Transcript Optically polarized atoms_ch_8_Coherene in

Optically polarized atoms
Marcis Auzinsh, University of Latvia
Dmitry Budker, UC Berkeley and LBNL
Simon M. Rochester, UC Berkeley
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Chapter 8: Coherence in atomic systems
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Exciting a 01 transition with z polarized light
Things are straightforward: the |1,0> state is
excited
What if light is x polarized ?
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Exciting a 01 transition with x polarized light
Recipe for
finding how
much of a
given basic
polarization is
contained in
the field E
1
1
0
1
E 
; E  0; E 
2
2
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x
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Note: light is in a superposition of σ+ and σ -
1
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Exciting a 01 transition with x polarized light
Coherent superposition -|1,-1>+|1,1> is excited
Why do we care that a coherent superposition is
excited?
Suppose we want to further excite atoms to a level J ’’
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Compare excitation rate to J ’’=0 for x and y polarized
E ’ light
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Compare excitation rate to J ’’=0 for x and y polarized
E ’ light
Calculate final-state amplitude as
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with
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First, for x polarized light
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Now repeat for y
polarized light !
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Compare excitation rate to J ’’=0 for x and y polarized E ’ light
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For y polarized light :
i
i
0
1
E 
; E  0; E 
2
2
1
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Or, with a common phase factor
1
1
0
1
E 
; E  0; E 
2
2
1
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So, finally, we have :
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y polarized light
x polarized light
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The state we prepared with x
polarized light E is a bright
state for x polarized light E ’
At the same time, it is a dark
state for y polarized light E ’
A quantum interference effect !
Two pathways from the initial to
final state; constructive or
destructive interference
This is the basic phenomenon underlying :
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EIT electromagnetically induced transparency
CPT coherent population trapping
STIRAP stimulated Raman adiabatic passage
NMOR nonlinear magneto-optical rotation
LWI lasing w/o inversion
“slow light” very slow and superluminal group velocities
coherent control of chemical reactions
…
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An important comment about bases
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We have considered excitation with x
polarized E light, and have seen an
“interesting” coherence effect (dark and
bright) excited states
If we choose quantization axis along light
polarization, things look trivial
Bright intermediate state for z
polarized light E’
Dark intermediate state for x or y
polarized light E’
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Quantum Beats
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Suppose we prepare a coherent superposition of
energy eigenstates with different energies
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For example, we can be exciting Zeeman sublevels
that are split by a magnetic field
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The wavefunction will be something like
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Quantum Beats
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As a specific example, again consider exciting a
01 transition with x polarized light
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Assume short, broadband excitation pulse at
t=0. Then, at a later time:
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Quantum Beats
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Now, as before, we excite further with second cw
(but spectrally broad and weak)
light field
The amplitude of excitation depends on time:
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Quantum Beats
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Excitation probability is harmonically modulated
Modulation frequency  energy intervals between
coherently excited states
The evolution of the intermediate state can be
seen on the plots of electron density
Note: Electron density plots are NOT the same as
the angular-momentum probability plots we use a
lot in this course !
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Quantum Beats
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In this case temporal evolution is simple – it is just
Larmor precession
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Quantum Beats
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Q: What will be seen with y polarized light E ’ ?
A: The same but with opposite phase
x:
y:
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Quantum beats in atomic spectroscopy were
discovered in 1960s by E. B. Alexandrov in USSR
and J.N. Dodd, G.W.Series, and co-workers in UK
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Yevgeniy Borisovich Alexandrov
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The Hanle Effect
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Now introduce relaxation: assume that amplitude
of state J’ decays at rate Γ/2
Amplitudes of excited sublevels evolve according
to :
With x polarized second excitation E’ , we have
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The Hanle Effect
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Assuming that both light fields are cw, and that
we are detecting steady-state signals as a function
of magnetic field, we have:
Limiting cases:   2L ;  ~ 2L ;   2L
This is a nice method for determining lifetimes
that does not require fast excitation,
photodetectors, or electronics
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The Hanle Effect
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What’s going on is clearly seen on electron-density plot for J’
L  0
L   / 2
L  
L  3 / 2
L  2
L  5 / 2
L  3
L  7 / 2
L  4
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The Hanle Effect
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A similar illustration can be done with angular-momentum
probability plots
Quite similar physics takes place in Nonlinear Faraday Effect
Transverse (w.r.t. magnetic field) alignment converted to
longitudinal alignment
The Hanle effect is sometimes called magnetic depolarization of
radiation. This refers to observation via emission from the
polarized state
L  0
L   / 2
L  
L  3 / 2
L  2
L  5 / 2
L  3
L  7 / 2
L  4
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