Master equations and quantum trajectories for squeezed wave packets

TL;DR

This paper develops a general input-output theory for narrowband squeezed wave-packet light, enabling analysis of matter-light interactions beyond the small correlation time approximation, including non-Markovian effects.

Contribution

It introduces a formalism for squeezed wave-packet modes that captures their statistics and shape, deriving input-output relations, master equations, and stochastic equations for detection scenarios.

Findings

Derived a hierarchy of equations for non-Markovian dynamics.

Showed effects on decay and resonance fluorescence of two-level atoms.

Provided a framework for analyzing squeezed light interactions beyond standard approximations.

Abstract

The interaction between matter and squeezed light has mostly been treated within the approximation that the field correlation time is small. Methods for treating squeezed light with more general correlations currently involve explicitly modeling the systems producing the light. We develop a general purpose input-output theory for a particular form of narrowband squeezed light -- a squeezed wave-packet mode -- that only cares about the statistics of the squeezed field and the shape of the wave packet. This formalism allows us to derive the input-output relations and the master equation. We also consider detecting the scattered field using photon counting and homodyne measurements which necessitates the derivation of the stochastic master equation. The non Markovian nature of the field manifests itself in the master equation as a coupled hierarchy of equations. We illustrate these with consequences for the decay and resonance fluorescence of two-level atoms in the presence of such fields.