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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum emission of light by medium with time-dependent refractive index

V. Hizhnyakov, Helle Kaasik

Published Jun 15, 2007• 1 citation
Publisher

Abstract

Zero-point quantum fluctuations in a medium with oscillation of optical length in time cause spontaneous two-quantum emission of light. This emission is usually very weak, but it strongly enhanced if a resonance condition for frequency and amplitude of the oscillation is fulfilled.
DOI
10.1117/12.751785

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A two-photon emission of a medium with periodically time-dependent refractive index is considered. The emission results from the zero-point fluctuations of the medium. Usually this emission is very weak. However, it can be strongly enhanced if the resonant condition ω0ω_0ω0​ = 2.94 c/l0c/l_0c/l0​ is fulfilled (here ω0ω_0ω0​ and $l_0 $ are the frequency and the amplitude of the oscillations of the optical length of the medium, respectively). Besides, a medium with resonant oscillations of the optical length performs the phase conjugated reflection with high efficiency. A similar resonant enhancement of the two-quantum emission of other bosons is also predicted.
We consider the two-photon emission by a dielectric where refractive index n oscillates in time. The oscillations of n cause analogous oscillations of the optical length. The velocity of the latter oscillations, in principle, may be arbitrarily large. If the maximal velocity of these oscillations V is much less than the light velocity c then the intensity of the emission will increase with V . However, if it strongly exceeds c then the opposite dependence takes place as the zero-point fluctuations cannot appreciably react on such a fast oscillations. Therefore, the crossover for the dependence of the emission on V exists at V r ∼ c and a resonant enhancement of it is observed at this value of V . Our calculation gives V r ≈ 3 c .
A nonlinear quantum-optical process is considered: emission of photon pairs by the reflecting end of a fiber excited by a standing laser wave. Radiation occurs due to periodic changes in the optical length of the fiber over time. This radiation can be significantly enhanced in long fibers. Because of this enhancement, a nonperturbative description of the process is required. Such a description presented here predicts a strong peak of radiation, if the amplitude of the oscillations of the optical length coincides with half of the laser wavelength. The considered phenomenon can be used to create a source of entangled photons.
We develop a perturbative theory that describes a superluminal refractive perturbation propagating in a dispersive medium and the subsequent excitation of the quantum vacuum zero-point fluctuations. We find a pro-cess similar to the anomalous Doppler effect: Photons are emitted in correlated pairs and mainly within a Cerenkov-like cone, one on the forward and the other in backward directions. The number of photon pairs emitted from the perturbation increases strongly with the degree of superluminality and under realizable experimental conditions; it can reach up to $\ensuremath{\sim}101010{}^{\ensuremath{-}2}$ photons per pulse. Moreover, it is, in principle, possible to engineer the host medium so as to modify the effective group refractive index. In the presence of ``fast-light'' media, e.g., a with group index smaller than unity, a further $\ensuremath{\sim}101010\ifmmode\times\else\texttimes\fi{}$ enhancement may be achieved and the photon emission spectrum is characterized by two sharp peaks that, in future experiments, would clearly identify the correlated emission of photon pairs.