Biphoton shaping with cascaded entangled-photon sources

Quantum entanglement is an integral part of quantum optics and has been exploited in areas such as computation, cryptography and metrology. The entanglement between photons can be present in various degrees of freedom (DOFs), and even the simplest bi-partite systems can occupy a large Hilbert space. Therefore, it is desirable to exploit this multi-dimensional space for various quantum applications by fully controlling the properties of the entangled photons in multiple DOFs. While current entangled-photon sources are capable of generating entanglement in one or more DOFs, there is currently a lack of practical techniques that can shape and control the entanglement properties in multiple DOFs. Here we show that cascading two or more entangled-photon sources with tunable linear media in between allows us to generate photon-pairs whose entanglement properties can be tailored and shaped in the frequency and polarisation domains. We first develop a quantum mechanical model to study the quantum state generated from the cascade structure with special considerations paid to the effects of pump temporal coherence, linear dispersion, and in-structure polarisation transformation applied between the entangled-photon sources. We then experimentally generate photon-pairs with tunable entanglement properties by manipulating the dispersion and birefringence properties of the linear medium placed in between two entangled-photon sources. This is done in an all-fibre, phase stable, and alignment-free configuration. Our results show that the cascade structure offers a great deal of flexibility in tuning the properties of entangled photons in multiple DOFs, opening up a new avenue in engineering quantum light sources