Time Refraction and the Quantum Properties of Vacuum

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 Time refraction (“flash” ionization); Classical: Temporal Fresnel formulae; Quantum: photon pair creation; Temporal beam splitter; Arbitrary time varying media; Dynamical Casimir effect; Euler-Heisenberg vacuum; Contracting plasma bubble; Conclusions.

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

4. Electric field for a given frequency mode (j = 0, 1) Sudden change in the medium: n0 --> n1 at t = 0. Temporal Snell’s law: 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) Time dependent Refractive index Squeezing transf.

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. Field envelopes for Gaussian pulses Forward propagation Backward propagation (For propagation in free space: a = b)

10. Temporal beam splitter • Two successive jumps in the medium: • n0 for t < 0, and t >  • n1 for 0 < t <  Transmitted and reflected intensities |n1- n0| =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 Perturbation with a finite duration n, kc t 0 t Final amplitude of the transmitted pulse Final amplitude of the reflected pulse

13. Timerefraction experiment in guided propagation n n’ n Optical Fiber Pump laser pulse

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

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 Hawking radiation Hunruh-Davies effect (accelerated frame) Dynamical Casimir effect Time refraction Superluminal boundary

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

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 t/t0 Possible explanation for sonoluminiscence!

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...