Transcript Document
CPT
EIT
LWI
|1>
p
p
c
c
|3>
|2>
1
i p t
p e
eict
c
p e
i p t
2
0
c e
ic t
0
3
CPT
Suppose
then
Population Trapping
i1t
i2t
(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.
i3t
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
22
32
13
23
33
1
i p t
p e
eict
c
11
21
31
12
22
32
p e
i p t
2
0
13
23
33
c e ict
0
3
i p t
p e
eict
c
11
21
31
p e
i p t
2
0
12
22
32
13
23
33
c e ict
211
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