Abstract
High dimensional quantum states are of fundamental interest for quantum information processing. They give access to large Hilbert spaces and, in turn, enable the encoding of quantum information on multiple modes. One method to create such quantum states is parametric down-conversion (PDC) in waveguide arrays (WGAs) which allows for the creation of highly entangled photon pairs in controlled, easily accessible spatial modes, with unique spectral properties.In this paper we examine both theoretically and experimentally the PDC process in a lithium niobate WGA. We measure the spatial and spectral properties of the emitted photon pairs, revealing correlations between spectral and spatial degrees of freedom of the created photons. Our measurements show that, in contrast to prior theoretical approaches, spectrally dependent coupling effects have to be taken into account in the theory of PDC in WGAs. To interpret the results, we developed a theoretical model specifically taking into account spectrally dependent coupling effects, which further enables us to explore the capabilities and limitations for engineering the spatial correlations of the generated quantum states.
Highlights
With this knowledge we explore the preparation of specific spatial correlations between the created photon pairs
Our analysis revealed that the spatial and spectral degrees of freedom of the parametric down-conversion (PDC) process in the waveguide arrays (WGAs) are connected via the phase-mismatch 1
A phase-mismatch introduced in the spectral domain 1 ! is compensated via an opposite phase-mismatch in the spatial domain 1 A, leading to spatiospectral correlations in the generated quantum states
Summary
Following the theoretical treatment of type-I PDC in nonlinear WGAs by Solntsev et al in [15] we start with the mathematical description of the quantized electric fields propagating through the WGA and use coupled mode theory to solve the corresponding Maxwell’s equations [36,37,38,39]. Where (0)(!) describes the propagation vector in a single waveguide at frequency !, given by (0)(!) = n(eff)(!)!/c, and k? Hereby the impact of the WGA on the dispersion is given by the coupling parameter C(!), which is firstly dependent on the distance between the individual waveguide channels and secondly impacted by the frequencies of the propagating fields The pump does not couple to neighbouring channels, because it resides at wavelengths far below signal and idler. In this regime the waveguide mode size is smaller, and the mode overlap governing the coupling parameter can be approximated as zero. The spatial illumination pattern of the pump A(n) in the nth waveguide is connected transformation
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