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CPT
EIT
LWI
|1>
p
p
c
c
|3>
|2>
 1

i p t
 p e
  eict
 c
 p e
 i p t
 c e
 ic t
2
0
0
3





CPT
Suppose
then
Population Trapping


i1t
i2t
 (0)  cos( ) 2  sin( )e
2
2
(t )  c1 (t )e
1  c2 (t )e
i
3
2  c3 (t )e
solving Schrodinger Equation


c1 (t )  c cos( )   p sin( )e
2
2
What if we’re sneaky and choose ,  , 
i
Such that c1(t)=0. Then we are trapped in the
two lower states.
i3t
3
CPT
In fact
So
Dark States
 0

 p
 c
c
 c2   2p
2 
 p
0
0
c 

0 
0 
p
 c2   2p
3


0







c


 2  2 
c
p






p

2
2 



c
p 


0


0







c


 2  2 
c
p






p

2
2 



c
p 


Is an eigenstate of the
interaction Hamiltonian
CPT
Coherent Population
Dark State density
matrix at t=0
0 0
0 
22

0 32
0 

 23 
33 
11(t )  0
Trapped in dark state
Incoherent mixture
density matrix at t=0
0 0
0 
22

0 0
0 

0 
33 
11(t )  0
Rabi Oscillations
EIT
|1>

c
p
 c strong
weak  p
|3>
|2>
d

i
 H ,    i (  )
dt
2
 11
i   21
  31
12 13 
 22  23  
 32  33 
 1

i p t
 p e
  eict
 c
 11

 21
 31
12
 22
32
 p e
 i p t
2
0
13 
 23  
33 
 c e ict 

0

3 

 

i p t
 p e
  eict
 c
 11

 21
 31
 p e
 i p t
2
0
12
 22
32
13 
 23  
33 
 c e ict 
211


0
i
 21
2

3
 31

12 13 
0
0
0
0



EIT
12 
 p
 c2   2  i
e
i p t
Im[n]


Re[n]-1
EIT
quant-ph/0204173
LWI
We can completely eliminate
absorption, can we do better?
|1>
l
l
The idea:

Pump atoms into dark
state, then emission
from |1> can exceed
absorption from ground
states.
c
c
|3>
|2>
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