# On the scalability of parametric down-conversion for generating higher-order Fock states

## TL;DR

This paper analyzes the fundamental limitations and trade-offs in using spontaneous parametric down-conversion (SPDC) for generating higher-order Fock states, providing a framework for assessing performance considering losses and multimode effects.

## Contribution

It introduces a theoretical framework for evaluating state fidelity and generation probability in SPDC, and experimentally demonstrates heralded Fock states up to four photons.

## Key findings

- Identifies fundamental limits of SPDC for higher-order Fock state generation.
- Shows a trade-off between fidelity and generation rate.
- Demonstrates heralded Fock states up to |4⟩ experimentally.

## Abstract

Spontaneous parametric down-conversion (SPDC) is the most widely-used method to generate higher-order Fock states ($n\geq 2$). Yet, a consistent performance analysis from fundamental principles is missing. Here we address this problem by introducing a framework for state fidelity and generation probability under the consideration of losses and multimode emission. With this analysis we show the fundamental limitations of this process as well as a trade-off between state fidelity and generation rate intrinsic to the probabilistic nature of the process. This identifies the parameter space for which SPDC is useful when generating higher-order Fock states for quantum applications. We experimentally investigate the strong pump regime of SPDC and demonstrate heralded Fock states up to $\lvert n\rangle =4$.