. Nonlinear Magneto-optical Rotation Low field resonance: Lrel On resonance: Light polarized along atomic polarization is transmitted, light of orthogonal polarization is absorbed. Low-fieldresonance is due to equilibrium rotated atomic polarization – at constant angle due to balance of pumping, precession, and relaxation.

  37. Nonlinear Magneto-optical Rotation In-phase component 87Rb D1 Line F = 2  1 m = 21 kHz  = 2220 MHz Out-of-phase (quadrature) component P 15 W

  38. Nonlinear Magneto-optical Rotation High field resonances: L>> rel • 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.

  39. Nonlinear Magneto-optical Rotation • Optical properties of the atomic medium are modulated at 2L. • A resonance occurs when m = 2L.

  40. Nonlinear Magneto-optical Rotation • Quadrature signals arise due to • difference in phase between • rotating medium and probe light. • Second harmonic signals appear for • m= L.

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

  42. Magnetometry Demonstrated sensitivity ~ 510-10

  43. Magnetometry Magnetic resonance imaging (MRI) in Earth field? Measurement of Xe nuclear spins.

  44. Magnetometry Magnetic resonance imaging (MRI) in Earth field? 129Xe 26% natural abundance, pressure = 5 bar

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

  46. Hexadecapole Resonance Arises due to creation and probing of hexadecapole moment ( = 4). Yashchuk, Budker, Gawlik, Kimball, Malakyan, Rochester (2003). PRL90, 253001.

  47. No resonance forF=1 Hexadecapole Resonance Highest moment possible:  = 2F

  48. Hexadecapole Resonance At low light powers: Quadrupole signal I2 Hexadecapole signal I4

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