Light as a quantum fluid : a new quantization technique of optical fields based on X-waves and its application to entanglement in parametric amplification

In the framework of the paraxial and of the slowly varying envelope approximations, with reference to a normally dispersive medium or to vacuum, I report a new approach to field quantization. The electromagnetic field is given as a continuous superposition of non-dispersive and non-diffracting wave-packets (namely X-waves). This enables a new representation of a pulsed beam as a quantum fluid. In the case of vacuum the particle mass m is given by mc = h̄ω, being ω the carrier angular frequency. Entangled states as pairs of elementary excitations traveling at (approximately) the same velocity are found in optical parametric amplification.