Hyperentanglement and femtosecond parametric down-conversion

Summary form only given. Entanglement has proven to be an important resource in generating completely new optical states that can be used in quantum information processing, secure communication, and precise optical measurement. The transition from this theoretical notion to experimental reality is often a challenging step, however. One of the most accessible sources of entangled-photon states is a nonlinear optical process called spontaneous parametric down-conversion (SPDC), in which an-optical crystal illuminated by a laser beam spontaneously generates pairs of photons. We present a formalism that incorporates the hyper-entangled nature of the quantum state generated via SPDC. The key to providing an adequate physical description of ultrafast parametric down conversion is to consider the initial entangled state in its entirety including the interplay among the different quantum variables.