On the Equations of the Rectangular Interferometer

F.J. Duarte

Christopher Alexiev, Jason C. C. Mak, Wesley D. Sacher +1 more

Multiport interferometer meshes can be used to implement unitary transformations on input vectors of light in both the classical and quantum domain. In practice, the phase-shifters in a mesh photonic circuit must be calibrated to compensate for phase errors due to fabrication variations. Calibration using photodetectors external to the mesh has been demonstrated for triangular meshes, but not rectangular meshes. Here, we propose an algorithm for the calibration of rectangular meshes using only external photodetectors and simulate it to evaluate its feasibility.

Ryan Hamerly, Saumil Bandyopadhyay, Dirk Englund

Multiport interferometers based on integrated beamsplitter meshes are widely used in photonic technologies. While the rectangular mesh is favored for its compactness and uniformity, its geometry resists conventional self-configuration approaches, which are essential to programming large meshes in the presence of fabrication error. Here, we present a configuration algorithm, related to the $2\ifmmode\times\else\texttimes\fi{}2$ block decomposition of a unitary matrix, that overcomes this limitation. Our proposed algorithm is robust to errors, requires no prior knowledge of the process variations, and relies only on external sources and detectors. We show that self-configuration using this technique reduces the effect of fabrication errors by the same quadratic factor observed in triangular meshes. This relaxes a significant limit to the size of multiport interferometers, removing a major roadblock to the scaling of optical quantum and machine-learning hardware.

John C. Shedd

B. Dubetsky

A new approach to the theory of atoms' interaction with chirped Raman pulses is developed. When the pulses have sufficiently close effective wave lengths, which are smaller than the atomic cloud size, equations for the family of the matrix elements of the atomic density matrix in the Wigner representation are derived. The solution, involving linear (in the pulse duration) phase corrections, is obtained for the rectangular pulse. The interferometric part of the atoms' excitation is calculated.

A. F. Boden