1. TIME REFRACTION and THE QUANTUM PROPERTIES OF VACUUM J. T. Mendonça CFP and CFIF, Instituto Superior Técnico Collaborators R. Bingham (RAL), G. Brodin (U. Umea), A. Guerreiro (U. Porto), M. Marklund (U. Umea), E. Ribeiro (IST), P. Shukla (U. Bochum), Ch. Wang (U. Aberdeen)

2. Outline 1.Time refraction (“flash” ionization); 2.Classical: Temporal Fresnel formulae; 3.Quantum: photon pair creation; 4.Temporal beam splitter; 5.Arbitrary time varying media; 6.Dynamical Casimir effect; 7.Euler-Heisenberg vacuum; 8.Contracting plasma bubble; 9.Conclusions.

3. n x  1 1 n 2   y n x  1 1 n 2   ct (Space) refractionTime refraction Photons cannot travel back in the past Reflection occurs in both cases

4. Electric field for a given frequency mode (j = 0, 1) Temporal Snell’s law: Sudden change in the medium: n 0 --> n 1 at t = 0. Momentum conservation implies a frequency jump (flash ionization)

5. Field continuity conditions Temporal Fresnel formulae Transmission and reflection coefficients Time refraction leads to (space) reflection!

6. Quantum theory of time-refraction Bogoliubov transform. (relating new and old field operators) Squeezing transf. Time dependent Refractive index

7. Creation of photon pairs from vacuum Relation between the new and the old quantum states

8. Time refraction for guided propagation Total electric field Axial field amplitude Dispersion relation Changes in the medium Frequency shift

9. Forward propagation Backward propagation (For propagation in free space:  Field envelopes for Gaussian pulses

10. Temporal beam splitter Two successive jumps in the medium: - n 0 for t  - n 1 for 0 < t <  Transmitted and reflected intensities |n 1 - n 0 | =0.1

11. Field operators for the temporal beam splitter Probability for the emission of m photon pairs (m=1) p(m) ~ p(1) m

12. Temporal beam splitter in guided propagation Final amplitude of the transmitted pulse Final amplitude of the reflected pulse t  0 n, k c Perturbation with a finite duration

13. Pump laser pulse Optical Fiber nnn’ Time refraction experiment in guided propagation

14. Initial Gaussian pulse (t = 0) Numerical illustration

15. Formation of a counter-propagating pulse

16. Secondary pulse resulting from time refraction

17. Arbitrary time-varying medium Classical field Instantaneous frequency Evolution equations

18. Approximate solutions for |E| >> |E’| Transmitted field Reflected field Formally identical to reflection in a non-homogeneous medium R (t) --> R (x)

19. Field operators Time-dependent Bogoliubov transformations

20. Manifestations of quantum vacuum 1.Hawking radiation 2.Hunruh-Davies effect (accelerated frame) 3.Dynamical Casimir effect 4.Time refraction 5.Superluminal boundary

21. Time refraction v. Dynamical Casimir Number of photons created from vacuum Time refraction stays valid in free space Squeezing parameter

22. Photon creation in a perturbed cavity

23. Superluminal fronts Reduces to time refraction by a Lorentz transformation Number of photons produced from vacuum Vacuum resonances! Mendonça and Guerreiro, PRA (2005)

24. How to create a superluminal front

25. Dynamical cavity in vacuum Dispersion relation of the cavity modes Geometric factor (  Laser intensity: I (r, t)

26. Time refraction in a contracting plasma bubble Possible explanation for sonoluminiscence! t/t 0

27. Conclusions Time refraction (TR) is a basic first order effect (such as refraction). TR implies space reflection and photon frequency shifts (temporal Snell’s law). Temporal interference can be observed and a temporal beam splitter can be built up. TR of short pulses in optical fibers can used for demonstration experiments. TR implies photon pair creation in vacuum. TR is related to the dynamical Casimir effect. It can also be used to study vacuum nonlinearities. TR can be applied to an expanding or contracting plasma bubble. TR can explain sono-luminiscence in a simple way (applications to astrophysics?). Long life to TR...