Quantum caustics in resonance fluorescence trajectories

TL;DR

This paper investigates quantum trajectories in resonance fluorescence using phase-sensitive detection, revealing caustics where multiple paths converge, supported by experimental data and theoretical analysis.

Contribution

It introduces a method to observe and analyze quantum caustics in fluorescence trajectories, linking experimental results with stochastic path integral theory.

Findings

Multiple most likely paths observed experimentally.

Quantitative agreement between theory and experiment.

Identification of caustics in quantum trajectories.

Abstract

We employ phase-sensitive amplification to perform homodyne detection of the resonance fluorescence from a driven superconducting artificial atom. Entanglement between the emitter and its fluorescence allows us to track the individual quantum state trajectories of the emitter conditioned on the outcomes of the field measurements. We analyze the ensemble properties of these trajectories by considering trajectories that connect specific initial and final states. By applying the stochastic path integral formalism, we calculate equations-of-motion for the most likely path between two quantum states and compare these predicted paths to experimental data. Drawing on the mathematical similarity between the action formalism of the most likely quantum paths and ray optics we study the emergence of caustics in quantum trajectories---places where multiple extrema in the stochastic action occur. We observe such multiple most likely paths in experimental data and find these paths to be in reasonable quantitative agreement with theoretical calculations.