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CPT
EIT
LWI
|2>
|1>
|3>
p cp c
3
2
1
0
0
tic
tip
tic
tip
c
p
cp
e
e
ee
CPT
3)2
sin(2)2
cos()0( ie
3)(2)(1)()( 321321
tititi etcetcetct
ipc etc )
2sin()
2cos()(1
Suppose
then
solving Schrodinger Equation
What if we’re sneaky and choose
Such that c1(t)=0. Then we are trapped in the two lower states.
,,
Population Trapping
CPT
In fact
22
22
0
pc
p
pc
c
00
00
0
c
p
cp
22
22
0
pc
p
pc
c0
So 322222pc
p
pc
c
Is an eigenstate of the interaction Hamiltonian
Dark States
CPT Coherent Population
3332
2322
0
0
000
33
22
00
00
000
Dark State density matrix at t=0
Incoherent mixture density matrix at t=0
0)(11 t 0)(11 t
Rabi Oscillations Trapped in dark state
EIT
|2>
|1>
|3>
p cp c
weak strong
)(2
, iHdt
di
3
2
1
0
0
tic
tip
tic
tip
c
p
cp
e
e
ee
3
2
0
0
tic
tip
tic
tip
c
p
cp
e
e
ee
333231
232221
131211
333231
232221
131211
i
333231
232221
131211
00
00
2
231
21
131211
i
EITti
c
p pei
2212
Re[n]-1
Im[n]
LWI We can completely eliminate absorption, can we do better?
|2>
|1>
|3>
l cl
c
The idea:
Pump atoms into dark state, then emission from |1> can exceed absorption from ground states.
BIB
Quantum Optics, Scully and Zubairy,Cambridge University press 1997
Resolving conundrums in lasing without inversion via exact solutions to simple models, Scully, Quantum Opt. 6 p 203, 1994
Slow, Ultraslow, stored, and Frozen Light, Matsko,et. al., Adv.Atm.Mol.Opt.Phys. 47, p191 2001
Electromagnetically Induced Transparency, Harris, Physics Today, July 1997, p36
