Nonlinear Magneto-Optical Rotation with Frequency-Modulated Light

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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 - PowerPoint PPT Presentation

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  • Nonlinear Magneto-Optical Rotation with Frequency-Modulated LightDerek KimballDmitry BudkerSimon RochesterValeriy YashchukMax Zolotorevand many others...

  • Some of the many others:D. EnglishK. KernerC.-H. LiT. MilletA.-T. NguyenJ. StalnakerA. Sushkov

    E. B. AlexandrovM. V. BalabasW. GawlikYu. P. MalakyanA. B. MatskoI. Novikova A. I. OkunevichS. PustelnyA. WeisG. R. Welch

    Budker Group:Non-Berkeley Folks:Technical Support:M. SolarzA. VaynbergG. WeberJ. DavisFunding: ONR, NSF

  • Plan:Linear Magneto-Optical (Faraday) RotationNonlinear Magneto-Optical Rotation (NMOR)Polarized atomsParaffin-coated cellsExperimentsNMOR with Frequency-Modulated light (FM NMOR)MotivationExperimental setupData: B-field dependence, spectrum, etc.A little mystery...MagnetometryReview: Budker, Gawlik, Kimball, Rochester, Yashchuk, Weis (2002). Rev. Mod. Phys. 74(4), 1153-1201.

  • Linear Magneto-Optical (Faraday) Rotation = (n+-n-)0l2c= (n+-n-)l1846-1855: Faraday discovers magneto-optical rotation1898,1899: Macaluso and Corbino discover resonant character of Faraday rotation

  • Linear Magneto-Optical (Faraday) Rotation1898: Voigt connects Faraday rotation to the Zeeman effect

  • Linear Magneto-Optical (Faraday) Rotation

  • Linear Magneto-Optical (Faraday) Rotation

  • 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 atomsAtomic velocityLight detuningIndex of refractionRe[n+-n-]B 0Small field NMOR enhanced!

  • Nonlinear Magneto-optical Rotationdue to atomic polarizationThree stage process:OpticalpumpingPrecessionin B-fieldProbingvia opticalrotation

  • Optical pumpingMF = -1MF = 0MF = 1zF = 1F = 0Circularly polarized light propagating in z directioncan create orientation along z.

  • Optical pumpingMF = -1MF = 0MF = 1zF = 1F = 0Medium is now transparent to lightwith right circular polarization in z direction!Circularly polarized light propagating in z directioncan create orientation along z.

  • Optical pumpingMF = -1MF = 0MF = 1zF = 1F = 0Light linearly polarized along z can create alignment along z-axis.

  • Optical pumpingMF = -1MF = 0MF = 1zF = 1F = 0Light linearly polarized along z can create alignment along z-axis.Medium is now transparent to lightwith linear polarization along z!

  • Optical pumpingMF = -1MF = 0MF = 1zF = 1F = 0Light linearly polarized along z can create alignment along z-axis.Medium strongly absorbs lightpolarized in orthogonal direction!

  • Visualization of Atomic PolarizationDraw 3D surface where distance from origin equals the probability to be found in a stretched state (M=F) along this direction.

  • Optical pumping process polarizes atoms.Optical pumping is most efficient whenlaser frequency (l) is tuned to atomic resonance frequency (0).Optical pumping

  • Precession in Magnetic FieldInteraction of the magnetic dipole momentwith a magnetic field causes the angular momentumto precess just like a gyroscope! L = gF B BB, F

  • torque causes polarized atoms to precess: BPrecession in Magnetic Field

  • Relaxation and probing of atomic polarization Relaxation of atomic polarization:(polarized atoms only)

  • Coherence Effects in NMORMagnetic-field dependence of NMOR due to atomic polarizationcan be described by the same formula we used for linear Faradayrotation, but rel :How can we get slowest possible rel?

  • Paraffin-coated cellsAcademician Alexandrov hasbrought us some beautifulholiday ornaments...

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

  • Paraffin-coated cellsPolarized atoms can bounce off the walls of a paraffin-coatedcell ~10,000 times before depolarizing!This can be seen using the method of relaxation in the dark.

  • Relaxation in the DarkMF = -1MF = 0MF = 1F = 1F = 0Light can be used to probe ground state atomic polarization:No absorption of right circularly polarized light.zPhotodiode

  • Relaxation in the DarkMF = -1MF = 0MF = 1F = 1F = 0Light can be used to probe ground state atomic polarization:Significant absorption of left circularly polarized light.zPhotodiode

  • Paraffin-coated cells

  • Experimental Setup

  • Magnetic ShieldingFour-layer ferromagnetic magnetic shielding with nearly spherical geometry reduces fields in all directions by a factor of 106!

  • Magnetic Shielding

  • 3-D coils allow controland cancellation of fieldsand gradients inside shields.

  • NMOR Coherence Effect in Paraffin-coated Cell85Rb D2 Line, I = 50 W/cm2,F=3 F=4 component rel = 2 0.9 HzKanorsky, Weis, Skalla (1995). Appl. Phys. B 60, 165.Budker, Yashchuk, Zolotorev (1998). PRL 81, 5788.Budker, Kimball, Rochester, Yashchuk, Zolotorev (2000). PRA 62, 043403.

  • Sensitive measurement of magnetic fields85Rb D2 line, F=3 F component,I = 4.5 mW/cm2

  • The dynamic range of an NMOR-based magnetometer islimited by the width of the resonance:B ~ 2 GHow can we increase the dynamic range?

  • NMOR with Frequency-Modulated Light Magnetic field modulates optical properties of medium at 2L.

    There should be a resonance when the frequency of light is modulated at the same rate! ExperimentalSetup:Inspired by:Barkov, Zolotorev (1978). JETP Lett. 28, 503.Barkov, Zolotorev, Melik-Pashaev (1988). JETP Lett. 48, 134.

  • In-phase componentOut-of-phase (quadrature) componentm = 21 kHz = 2220 MHzP 15 W87Rb D1 LineF = 2 1Budker, Kimball,Yashchuk, Zolotorev (2002).PRA 65, 055403.Nonlinear Magneto-optical Rotation

  • Low-field resonance is due to equilibriumrotated atomic polarization at constantangle due to balance of pumping, precession, and relaxation.

    Low field resonance:L rel

    Nonlinear Magneto-optical RotationOn resonance:Light polarized alongatomic polarization is transmitted,light of orthogonal polarizationis absorbed.

  • In-phase componentOut-of-phase (quadrature) componentm = 21 kHz = 2220 MHzP 15 W87Rb D1 LineF = 2 1Nonlinear Magneto-optical Rotation

  • 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

    Nonlinear Magneto-optical Rotation

  • Optical properties of the atomic medium are modulated at 2L.

    A resonance occurs when m = 2L.

    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.Nonlinear Magneto-optical Rotation

  • NMOR with Frequency-Modulated LightLow field resonanceHigh field resonanceNote that spectrum ofFM NMOR First Harmonicis related to NMOR spectrum:For 2nd harmonic (not shown):

  • Demonstrated sensitivity ~ 510-10 Magnetometry

  • MagnetometryMagnetic resonance imaging (MRI) in Earth field?Measurement of Xe nuclear spins.

  • MagnetometryMagnetic resonance imaging (MRI) in Earth field?129Xe 26% natural abundance, pressure = 5 bar

  • A mystery...m = 4 L See new resonances atfor high light power!

  • Hexadecapole ResonanceArises due to creation and probing ofhexadecapole moment ( = 4).Yashchuk, Budker, Gawlik, Kimball, Malakyan, Rochester (2003). PRL 90,253001.

  • Hexadecapole ResonanceHighest moment possible: = 2F

  • Hexadecapole ResonanceAt low light powers:

    Quadrupole signal I2Hexadecapole signal I4