a. lezama

Paraty, September 2009Paraty, September 2009 alezama@fing.edu.uyalezama@fing.edu.uy

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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795 nm

g

e1

e2

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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