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arXiv:quant-ph/0306095

Strong two-photon emission by a medium with periodically time-dependent refractive index

V. Hizhnyakov

Published Jun 13, 2003• 4 citations
arXivHTMLPDF

Abstract

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 $ω_0$ = 2.94 $c/l_0$ is fulfilled (here $ω_0$ 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.

DOI
10.48550/arxiv.quant-ph/0306095

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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 l0l_0 l0​ 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.
By utilizing the interference between an absorptive resonance and an amplifying resonance, one can achieve an enhanced refractive index without an increase in absorption to the beam. We analyze noise added to the beam due to spontaneous emission while propagating through such an index enhanced medium. We find that, for a medium with a refractive index of nnn and of length LLL, $\ensuremath{\approx}(n\ensuremath{-}1)(2\ensuremath{\pi}∕{\ensuremath{\lambda}}_{0})L$ noise photons are added to the beam.