Transcript Optically polarized atoms

Optically polarized atoms
Dr. A. O. Sushkov,
May 2007
A 12-T superconducting
NMR magnet at the
EMSL(PNNL) laboratory,
Richland, WA
Censorship
Marcis Auzinsh, University of Latvia
Dmitry Budker, UC Berkeley and LBNL
Simon M. Rochester, UC Berkeley
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Chapter 4: Atoms in external fields

1845, Michael Faraday: magneto-optical rotation
Linear Polarization
Medium
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Circular
Components
Magnetic
Field
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Zeeman effect: a brief history
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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
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Resonant Faraday Rotation
Diffraction
Grating
Monochromator
Electromagnet
Polarizer
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)
Flames of Na and Li
Analyzer
Photographic
Plate
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“Normal” Zeeman effect
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Energy in external field:
Consider an atom with S=0  J=L
In this case,
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For magnetic field along z:
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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
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“Normal” Zeeman effect
E1 selection rule: DM=0,1
M=
-2
-1
0
1
2
Three lines !
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“Normal” Zeeman effect
Classical Model: electron on a spring
Eigenmodes:
B
Three eigenfrequencies !
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Zeeman effect when S0
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The magnetic moment of a state with given J is
composed of
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Zeeman effect for hyperfine levels
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Neglect interaction of nuclear magnetic moment
with external magnetic field (it is ~2000 x smaller)
However, average μ now points along F, not J
A vector-model calculations a la the one we just did
yields:
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The actual calculation…
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Definition of gF : μ   gF BF /
The magnetic moment is dominated by the
electron, for which we have: μJ   gJ B J /
To find μ, we need to find the average
projection of J on F, so that
JF
μ   g J B
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Now, find
JF
Finally,
F/
F  J  Ι  F  J  Ι   F  J   Ι2
2
 JF 
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F
2
F ( F  1)  J ( J  1)  I ( I  1)
2
F ( F  1)  J ( J  1)  I ( I  1)
gF  gJ
2 F ( F  1)
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Zeeman effect for hyperfine levels (cont’d)
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Consider 2S1/2 atomic 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
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the fact that μ
comes from J
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Zeeman effect for hyperfine levels in
stronger fields: magnetic decoupling
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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
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Zeeman effect for hyperfine levels in
stronger fields: magnetic decoupling
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Zeeman effect for hyperfine levels in
stronger fields: magnetic decoupling
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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)
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Atoms in electric field: the Stark effect
or LoSurdo phenomenon
Johannes Stark (1874-1957)
Nazi
Fascist
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Atoms in electric field: the Stark effect
or LoSurdo phenomenon
Magnetic:
Electric:
However, things are as different as they can be…
Permanent dipole:
OK
NOT OK
(P and T violation)
First-order effect
Second-order effect
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Atoms in electric field: the Stark effect
Polarizability of a conducting sphere
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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:

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Atoms in electric field: the Stark effect
Classical insights
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Natural scale for atomic polarizability is the cube of
Bohr radius
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(a0)3 is also the atomic unit of polarizability
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In practical units:
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Atoms in electric field: the Stark effect
Hydrogen ground state
n l m Neglect spin!
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Polarizability can be found from
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Atoms in electric field: the Stark effect
Hydrogen ground state (cont’d)
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The calculation simplifies by approximating
=1
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Atoms in electric field: the Stark effect
Hydrogen ground state (cont’d)
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Alas, this is Hydrogen, so use explicit wavefunction:
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Finally, our estimate is
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Exact calculation:
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Atoms in electric field: the Stark effect
Polarizabilities of Rydberg states
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The sum is dominated by terms with ni  nk
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Better overlap of wavefunctions
Smaller energy denominators
n2 . Indeed,
  n n  n
4
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dik 
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(Ek-Ei)-1 scale as n3 E  1 ; dE  1 ;
2
3
n
dn
n
3
1
 n3
Ei  Ek
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Atoms in electric field: the linear Stark effect
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Stark shifts increase, while energy intervals decrease
for large n
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. A 69, 042507 (2004)
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The bizarre Stark effect in Ba
Chih-Hao Li
Misha Kozlov
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The bizarre Stark effect in Ba (cont’d)
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The bizarre Stark effect 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. A 69, 042507 (2004)
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Atoms in electric field: the linear Stark effect
Hydrogen 2s-2p states
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Opposite-parity levels are separated only by the
Lamb shift
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Secular equation with a 2x2 Hamiltonian:
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Eigenenergies:
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Not EDM !
Quadratic
Linear
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Atoms in electric field: the linear Stark effect
Hydrogen 2s-2p states (cont’d)
Neglect spin!
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Linear shift occurs for
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Lamb Shift: ωsp/21058 GHz
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
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Atoms in electric field: polarizability formalism
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Back to quadratic Stark, neglect hfs
Quantization axis along E  MJ is a good quantum #
Shift is quadratic in E  same for MJ and -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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