Non Gaussianity for the two photon spatial state of SPDC using Hermite Gaussian pump beams

L REBÓN; E. S. GÓMEZ; G. LIMA; C. H. MONKEN; W. A. T. NOGUEIRA

Mar del Plata

Conferencia; VII Quantum Optics Conference; 2014

One of the goals in the area of Quantum Information is to identify and develop quantum resources. In this context, non-Gaussianity (nG) of states and operations has been considered a resource in the Continuous Variable domain, since it is either necessary or desirable for several tasks. A method to generate non-Gaussian quantum states is the non-linear optical process known as spontaneous parametric down-conversion (SPDC). Since it was demonstrated that the spatial information of the pump laser field is transferred to the two-photon spatial state (TPSS), it is possible to prepare different non-Gaussian TPSS by the control of the angular spectrum of the laser field. Here, we present the quantification of the non-Gaussianity of a TPSS when the pump beam field that is used in the SPDC process is a Hermite-Gaussian mode. The measure that we use is based on a statistical quantity called negentropy. The measure of the non-Gaussianity is defined as the sum of negentropies for the far-and near-fields, and it is called total non-Gaussianity (nGT). This measure was recently introduced and was used to quantify the TPSS when the pump beam field is a Gaussian mode. It appears to be operationally practical, and experimentally accessible, since it can be obtained from the results of the measurements in two well-known geometries, which are largely used in experiments related to TPSS. In fact, while other non-Gaussian measures require the knowledge of the full density matrix, nGT only requires the knowledge of near and far-field joint probability distributions. The explicitly analytical expression for nGT was obtained and its behavior was compared with the non-Gaussianity measure known as quantum relative entropy (QRE), showing the same behavior. Also, both quantities show dependence only on the shape of the pump beam, but not on the experimental parameters as the width of the laser profile, wave number of the pump beam and thickness of the crystal. Since QRE is becoming the standard quantifier of non-Gaussianity, those facts suggests that nGT is a good quantifier for the non-Gaussianity of a TPSS. Finally, as Hermite-Gaussian laser modes constitute a basis for describing any laser mode, our results can be used for the research of non-Gaussianity of the TPSS when Laguerre-Gaussian pump beams are used.