<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi></mml:math>-way parametric frequency beamsplitter for quantum photonics

Optical networks are the leading platform for the transfer of information due to their low loss and ability to scale to many information channels using optical frequency modes. To fully leverage the quantum properties of light in this platform, it is desired to manipulate higher-dimensional superpositions by orchestrating linear, beamsplitter-type interactions between several channels simultaneously. We propose a method of achieving simultaneous, all-to-all coupling between <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>N</a:mi></a:math> optical frequency modes via <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>N</b:mi></b:math>-way Bragg-scattering four-wave mixing. By exploiting the frequency degree of freedom, additional modes can be multiplexed in an interaction medium of fixed volume and loss while avoiding the introduction of excess noise. We generalize the theory of the frequency-encoded two-mode interaction to <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi>N</c:mi></c:math> modes under this four-wave-mixing approach, finding that arbitrary unitary transformations are possible through successive four-wave-mixing pump configurations. We experimentally verify the quantum nature of this scheme by demonstrating three-way multiphoton interference. Two input photons are shared among three frequency modes and display interference differing from that of two classical (coherent-state) inputs. These results show the potential of our approach for the scalability of photonic quantum information processing to general <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mi>N</d:mi></d:math>-mode systems in the frequency domain.