TIME REFRACTION and THE QUANTUM PROPERTIES OF VACUUM

J. T. MendonçaCFP and CFIF, Instituto Superior Técnico

CollaboratorsR. 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)

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.

n x

1

1

n2

y

n x

1

1

n2

ct

(Space) refraction Time refraction

Photons cannot travel back in the past Reflection occurs in both cases

Electric field for a given frequency mode

(j = 0, 1)

Temporal Snell’s law:

Sudden change in the medium: n0 --> n1 at t = 0.

Momentum conservation implies a frequency jump (flash ionization)

Field continuity conditions

Temporal Fresnel formulae

Transmission and reflection coefficients

Time refraction leads to (space) reflection!

Quantum theory of time-refraction

Bogoliubov transform. (relating new and old field operators)

Squeezing transf.

Time dependentRefractive index

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n(t) = n1H(−t) + n2H(t)

Creation of photon pairs from vacuum

Relation between the new and the old quantum states

Time refraction for guided propagation

Total electric field

Axial field amplitude

Dispersion relation

Changes in the medium

Frequency shift

Forward propagation

Backward propagation

(For propagation in free space:

Field envelopes for Gaussian pulses

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

Field operators for the temporal beam splitter

Probability for the emission of m photon pairs

(m=1)

p(m) ~ p(1)m

Temporal beam splitter in guided propagation

Final amplitude of the transmitted pulse

Final amplitude of the reflected pulse

t0

n, kcPerturbation with a finite duration

Pump laser pulse

Optical Fiber

n nn’

Time refraction experiment in guided propagation

Initial Gaussian pulse (t = 0)

Numerical illustration

Formation of a counter-propagating pulse

Secondary pulse resulting from time refraction

Arbitrary time-varying medium

Classical field

Instantaneous frequency

Evolution equations

Approximate solutions for |E| >> |E’|

Transmitted field

Reflected field

Formally identical to reflection in a non-homogeneous medium R (t) --> R (x)

Field operators

Time-dependent Bogoliubov transformations

Manifestations of quantum vacuum

1. Hawking radiation2. Hunruh-Davies effect (accelerated frame)3. Dynamical Casimir effect4. Time refraction5. Superluminal boundary

Time refraction v. Dynamical Casimir

Number of photons created from vacuum

Time refraction stays valid in free space

Squeezing parameter

Photon creation in aperturbed cavity

Superluminal fronts

Reduces to time refraction by a Lorentz transformation

Number of photons produced from vacuum

€

< Nk (t − x /u) >= sinh2[α .r(t − x /u)]

Vacuum resonances!

Mendonça and Guerreiro, PRA (2005)

How to create a superluminal front

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Dynamical cavity in vacuum

Dispersion relation of the cavity modes

Geometric factor (

Laser intensity: I (r, t)

Time refraction in a contracting plasma bubble

Possible explanation for sonoluminiscence!

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ω(t / t0) = k 2c 2 +ωp0

2

(1− t / t0)

⎡

⎣ ⎢

⎤

⎦ ⎥

1/ 2

€

ω(t)ω0

t/t0

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...