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arXiv:1201.2354 · Physical Review A

Emission of correlated photon pairs from superluminal perturbations in dispersive media

Francesco Dalla Piazza, F. Belgiorno, Sergio L. Cacciatori, Daniele Faccio

Published Mar 27, 2012• 9 citations

Abstract

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}$10${}^{\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}$10$\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.

DOI: 10.1103/physreva.85.033833

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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}

10

{}^{\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}

10

\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.

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.

\n Using pulses based on functions with compact support and perfectly smooth infinitely differentiable zero-intensity nonanalytical points, a new approach to model information propagating through an anomalous dispersive medium is demonstrated. Information can be unambiguously associated to the nonanalytical point in the pulse's leading edge, and its velocity investigated numerically and experimentally in fast-light media. We have clearly observed that the velocity of this nonanalytical point is bounded by Einstein causality and it is exactly equal to the light speed in vacuum c when the pulse's group velocity is superluminal. Moreover, we observed that causality can also cause steepening and a pulse shock-like effect.\n

We investigate a light-pulse propagation with negative group velocity in a nonlinear coherent medium. We show that the necessary conditions for nonlinear superluminal effects to be observable are realized in a three-level $\ensuremath{\Lambda}$ system interacting with a linearly polarized laser field in the presence of a static magnetic field. The initially prepared Zeeman coherence cancels the resonant absorption of the medium almost completely, but preserves its dispersion anomalous and very high. In this medium the light pulse propagates superluminally in the sense that the peak of the transmitted pulse exits the medium before the peak of the incident pulse enters. At the same time the pulse group velocity is intensity dependent, which leads to the self-steepening of the pulse trailing edge due to the fact that the more intense parts of the pulse travel slower. This is in contrast with the shock wave generation in a nonlinear medium with normal dispersion. The predicted effect can be easily observed in the well-known schemes employed in the studies of nonlinear magneto-optical rotation. The upper bound of sample length is found from the criterion that the pulse self-steepening and group-advance time are observable without pulse distortion caused by the group-velocity dispersion.

Anomalous dispersion cannot occur in a transparent passive medium where electromagnetic radiation is being absorbed at all frequencies, as pointed out by Landau and Lifshitz. Here we show, both theoretically and experimentally, that transparent linear anomalous dispersion can occur when a gain doublet is present. Therefore, a superluminal light-pulse propagation can be observed even at a negative 7group velocity through a transparent medium with almost no pulse distortion. Consequently, a negative transit time is experimentally observed resulting in the peak of the incident light pulse to exit the medium even before entering it. This counterintuitive effect is a direct result of the rephasing process owing to the wave nature of light and is not at odds with either causality or Einstein's theory of special relativity.

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 .