Nonlinear Magneto-Optical Rotation with Frequency-Modulated Light
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DESCRIPTIONNonlinear 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
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
Magnetic ShieldingFour-layer ferromagnetic magnetic shielding with nearly spherical geometry reduces fields in all directions by a factor of 106!
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