Wigner spectrum and coherent feedback control of continuous-mode single-photon Fock states

TL;DR

This paper introduces the Wigner spectrum as a tool for analyzing continuous-mode single-photon Fock states, enabling simultaneous time-frequency analysis and improved insight into their properties, while also exploring coherent feedback control to shape photon pulses.

Contribution

It proposes the Wigner spectrum for analyzing single-photon states in both time and frequency domains, offering advantages over traditional methods, and investigates coherent feedback control for pulse shaping.

Findings

Wigner spectrum allows simultaneous time-frequency analysis of single-photon states.

The method can handle Dirac delta functions directly, providing richer information.

Coherent feedback control can manipulate photon pulse shapes effectively.

Abstract

Single photons are very useful resources in quantum information science. In real applications it is often required that the photons have a well-defined spectral (or equivalently temporal) modal structure. For example, a rising exponential pulse is able to fully excite a two-level atom while a Gaussian pulse cannot. This motivates the study of continuous-mode single-photon Fock states. Such states are characterized by a spectral (or temporal) pulse shape. In this paper we investigate the statistical property of continuous-mode single-photon Fock states. Instead of the commonly used normal ordering (Wick order), the tool we proposed is the Wigner spectrum. The Wigner spectrum has two advantages: 1) it allows to study continuous-mode single-photon Fock states in the time domain and frequency domain simultaneously; 2) because it can deal with the Dirac delta function directly, it has the potential to provide more information than the normal ordering where the Dirac delta function is always discarded. We also show how various control methods in particular coherent feedback control can be used to manipulate the pulse shapes of continuous-mode single-photon Fock states.