Paraty, September 2009 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.

Paraty, September 2009 Outline: I.Background II.Renewed interest III.Numerical calculation IV.Back to experiments V.Future

Paraty, September 2009 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

Paraty, September 2009 Squeezing via polarization self-rotation (PSR) A.B. Matsko et al, Phys. Rev. A 66, (2002)

Paraty, September 2009 A.B. Matsko et al, Phys Rev. A 66, (2002)

Paraty, September 2009 from Ries et al Phys. Rev. A 68, (2003)‏

Paraty, September 2009 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 torr Ne D1 line ω = 1.2 MHz

Paraty, September 2009 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

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

Paraty, September 2009 See details in Lezama et al. Phys. Rev. A 77, (2008) Cooperativity parameter Mean atomic response Quantum atomic fluctuations

Paraty, September 2009 atoms x y z noise analysis laser L

Paraty, September 2009 Pure two-level system Amplitude Phase Results ω Ω Ω C Ω

Paraty, September 2009 Total noise Semiclassical Quantum atomic fluctuations

Paraty, September 2009 Open three-level system Four level system X amplitude X phase Y amplitude Y phase X amplitude X phase Y amplitude Y phase

Paraty, September 2009 X amplitude X phase Y amplitude Y phase Multilevel system

Paraty, September → 2 1 → 1 2 → 2 2 → Back to experiments E.E. Mikhailov, I. Novikova, Opt. Lett. 33, 1213 (2008)

Paraty, September nm g e1e1 e2e2

Paraty, September 2009 S.M. Rochester et al, Phys. Rev. A 63, (2003)

Paraty, September 2009 S.M. Rochester et al, Phys. Rev. A 63, (2003) 1 → 2 1 → 1

Paraty, September 2009 “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).

Paraty, September e2e2 e1e1 +-

Paraty, September 2009 F=2→2F=2→1 Noise frequency 0.2Γ

Paraty, September 2009 ωLωL e2e2 e1e1 + - Δ2Δ2

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

Paraty, September 2009 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