Modeling integrated frequency shifters and beam splitters

TL;DR

This paper introduces a flexible, composable methodology for designing frequency-mode beam splitters using coupled resonator arrays, advancing photonic quantum computing hardware with novel transfer matrix construction techniques.

Contribution

It presents a new methodology based on the SLH formalism for designing and analyzing frequency-mode beam splitters with coupled resonators, including a no-go theorem for certain configurations.

Findings

Developed a flexible transfer matrix construction method

Analyzed specific resonator-based devices like phase shifters and interferometers

Proved limitations on native generation of certain N-mode beam splitters

Abstract

Photonic quantum computing is a strong contender in the race to fault-tolerance. Recent proposals using qubits encoded in frequency modes promise a large reduction in hardware footprint, and have garnered much attention. In this encoding, linear optics, i.e., beam splitters and phase shifters, is necessarily not energy-conserving, and is costly to implement. In this work, we present designs of frequency-mode beam splitters based on modulated arrays of coupled resonators. We develop a methodology to construct their effective transfer matrices based on the SLH formalism for quantum input-output networks. Our methodology is flexible and highly composable, allowing us to define $N$-mode beam splitters either natively based on arrays of $N$-resonators of arbitrary connectivity or as networks of interconnected $l$-mode beam splitters, with $l<N$. We apply our methodology to analyze a two-resonator device, a frequency-domain phase shifter and a Mach-Zehnder interferometer obtained from composing these devices, a four-resonator device, and present a formal no-go theorem on the possibility of natively generating certain $N$-mode frequency-domain beam splitters with arrays of $N$-resonators.