Femtosecond laser written photonic circuits for quantum simulation

Abstract

Summary form only given. High-accuracy integrated photonic circuits are desired in many applications, ranging from telecommunications to sensing, especially where many optical modes or many wavelengths are involved. Particularly challenging are the requirements needed for quantum information applications [1], which have recently found in the integrated optics technology a quite unique and powerful platform [2]. In fact, quantum and classical interference effects are ubiquitously exploited in quantum photonic devices, thus requiring a tight fabrication control not only on the power splitting elements inside the circuit, but also on the phase induced by the various paths. Difficulties grow in case quantum simulation tasks [3] are addressed: the need to model other physical systems increases the circuit complexity and many elements need to be integrated without losing in precision.Femtosecond laser microfabrication has recently emerged as an ideal approach to fabricate integrated photonic circuits for quantum applications [4, 5]. *n the one hand it is appreciated for its low costs and fast-prototyping capabilities. *n the other hand, femtosecond laser written waveguides, due to their low birefringence, can support polarization-entangled two-photon states [5], which are useful to implement many quantum information protocols.In this work we demonstrate the capability of femtosecond laser writing technology to fabricate complex waveguide circuits, with tight phase control and polarization independent behaviour. Specifically, we manufacture optical circuits consisting of cascaded directional couplers, which implement discrete-time quantum walks of polarization entangled photon pairs. The scheme of a circuit realizing a four-steps quantum walk on an ordered one-dimensional lattice is shown in Fig. 1(a). To achieve a perfect polarization insensitive behaviour, directional couplers with an innovative three-dimensional geometry are employed (see the blow-up in Fig. 1(a)). In fact, waveguide birefringence causes a slight polarization dependence of the dimension and of the ellipticity of the guided mode, which may affect the coupling coefficients. We show that, by fabricating the two waveguides constituting the coupler on different planes, it is possible to find a condition in which the overlap integrals for differently polarized guided modes are equal, thus providing the desired polarization insensitivity in the coupling. In Fig. 1(b) the experimental two-photon correlations are reported, obtained by injecting polarization-entangled two-photon states with different symmetry, compared with the theoretical ones. This is equivalent to perform quantum walks of quantum particle pairs with bosonic or fermionic symmetry [6]. *ne can note the excellent agreement between the theory and the experiment, which testifies the accuracy of our fabrication process. We will also show how similar circuits, involving more optical modes and implementing arbitrary phase maps, enable to study quantum walks with disorder-induced effects and thus to observe phenomena such as Anderson localization.