# The quantum and classical field scattered on a single two-level system

## TL;DR

This paper compares quantum and classical scattering on a two-level system using superconducting qubits, revealing subtle differences and optimal conditions for mimicking quantum superpositions with classical pulses.

## Contribution

It introduces a cascaded waveguide-QED setup to analyze and compare quantum and classical scattering, identifying conditions where classical pulses approximate quantum superpositions.

## Key findings

- Discrepancy observed between quantum and classical scattering cases.
- Optimal classical pulse amplitude $\\Omega_{*}$ minimizes differences.
- Differences are small but practically unmeasurable.

## Abstract

In many problems, the scattering amplitudes of weak coherent pulse are almost equivalent to the ones of single propagating photon. We thoroughly compare the scattering of: (i) short microwave coherent pulse from rf generator and (ii) vacuum-photon coherent superposition from the two-level Emitter, both directed to a single two-level system (the Probe). To do that, we use two superconducting qubits to implement Emitter and Probe, both strongly coupled to the same waveguide. However, with the use of magnetic circulator we couple the field from Emitter to the Probe without reverse backaction, thereby working with a cascaded atomic system implemented in waveguide-QED setup. By measuring the dynamics of scattered field, we find a certain discrepancy between two cases, confirmed by analytical and numerical study. Particularly, we find the optimal amplitude $\Omega_{*}$ of classical pulse mimicking the superposition from Emitter, for which the difference becomes very small (but non-vanishing), and is almost unavailable to measure in practice.