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Physical Review A

Fourier multiport devices

Apostol Vourdas, Jacob Dunningham

Published Jan 13, 2005• 27 citations
Publisher

Abstract

A formalism for multiport devices is developed in which the creation and annihilation operators at the output are related with those at the input through a finite Fourier transform. By considering two specific inputs of number states and coherent states, we show how these devices can be used to produce multimode Schr\"odinger cat states and can be combined to create multipath interferometers. We introduce uncertainty relations for the distributions of particles in the input modes and the correlations between the output modes. These allow us to determine how the phase resolution of the output state scales with the number of ports and particles. This scaling is of fundamental interest for schemes that seek to use multipath interferometers for enhanced measurement precision.

DOI
10.1103/physreva.71.013809

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A formalism for multiport devices is developed in which the creation and annihilation operators at the output are related with those at the input through a finite Fourier transform. By considering two specific inputs of number states and coherent states, we show how these devices can be used to produce multimode Schr"odinger cat states and can be combined to create multipath interferometers. We introduce uncertainty relations for the distributions of particles in the input modes and the correlations between the output modes. These allow us to determine how the phase resolution of the output state scales with the number of ports and particles. This scaling is of fundamental interest for schemes that seek to use multipath interferometers for enhanced measurement precision.
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Integrated multi-port interferometers are the second step in programmable photonics. Initially conceived and designed to implement fixed linear optics unitary transformations between N input and N output ports to support mode transformations in quantum optics, the rapid development of this field and the possibility of applying these structures to other areas stimulated development of devices capable of supporting arbitrary linear transformations by suitable programming and surpassing use in square matrix transformations and unitary operators. This chapter reviews some basic concepts on unitary N×N matrices and then describes in detail the basic design principles and integrated optics implementations of triangular and rectangular designs for multi-port interferometers. It then considers more specific interferometer designs, which do not provide possible implementation of general linear transformations but are optimised for performing important operations, e.g. the Fourier transform. Lastly, it covers the linear universal component, which integrates both universal beam couplers and integrated multi-port interferometers.
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In this work, we investigate the generation of squeezed Schrödinger cat states in schemes based on photon-number-resolving measurements on multimode Gaussian states. We derive analytical expressions for the states generated in two- and three-mode schemes, as well as formulas for their fidelity with squeezed Schrödinger cat states. We analyze how the amplitude of the generated states scales with the number of detected particles. Furthermore, we derive an upper bound on the achievable generation fidelity and identify the conditions under which multimode schemes can enhance the quality of the generated states.