1. Quantum Optics SUPERLUMINALITY: Breaking the Universal Speed Limit 21 April 2004 1 Brian Winey Department of Physics and Astronomy University of Rochester

2. Quantum Optics Department of Physics and Astronomy, University of Rochester SUPERLUMINALITY 21 April 2004 2  People  Advisor: John Howell  Authors of several papers

3. Quantum Optics Department of Physics and Astronomy, University of Rochester SUPERLUMINALITY 21 April 2004 3  Overview  Review of Pulse Propagation  Pulse Propagation in Dispersive Media  Description of Fast Light  Experimental Demonstrations  Information Theory and Special Relativity

4. Quantum Optics Department of Physics and Astronomy, University of Rochester SUPERLUMINALITY 21 April 2004 4 Phase E z t Plane Waves: Phase Velocity

5. Quantum Optics Department of Physics and Astronomy, University of Rochester SUPERLUMINALITY 21 April 2004 5 E E z z t Group Velocity A “Bunch” of plane waves Pulse

6. Quantum Optics Department of Physics and Astronomy, University of Rochester SUPERLUMINALITY 21 April 2004 6 Possible Group Velocities Since with Slow Light Fast Light Boyd et. al. Wang et.al. Gauthier et.al.

7. Quantum Optics Department of Physics and Astronomy, University of Rochester SUPERLUMINALITY 21 April 2004 7  Some questions:  What is the physical meaning of fast light?  What is the physical meaning of a negative group velocity?  What would fast light look like?

8. Quantum Optics Department of Physics and Astronomy, University of Rochester SUPERLUMINALITY 21 April 2004 8 A guess by Gauthier and Stenner: But, electromagnetic wave propagation in media is a complicated topic…

9. Quantum Optics Department of Physics and Astronomy, University of Rochester SUPERLUMINALITY 21 April 2004 9  How would one produce fast light pulses? Super Duper Superluminal Pulse Machine TURBO

10. Quantum Optics Department of Physics and Astronomy, University of Rochester SUPERLUMINALITY 21 April 2004 10  Regions of Anomalous Dispersion Between Two Gain Peaks  Anomalous Dispersion: when  Index of Refraction (n)  Susceptibility  For two gain peaks: But there’s the imaginary part of the story…

11. Quantum Optics Department of Physics and Astronomy, University of Rochester SUPERLUMINALITY 21 April 2004 11  Absorption Coefficient of Media is determined by Im χ  Im χ and Re χ are related by the Kramers-Kronig Thm.

12. Quantum Optics Department of Physics and Astronomy, University of Rochester SUPERLUMINALITY 21 April 2004 12  Due to the relationship of Im χ and Re χ, in regions of anomalous dispersion there is optical gain instead of absorption.  But the situation is slightly more complicated: we want two gain peaks.

13. Quantum Optics Department of Physics and Astronomy, University of Rochester SUPERLUMINALITY 21 April 2004 13  How does one “find” two gain peaks? Gain Peak 1 Gain Peak 2 “As we round the corner, the famous Swiss Gain Peaks will come into view.”

14. Quantum Optics Department of Physics and Astronomy, University of Rochester SUPERLUMINALITY 21 April 2004 14  Achieve  Achieve a gain doublet using stimulated Raman scattering with a bichromatic pump field Classifieds: SRP: Lonely probe field photon seeks excited atoms willing to return to their ground states. Prefers photon of same frequency. Wang et. al.

15. Quantum Optics Department of Physics and Astronomy, University of Rochester SUPERLUMINALITY 21 April 2004 15  Scanning the probe field reveals the gain experienced when resonant with the two pump fields Wang et. al.

16. Quantum Optics Department of Physics and Astronomy, University of Rochester SUPERLUMINALITY 21 April 2004 16  A look at an experimental realization of a gain doublet Wang et. al.

17. Quantum Optics Department of Physics and Astronomy, University of Rochester SUPERLUMINALITY 21 April 2004 17  Results of Wang et.al.

18. Quantum Optics Department of Physics and Astronomy, University of Rochester SUPERLUMINALITY 21 April 2004 18  Why do we want two gain peaks?  Between the two turning points, there is a nearly constant region of anomalous dispersion.  Having two peaks also increases the frequency width of our region of interest. Wang et. al.

19. Quantum Optics Department of Physics and Astronomy, University of Rochester SUPERLUMINALITY 21 April 2004 19  Information Theory and Special Relativity  L. Brillouin, Wave Propagation and Group Velocity (Academic Press, New York, 1960).  R.W. Boyd and D. Gauthier, Progress in Optics 43, ed. by E. Wolf (Elsevier,Amsterdam, 2002), Chap. 6.  L.J. Wang, A. Kuzmich and A. Dogariu, Nature (London) 406, 277 (2000).  M. Stenner, D. Gauthier, and M. Neifeld, Nature (London) 425, 695 (2003).

20. Quantum Optics Department of Physics and Astronomy, University of Rochester SUPERLUMINALITY 21 April 2004 20  Starting Point: What is information and how fast can it travel?  Information: a non-analytical point of an electromagnetic wave, Stenner et. al. and others.  Special Relativity: No wave can travel faster than c.  But, as shown, a pulse group velocity can exceed c.  Can a non-analytical point travel faster than c?

21. Quantum Optics Department of Physics and Astronomy, University of Rochester SUPERLUMINALITY 21 April 2004 21  Early Predictions:  Sommerfeld and Brillouin (1960) said that speed of electron interactions govern the speed of a wave front, a non-analytical point, such as a square wave front.  Electrons can not interact faster than c.  Therefore, the wave front cannot travel faster than c.  “Proved” through a long saddle point integration method, that the wave front suffers extreme distortion. Thus, loss of information. Sommerfeld Brillouin

22. Quantum Optics Department of Physics and Astronomy, University of Rochester SUPERLUMINALITY 21 April 2004 22   Garrett et al. (1970) proposed using Gausian wave packets, instead of Brillouin and Sommerfeld’s square waves.   Showed little distortion of wave front in regions of anomalous dispersion   Failed to deal with the trouble of information transfer

23. Quantum Optics Department of Physics and Astronomy, University of Rochester SUPERLUMINALITY 21 April 2004 23  Recently:  Stenner et.al., Wang et.al., and Chiao et.al. have all tried to deal with information transfer and superluminal signaling.  Use Non-analytical “signal” point  Optical response time of “signal” machine (EOM,etc)

24. Quantum Optics Department of Physics and Astronomy, University of Rochester SUPERLUMINALITY 21 April 2004 24  Results of Information Study by Stenner et.al. Stenner et.al. Signal Propagation Bit-Error-Rate (BER)

25. Quantum Optics Department of Physics and Astronomy, University of Rochester SUPERLUMINALITY 21 April 2004 25  General consensus: quantum noise added to the signal during pulse propagation saves our dear friend causality. Quantum Noise But is this the end of the game….? Garrison et.al. Superluminality

26. Quantum Optics Department of Physics and Astronomy, University of Rochester SUPERLUMINALITY 21 April 2004 26  Conclusions:  Light Pulses have been shown to travel faster than c in regions of anomalous dispersion  Causality is preserved in fast light experiments by the introduction of quantum noise fluctuations in photon number.

27. Quantum Optics Department of Physics and Astronomy, University of Rochester SUPERLUMINALITY 21 April 2004 27  Future Questions  Is there a limit to the speed of fast light? Singularity?  Are there better definitions of information that could allow for superluminal signal propagation and low BER?  Quantum noise seems like a weak solution to causal paradoxes.

28. Quantum Optics Department of Physics and Astronomy, University of Rochester SUPERLUMINALITY 21 April 2004 28  Questions? Quantum Noise