Transcript Radiation from an Extended Sample
Energy Level diagram for n- 2 level atoms
r
n
2
r
n
2 1
r
n
2 2
m
n
2
m
n
2 1
m
n
2 2
nI o
2 (
n
1 )
I o
3 (
n
2 )
I o n
1 fold degenerate 2 (
n
2 )
I o n
(
n
2 3 ) fold degenerate (
n
4 )
I o m
2
n
1
m
n
2
nI o
(
n
2 )
I o
Radiation from an Extended Sample Interaction with Radiation field Destroy photon Raise Energy level
H int
1 2
k
a k
(
e
x
i
e
y n
)
j
1
R j
exp(
i
k
r
) 1 2
k
a k
* (
e
x
i
e
y n
)
j
1
R j
exp(
i
k
r
)
Radiation from an Extended Sample By some sort of change in basis:
H int
1 2
k
a
k
e
R
k
a
k
*
e
*
R
k
R
k
j n
1
R j
exp(
i
k
r
j
)
“Spin” operators are the same as before
R
k
2
R
k
x
2
R
k
y
2
R
k
z
2
R
k
2
mr
r
(
r
1 )
mr R z
mr
m
mr
Absorption or emission of a photon with momentum k,
r
0
m
1 Radiation Rate in
k
I
(
k
)
I o
[(
r
direction:
m
)(
r
m
1 )]
Non-linear Rayleigh scattering/superradiance
Collective scattering: Dicke superradiance Rayleigh: Inouye et al., Science (1998)
Non-linear Rayleigh scattering/superradiance
Recoiling atoms interfere with stationary atoms to form a diffraction grating, which then enhances scattering into that mode
N
mod 2
N o N k
The Scattered Power
P
~
N
2 mod
Dicke’s Superradiance?
m
n
2
m
n
2 1
m
n
2 2
r
n
2
nI o
2 (
n
1 )
I o
3 (
n
2 )
I o r
n
2 1
n
1 fold degenerate (
n
2 )
I o
2 (
n
2 )
I o r
n
2 2
n
(
n
3 ) fold degenerate 2 (
n
4 )
I o
m
n
2 1
m
n
2
nI o
(
n
2 )
I o
Non-linear Rayleigh scattering/superradiance
Dipolar emission pattern radiates weakly along polarization axis, collective scattering is stronger along long axis I ~ 1-100mW/cm^2 t ~ 50 m s Normal decay of atoms Superradiant decay of atoms
References Coherence in Spontaneous Radiation Processes Dicke,
Phys. Rev
.
93
1 99 (1954) Superradiant Rayliegh Scattering from a Bose Einstein Condensate S. Inouye,
Science
,
285
571 (1999) Cargese lecture notes W. Ketterle and S. Inouye: Collective enhancement and suppression in Bose-Einstein condensates.
Compte rendus de l'académie des sciences, Série IV - Physique Astrophysique, vol. 2, pp. 339-380 (2001); e-print cond mat/0101424.