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Censorship. Optically polarized atoms. Dr. A. O. Sushkov, May 2007. A 12-T superconducting NMR magnet at the EMSL(PNNL) laboratory, Richland, WA. Marcis Auzinsh, University of Latvia Dmitry Budker, UC Berkeley and LBNL Simon M. Rochester, UC Berkeley. Linear Polarization. Medium. .

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Optically polarized atoms

Censorship

Optically polarized atoms

Dr. A. O. Sushkov, May 2007

A 12-T superconducting NMR magnet at the EMSL(PNNL) laboratory, Richland, WA

Marcis Auzinsh, University of Latvia

Dmitry Budker, UC Berkeley and LBNL

Simon M. Rochester, UC Berkeley


Chapter 4 atoms in external fields

Linear Polarization

Medium

Circular

Components

Magnetic

Field

Chapter 4: Atoms in external fields

  • 1845, Michael Faraday: magneto-optical rotation


Zeeman effect a brief history
Zeeman effect: a brief history

  • Faraday looked for effect of magnetic field on spectra, but failed to find it

  • 1896, Pieter Zeeman: sodium lines broaden under B

  • 1897, Zeeman observed splitting of Cd lines into three components (“Normal” Zeeman effect)

  • 1897, Hendrik Lorentz: classical explanation of ZE

  • 1898, discovery of Resonant Faraday Effect by Macaluso and Corbino


Resonant faraday rotation
Resonant Faraday Rotation

rotation of the plane of linear light polarization by a medium in a magnetic field applied in the direction of light propagation in the vicinity of resonance absorption lines

D.Macaluso e O.M.Corbino, Nuovo Cimento 8, 257 (1898)

Diffraction

Grating

Monochromator

Electromagnet

Polarizer

Flames of Na and Li

Analyzer

Photographic Plate


Normal zeeman effect
“Normal” Zeeman effect

  • Energy in external field:

  • Consider an atom with S=0  J=L

  • In this case,

  • For magnetic field along z:

  • This is true for other states in the atom

  • If we have an E1 transition, ,

  • A transition generally splits into 3 lines

  • This agrees with Lorentz’ classical prediction (normal modes), not the case for S0


Normal zeeman effect e1 selection rule d m 0 1
“Normal” Zeeman effectE1 selection rule: DM=0,1

M= -2 -1 0 1 2

Three lines !


Normal zeeman effect classical model electron on a spring
“Normal” Zeeman effectClassical Model: electron on a spring

Eigenmodes:

B

Three eigenfrequencies !


Zeeman effect when s 0
Zeeman effect when S0

  • The magnetic moment of a state with given J is composed of


Zeeman effect for hyperfine levels
Zeeman effect for hyperfine levels

  • Neglect interaction of nuclear magnetic moment with external magnetic field (it is ~2000 x smaller)

  • However, average μnow points along F, not J

  • Avector-model calculations a la the one we just did yields:


The actual calculation
The actual calculation…

  • Definition of gF :

  • The magnetic moment is dominated by the electron, for which we have:

  • To find μ, we need to find the average projection of J on F, so that

  • Now, find

  • Finally,


Zeeman effect for hyperfine levels cont d
Zeeman effect for hyperfine levels (cont’d)

  • Consider 2S1/2atomic states (H, the alkalis, group 1B--Cu, Ag, and Au ground states)

  • L=0; J=S=1/2 F=I1/2

  • This can be

    understood from

    the fact thatμ

    comes fromJ


Zeeman effect for hyperfine levels in stronger fields magnetic decoupling
Zeeman effect for hyperfine levels in stronger fields: magnetic decoupling

  • Hyperfine energies are diagonal in the coupled basis:

  • However, Zeeman shifts are diagonal in the uncoupled basis: because

  • The bases are related, e.g., for S=I=1/2 (H)

    F,MF MS, MI


Zeeman effect for hyperfine levels in stronger fields magnetic decoupling1
Zeeman effect for hyperfine levels in stronger fields: magnetic decoupling


Zeeman effect for hyperfine levels in stronger fields magnetic decoupling2
Zeeman effect for hyperfine levels in stronger fields: magnetic decoupling


Zeeman effect for hyperfine levels in stronger fields magnetic decoupling3
Zeeman effect for hyperfine levels in stronger fields: magnetic decoupling

  • Breit-Rabi diagrams

  • Nonlinear Zeeman Effect (NLZ)

    • But No NLZ for

  • F=I+1/2, |M|=F states

  • Looking more closely at the upper two levels for H :

  • These levels eventually cross! (@ 16.7 T)


Atoms in electric field the stark effect or losurdo phenomenon
Atoms in electric field: the Stark effectorLoSurdo phenomenon

Johannes Stark (1874-1957)

Nazi Fascist


Atoms in electric field the stark effect or losurdo phenomenon1

Electric:

Atoms in electric field: the Stark effectorLoSurdo phenomenon

Magnetic:

However, things are as different as they can be…

Permanent dipole:

OK NOT OK

(P and T violation)

First-order effect Second-order effect


Atoms in electric field the stark effect polarizability of a conducting sphere
Atoms in electric field: the Stark effectPolarizability of a conducting sphere

  • Outside the sphere, the electric field is a sum of the applied uniform field and a dipole field

  • Field lines at the surface are normal, for example, at equator:


Atoms in electric field the stark effect classical insights
Atoms in electric field: the Stark effectClassical insights

  • Natural scale for atomic polarizability is the cube of Bohr radius

  • (a0)3is also the atomic unit of polarizability

  • In practical units:


Atoms in electric field the stark effect hydrogen ground state
Atoms in electric field: the Stark effectHydrogen ground state

n l m Neglect spin!

  • Polarizability can be found from


Atoms in electric field the stark effect hydrogen ground state cont d
Atoms in electric field: the Stark effectHydrogen ground state (cont’d)

  • The calculation simplifies by approximating

=1


Atoms in electric field the stark effect hydrogen ground state cont d1
Atoms in electric field: the Stark effectHydrogen ground state (cont’d)

  • Alas, this is Hydrogen, so use explicit wavefunction:

  • Finally, our estimate is

  • Exact calculation:


Atoms in electric field the stark effect polarizabilities of rydberg states
Atoms in electric field: the Stark effectPolarizabilities of Rydberg states

  • The sum is dominated by terms with ni  nk

    • Better overlap of wavefunctions

    • Smaller energy denominators

  • dik  n2 . Indeed,

  • (Ek-Ei)-1scale as n3


  • Atoms in electric field the linear stark effect
    Atoms in electric field: the linearStark effect

    • Stark shifts increase, while energy intervals decrease for largen

    • When shifts are comparable to energy intervals – the nondegenerate perturbation theory no longer works even for lab fields <100 kV/cm  use degenerate perturbation theory

    • Also in molecules, where opposite-parity levels are separated by rotational energy ~10-3 Ry

    • Also in some special cases in non-Rydberg atoms: H, Dy, Ba…

    • In some Ba states, polarizability is >106 a.u.

    C.H. Li, S.M. Rochester, M.G. Kozlov, and D. Budker, Unusually large polarizabilities and "new" atomic states in Ba, Phys. Rev. A69, 042507 (2004)


    The bizarre stark effect in ba
    The bizarreStarkeffect in Ba

    Chih-Hao Li Misha Kozlov


    The bizarreStarkeffect in Ba (cont’d)


    The bizarreStarkeffect in Ba (cont’d)

    C.H. Li, S.M. Rochester, M.G. Kozlov, and D. Budker, Unusually large polarizabilities and "new" atomic states in Ba, Phys. Rev. A69, 042507 (2004)


    Atoms in electric field the linear stark effect hydrogen 2s 2p states
    Atoms in electric field: the linearStarkeffectHydrogen 2s-2p states

    • Opposite-parity levels are separated only by the Lamb shift

    • Secular equation with a 2x2 Hamiltonian:

    • Eigenenergies:

    Not EDM !

    Quadratic

    Linear


    Atoms in electric field the linear stark effect hydrogen 2s 2p states cont d
    Atoms in electric field: the linearStarkeffectHydrogen 2s-2p states (cont’d)

    Neglect spin!

    • Linear shift occurs for

      • Lamb Shift: ωsp/21058 GHz


    Atoms in electric field polarizability formalism
    Atoms in electric field: polarizability formalism

    • Back to quadratic Stark, neglect hfs

    • Quantization axis along E  MJis a good quantum #

    • Shift is quadratic inE  same for MJand -MJ

    • A slightly involved symmetry argument based on tensors leads to the most general form of shift

    Scalar polarizability

    Tensor polarizability


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