Heralding probability optimization for nonclassical light generated by photon counting measurements on multimode Gaussian states

TL;DR

This paper presents an efficient method to optimize heralding probability in nonclassical light generation using photon counting on multimode Gaussian states, enhancing quantum state preparation rates.

Contribution

It formulates heralding probability maximization as solving polynomial equations, enabling optimal configuration determination with bounds on squeezing incorporated.

Findings

The approach efficiently finds optimal configurations for heralding probability.

It can be extended to generate squeezed superpositions of Fock states.

The method applies to single-mode and two-mode Gaussian states with practical bounds.

Abstract

Generation of highly non-classical quantum states of light is essential for optical quantum information processing and quantum metrology. Given the lack of sufficiently strong nonlinear interactions between optical fields, the commonly employed optical quantum-state preparation schemes are conditional, based on nonlinearity induced by heralding photon number measurement on a part of a multimode squeezed Gaussian state. Development and optimization of such probabilistic quantum-state engineering schemes represents one of the central challenges in current quantum optics. As technology advances and experiments progress to detection of higher numbers of photons, the maximization of the heralding probability becomes essential to ensure sufficiently high state-preparation rates. Here, we show that for the conditional quantum state preparation schemes based on Gaussian states and photon number measurements the maximization of the heralding probability can be formulated as finding solution to a system of polynomial equations, which offers an efficient way to find the optimal configuration and allows us to apply techniques dedicated specifically to solving such systems of equations. Our approach can seamlessly incorporate bounds on the available single-mode quadrature squeezing, which is highly experimentally relevant. We mainly consider generation of finite superpositions of Fock states but show that the approach can be straightforwardly extended to generation of squeezed superpositions of Fock states. We focus on Gaussian states with vanishing coherent displacements, hence the conditionally generated states have well defined photon number parity. We illustrate our general methodology on examples of generation of single-mode and two-mode states with two heralding modes.