A. Lezama
description
Transcript of A. Lezama
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A. Lezama
Instituto de Física, Facultad de Ingeniería, Casilla de
Correo 30, 11000, Montevideo, Uruguay
Quantum fluctuations in the light transmitted through an atomic vapor.
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Outline:
I. Background
II. Renewed interest
III. Numerical calculation
IV. Back to experiments
V. Future
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I. Background. atoms
LLaser beam
(fluctuating)
Transmitted field
(modified fluctuations)
Early predictions and experiments
Walls and Zoller (1981)Mandel (1982)M. Collett, D. Walls, P. Zoller (1984)Heidmann and Reynaud (1985)---------------------------------------S.-T. Ho, P. Kumar, J. H. Shapiro (1987)S. Ho, N. Wong, J. Shapiro (1991)
, Ω0
g
e
0
Δ
0
220
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LIg )(
Squeezing via polarization self-rotation (PSR)
A.B. Matsko et al, Phys. Rev. A 66, 043815 (2002)
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A.B. Matsko et al, Phys Rev. A 66, 043815 (2002)
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from Ries et al Phys. Rev. A 68, 025801 (2003)
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M. T. L. Hsu, G. Hétet, A. Peng, C. C. Harb, H.-A. Bachor, M. T. Johnsson, J. J. Hope, P. K. Lam, A. Dantan, J. Cviklinski, A. Bramati, M. Pinard (2006)
Controversy…
Vacuum squeezing via polarization self-rotation
J. Ries, B. Brezger, A. I. Lvovsky (2003)
87Rb D2 line
ω = 5 MHz
E.E. Mikhailov, I. Novikova, Opt. Lett. 33, 1213 (2008)
87Rb + 2.5 torr Ne D1 line
ω = 1.2 MHz
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Fg=1
Fe=2
Arbitrary atomic level angular momenta
Free choice of incident polarization
Quadrature noise analysis on arbitrary output polarization
Optically thick medium
Longitudinal magnetic field
Realistic modelling
atoms
x
yz
W1 W2
P1 P2
noise analysis
noise analysis
vacuum
laser
L
B
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Evolution: Maxwell & Heisenbeg-Langevin equations
0),(),(
),()(),(
),()(),(
tztza
tzztz
tzazatza
ij
ijijij
Linearization:
Calculation outline [based upon A. Dantan and M. Pinard, Phys. Rev. A 69, 043810 (2005)]
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2
2
1
1
),(
a
a
a
a
zA
See details in Lezama et al. Phys. Rev. A 77, 013806 (2008)
Cooperativity parameter
Mean atomic responseQuantum atomic fluctuations
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atoms
x
yz
noise analysis
noise analysis
laser
L
0000
0100
0000
0001
)0(S
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Pure two-level system
01.0
1
0
C
0 1 2 3 4 50,8
1,0
1,2
1,4
1,6
1,8
2,0
2,2
Fg=0
Fe=1
0.5
1
5
Nor
mal
ized
noi
se p
ower
/
r
Amplitude
Phase
Results
ω
Ω
Ω
01.0
10
10
r
0 5 10 15 20 25 30
0,8
0,9
1,0
1,1
1,2
1,3
1,4
1,5
Fg=0
Fe=1
110
100
Norm
aliz
ed n
ois
e p
ow
er
/
C
Ω 0
220
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Total noise
Semiclassical
Quantum atomic fluctuations
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Open three-level system
0 2 4 6 8 10 12 140,95
1,00
1,05
1,10
1,15
Fg=1
Fe=0
N
orm
aliz
ed n
oise
pow
er
/
0 2 4 6 8 10 12 140,9
1,0
1,1
1,2
1,3
0.0 0.5 1.0
1.0
1.1
1.2
1.3
Fg=1/2
Fe=1/2
/
Norm
aliz
ed n
ois
e p
ow
er
Four level system
01.0
10
10
10
C
r
X amplitude
X phase
Y amplitude
Y phase
X amplitude
X phase
Y amplitude
Y phase
01.0
10
10
10
C
r
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0 5 10 15 20 25 30
1
3
5
7
9
11
0 1 2 31
5
9
Fg=1
Fe=2
/N
orm
aliz
ed n
oise
pow
er
X amplitude
X phase
Y amplitude
Y phase
01.0
100
40
10
C
r
Multilevel system
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1 → 2
1 → 1
2 → 2
2 → 1
-1 0 +1
-1 0 +1
Back to experiments
E.E. Mikhailov, I. Novikova, Opt. Lett. 33, 1213 (2008)
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S.M. Rochester et al, Phys. Rev. A 63, 043814 (2003)
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S.M. Rochester et al, Phys. Rev. A 63, 043814 (2003) 1 → 2
1 → 1
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“Vacuum squeezing via polarization self-rotation and excess noise in hot Rb vapors”
E.E. Mikhailov, A. Lezama, T. Noel, and I. Novikova, J. Mod. Opt. (2009).
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-1 0 +1 +2-2
-1 0 +1
-1 0 +1
e2
e1
+ -
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-1.5 -1.0 -0.5 0.0 0.5-2
0
2
4
6
8
Nor
mal
ized
noi
se p
ower
(dB
)
Laser detuning (GHz)
Min. noise Max. noise
-1.5 -1.0 -0.5 0.0 0.5
-6
-4
-2
0
2
4
6
8
No
rma
lize
d n
ois
e p
ow
er
(dB
)
Laser detuning (GHz)
Min. noise Max. noise
-1.5 -1.0 -0.5 0.0 0.5
0
2
4
6
8
=30C=100=0.01
No
rma
lize
d n
ois
e p
ow
er
(dB
)
Laser detuning (GHz)
F=2→2F=2→1
Noise frequency 0.2Γ
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)1( NB
HF
iii
12
220
)1( NA
)(NA
)(NB
)1( NA
)1( NB
)1( ND
)(NC
)1( NC
)1( NC
)1( ND
22
21
)(ND
22
ωL
22
0
iHF
e2
e1
+ -
Δ2
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Current issues: •Parameter optimization
•Theory improvement
•Optical pumping effects
•Buffer gas collisions
•Radiative quenching
Conclusions:
•Squeezing via PSR is possible in atomic vapor under suitable conditions.
•Non-resonant transitions play a key role
•Low frequency noise squeezing due to differential AC Stark shift
•Resonant transitions between dressed levels are responsible for excess noise
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Comments and discussions:
P. Barberis
N. Zagury
L. Davidovich
Acknowledgments
H. Failache
S. Barreiro
P. Valente
P. Nussenzveig
M. Martinelli
I. Novikova
E. Mikhailov
Montevideo
São Paulo
Williamsburg