Optimal two-photon excitation of bound states in non-Markovian waveguide QED

TL;DR

This paper investigates the maximum probability of exciting bound states in non-Markovian waveguide QED systems using two-photon states, providing theoretical limits and methods to optimize excitation with potential applications in quantum information processing.

Contribution

It introduces a scattering theory approach to determine upper bounds on two-photon excitation probabilities and constructs wave-packets for exciting superpositions of multiple bound states.

Findings

Upper limits on two-photon excitation probability derived

Optimal two-photon wave-packets identified for exciting bound states

Analysis of multi-emitter systems with bound state superpositions

Abstract

Bound states arise in waveguide QED systems with a strong frequency-dependence of the coupling between emitters and photonic modes. While exciting such bound-states with single photon wave-packets is not possible, photon-photon interactions mediated by the emitters can be used to excite them with two-photon states. In this letter, we use scattering theory to provide upper limits on this excitation probability for a general non-Markovian waveguide QED system and show that this limit can be reached by a two-photon wave-packet with vanishing uncertainty in the total photon energy. Furthermore, we also analyze multi-emitter waveguide QED systems with multiple bound states and provide a systematic construction of two-photon wave-packets that can excite a given superposition of these bound states. As specific examples, we study bound state trapping in waveguide QED systems with single and multiple emitters and a time-delayed feedback.