paraty, september 2009 [email protected] a. lezama instituto de física, facultad de ingeniería,...

Paraty, September 2009Paraty, September 2009 [email protected]@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.


Outline:

I. Background

II. Renewed interest

III. Numerical calculation

IV. Back to experiments

V. Future


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


LIg )(

Squeezing via polarization self-rotation (PSR)

A.B. Matsko et al, Phys. Rev. A 66, 043815 (2002)


A.B. Matsko et al, Phys Rev. A 66, 043815 (2002)


from Ries et al Phys. Rev. A 68, 025801 (2003)


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


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


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)]


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


atoms

x

yz

noise analysis

noise analysis

laser

L

0000

0100

0000

0001

)0(S


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


Total noise

Semiclassical

Quantum atomic fluctuations


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


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


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)


795 nm

g

e1

e2


S.M. Rochester et al, Phys. Rev. A 63, 043814 (2003)


S.M. Rochester et al, Phys. Rev. A 63, 043814 (2003) 1 → 2

1 → 1


“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).


-1 0 +1 +2-2

-1 0 +1

-1 0 +1

e2

e1

+ -


-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

)


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

)


F=2→2F=2→1

Noise frequency 0.2Γ


)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


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


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

paraty, september 2009 [email protected] a. lezama instituto de física, facultad de ingeniería,...

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