1. Paraty, September 2009 alezama@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.

2. Paraty, September 2009 alezama@fing.edu.uy Outline: I.Background II.Renewed interest III.Numerical calculation IV.Back to experiments V.Future

3. Paraty, September 2009 alezama@fing.edu.uy I. Background. atoms L Laser 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) , Ω 0 g e 00 Δ

4. Paraty, September 2009 alezama@fing.edu.uy Squeezing via polarization self-rotation (PSR) A.B. Matsko et al, Phys. Rev. A 66, 043815 (2002)

5. Paraty, September 2009 alezama@fing.edu.uy A.B. Matsko et al, Phys Rev. A 66, 043815 (2002)

6. Paraty, September 2009 alezama@fing.edu.uy from Ries et al Phys. Rev. A 68, 025801 (2003)‏

7. Paraty, September 2009 alezama@fing.edu.uy 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) 87 Rb D2 line ω = 5 MHz E.E. Mikhailov, I. Novikova, Opt. Lett. 33, 1213 (2008) 87 Rb + 2.5 torr Ne D1 line ω = 1.2 MHz

8. Paraty, September 2009 alezama@fing.edu.uy F g =1 F e =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 y z W1W1 W2W2 P1P1 P2P2 noise analysis vacuum laser L B

9. Paraty, September 2009 alezama@fing.edu.uy Evolution: Maxwell & Heisenbeg-Langevin equations Linearization: Calculation outline [based upon A. Dantan and M. Pinard, Phys. Rev. A 69, 043810 (2005)]

10. Paraty, September 2009 alezama@fing.edu.uy See details in Lezama et al. Phys. Rev. A 77, 013806 (2008) Cooperativity parameter Mean atomic response Quantum atomic fluctuations

11. Paraty, September 2009 alezama@fing.edu.uy atoms x y z noise analysis laser L

12. Paraty, September 2009 alezama@fing.edu.uy Pure two-level system Amplitude Phase Results ω Ω Ω C Ω

13. Paraty, September 2009 alezama@fing.edu.uy Total noise Semiclassical Quantum atomic fluctuations

14. Paraty, September 2009 alezama@fing.edu.uy Open three-level system Four level system X amplitude X phase Y amplitude Y phase X amplitude X phase Y amplitude Y phase

15. Paraty, September 2009 alezama@fing.edu.uy X amplitude X phase Y amplitude Y phase Multilevel system

16. Paraty, September 2009 alezama@fing.edu.uy 1 → 2 1 → 1 2 → 2 2 → 1 0 +1 0 +1 Back to experiments E.E. Mikhailov, I. Novikova, Opt. Lett. 33, 1213 (2008)

17. Paraty, September 2009 alezama@fing.edu.uy 795 nm g e1e1 e2e2

18. Paraty, September 2009 alezama@fing.edu.uy S.M. Rochester et al, Phys. Rev. A 63, 043814 (2003)

19. Paraty, September 2009 alezama@fing.edu.uy S.M. Rochester et al, Phys. Rev. A 63, 043814 (2003) 1 → 2 1 → 1

20. Paraty, September 2009 alezama@fing.edu.uy “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).

21. Paraty, September 2009 alezama@fing.edu.uy 0 +1 +2 -2 0 +1 0 +1 e2e2 e1e1 +-

22. Paraty, September 2009 alezama@fing.edu.uy F=2→2F=2→1 Noise frequency 0.2Γ

23. Paraty, September 2009 alezama@fing.edu.uy ωLωL e2e2 e1e1 + - Δ2Δ2

24. alezama@fing.edu.uy 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

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