Spatial variables of light: From controlled decoherence in quantum key distribution to the spatial Franson interferometer

Abstract

In this thesis, the spatial variables of light are used in the practical and fundamental realms. In the practical domain, a theoretical and experimental study of the method that is referred to as the controllable decoherence assisted scheme is presented. The scheme is based on the possibility of introducing decoherence in a controllable way. Theoretically, it is shown that the method allows reducing the amount of information that an eavesdropper can obtain in the BB84 protocol under the entangling probe attack. Experimentally, two proof-of-principle experiments using heralded single photons were performed. One in which the BB84 protocol is implemented without adding decoherence, and another in which the controllable decoherence assisted scheme is used in the BB84 protocol. In the first one, it is found an average value of QBER= 3.9 ± 0.3 % for five keys of ¿ 1000 bits each one. In the second experiment, it is observed that the controllable decoherence introduced in Alice's site is indeed canceled, allowing to recover low values of the QBER. Regarding the study of fundamental concepts by means of light spatial variables, the generation of spatial-bin entanglement is addressed. Specifically, the spatial analog of the Franson interferometer is presented. The Franson interferometer is used to obtain time-bin entanglement. This is achieved by using pairs of temporarily correlated photons and two Mach-Zehnder interferometers to have the option of light traveling by long or short paths that will constitute the basis of time-bin entanglement. In the spatial version proposed, the interferometers are replaced by tunable beam displacers to obtain left or right spatial modes that will constitute the spatial-bin entanglement. Moreover, it is explained how to violate the Bell inequality in the position-transverse momentum domain using the spatial Franson interferometer.