# Quantum jump statistics with a shifted jump operator in a chiral waveguide

## TL;DR

This paper explores how shifting the jump operator in a master equation affects photon counting statistics in a waveguide-QED system, revealing a range of quantum statistical behaviors beyond the traditional sub-Poissonian regime.

## Contribution

It introduces a novel approach using shifted jump operators in master equations, demonstrating their impact on photon statistics in a chiral waveguide setup.

## Key findings

- Shifted jump operators can produce sub-Poissonian, Poissonian, or super-Poissonian statistics.
- The Mandel Q parameter is used to characterize the photon statistics.
- Large deviation theory is employed to compute long-time counting statistics.

## Abstract

Resonance fluorescence, consisting of light emission from an atom driven by a classical oscillating field, is well-known to yield a sub-Poissonian photon counting statistics. This occurs when only emitted light is detected, which corresponds to a master equation (ME) unraveling in terms of the canonical jump operator describing spontaneous decay. Formally, an alternative ME unraveling is possible in terms of a shifted jump operator. We show that this shift can result in sub-Poissonian, Poissonian or super-Poissonian quantum jump statistics. This is shown in terms of the Mandel Q parameter in the limit of long counting times, which is computed through large deviation theory. We present a waveguide-QED setup, comprising a chiral waveguide coupled to a driven atom, where photon counting is described by the considered class of shifted jump operators.