Scattering into one-dimensional waveguides from a coherently-driven quantum-optical system

TL;DR

This paper introduces a new computational framework for analyzing photon scattering in one-dimensional waveguides, especially with energy-nonconserving Hamiltonians and coherent drives, enabling detailed characterization of quantum optical systems.

Contribution

The authors develop a discretized time-based method to accurately compute photon scattering and entanglement in quantum optical systems with nonconserving energy Hamiltonians, overcoming previous singularity issues.

Findings

Provides analytical solutions for two-level systems with short laser pulses.

Offers numerically exact solutions for SPDC and SFWM sources.

Demonstrates the method's applicability to small photon number scattering scenarios.

Abstract

We develop a new computational tool and framework for characterizing the scattering of photons by energy-nonconserving Hamiltonians into unidirectional (chiral) waveguides, for example, with coherent pulsed excitation. The temporal waveguide modes are a natural basis for characterizing scattering in quantum optics, and afford a powerful technique based on a coarse discretization of time. This overcomes limitations imposed by singularities in the waveguide-system coupling. Moreover, the integrated discretized equations can be faithfully converted to a continuous-time result by taking the appropriate limit. This approach provides a complete solution to the scattered photon field in the waveguide, and can also be used to track system-waveguide entanglement during evolution. We further develop a direct connection between quantum measurement theory and evolution of the scattered field, demonstrating the correspondence between quantum trajectories and the scattered photon state. Our method is most applicable when the number of photons scattered is known to be small, i.e. for a single-photon or photon-pair source. We illustrate two examples: analytical solutions for short laser pulses scattering off a two-level system and numerically exact solutions for short laser pulses scattering off a spontaneous parametric downconversion (SPDC) or spontaneous four-wave mixing (SFWM) source. Finally, we note that our technique can easily be extended to systems with multiple ground states and generalized scattering problems with both finite photon number input and coherent state drive, potentially enhancing the understanding of, e.g., light-matter entanglement and photon phase gates.