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Quantum Light Emission from Waveguide-QED Systems with a Time-Delayed Coherent Feedback

Gavin Crowder

Published Jan 14, 2026• 0 citations
Publisher

Abstract

To continue developing quantum technologies, such as quantum computing, quantum communication and quantum cryptography, we need reliable sources of quantum states of light. These quantum states of light can come in many forms; single photons, entangled pairs, bunched and anti-bunched light, all have uses in current quantum technologies, but for the best performance, this light must maintain its coherence. Time-delayed coherent feedback is a passive feedback method proposed for waveguide quantum electrodynamic systems to improve their performance and unlock new quantum optical phenomena. Additionally, due to its underlying non-Markovian dynamics, feedback is also an interesting theoretical problem to study. In this thesis, we use a quantum trajectory discretized waveguide (QTDW) model to simulate feedback dynamics and investigate its effects in a variety of applications. Originally proposed by Whalen in 2018, we develop the QTDW model beyond its initial implementation to now calculate quantum correlation functions, output spectra, waiting time distributions, and single photon source figures of merit. First, we present an explanation of quantum trajectory theory which is used to model the time dynamics in the QTDW approach, and discuss feedback in the linear regime to highlight the differences between Markovian and non-Markovian dynamics with coherent feedback. We next present nonlinear spectra and multi-photon effects from coherent feedback highlighting how the typical Mollow triplet is dressed by the feedback to create new resonances in the output field. This is followed by a collaborative theory and experiment work which observed our predicted non-Markovian signatures in the nonlinear output spectrum along with new non-Markovian phenomena in the linear regime. We then investigate how pulse-triggered single photon sources can be improved through the inclusion of a time-delayed coherent feedback, presenting the possible improvement to the performance figures of merit. Lastly, the modeling techniques developed for single photon sources with feedback are used to compare the performance of three new off-resonant driving techniques for on-demand single photon sources. These findings show time-delayed coherent feedback is an excellent degree of control to include in future waveguide quantum electrodynamic systems to unlock better performance and new phenomena in the system under investigation.

DOI
10.20381/ruor-31679

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To continue developing quantum technologies, such as quantum computing, quantum communication and quantum cryptography, we need reliable sources of quantum states of light. These quantum states of light can come in many forms; single photons, entangled pairs, bunched and anti-bunched light, all have uses in current quantum technologies, but for the best performance, this light must maintain its coherence. Time-delayed coherent feedback is a passive feedback method proposed for waveguide quantum electrodynamic systems to improve their performance and unlock new quantum optical phenomena. Additionally, due to its underlying non-Markovian dynamics, feedback is also an interesting theoretical problem to study. In this thesis, we use a quantum trajectory discretized waveguide (QTDW) model to simulate feedback dynamics and investigate its effects in a variety of applications. Originally proposed by Whalen in 2018, we develop the QTDW model beyond its initial implementation to now calculate quantum correlation functions, output spectra, waiting time distributions, and single photon source figures of merit. First, we present an explanation of quantum trajectory theory which is used to model the time dynamics in the QTDW approach, and discuss feedback in the linear regime to highlight the differences between Markovian and non-Markovian dynamics with coherent feedback. We next present nonlinear spectra and multi-photon effects from coherent feedback highlighting how the typical Mollow triplet is dressed by the feedback to create new resonances in the output field. This is followed by a collaborative theory and experiment work which observed our predicted non-Markovian signatures in the nonlinear output spectrum along with new non-Markovian phenomena in the linear regime. We then investigate how pulse-triggered single photon sources can be improved through the inclusion of a time-delayed coherent feedback, presenting the possible improvement to the performance figures of merit. Lastly, the modeling techniques developed for single photon sources with feedback are used to compare the performance of three new off-resonant driving techniques for on-demand single photon sources. These findings show time-delayed coherent feedback is an excellent degree of control to include in future waveguide quantum electrodynamic systems to unlock better performance and new phenomena in the system under investigation.
We study the nonlinear spectra and multiphoton correlation functions of a waveguide system coupled to a two-level system (including realistic dissipation channels) with a time-delayed coherent feedback. We compute these observables by extending a recent quantum trajectory discretized-waveguide (QTDW) approach which exploits quantum trajectory simulations and a collisional model for the waveguide to efficiently simulate the quantum dynamics. Following a description of the general technique, we show how to calculate the first- and second-order quantum correlation functions, in the presence of a coherent pumping field. With a short delay time, we show how feedback can be used to filter out the central peak of the Mollow triplet or switch the output between bunched and antibunched photons by proper choice of round trip phase. We further show how the loop length and round trip phase affect the zero-time second-order quantum correlation function, an indicator of bunching or antibunching. New resonances introduced through the feedback loop are also shown through their appearance in the incoherent output spectrum from the waveguide. We explain these results in the context of the waiting time distributions of the system output and individual trajectories, uniquely stochastic observables that are easily accessible with the QTDW model.
The emergence of integrated (or solid state) photonic systems, including quantum dots, waveguides, and cavities, has provided a base to harness quantum optic phenomena for use in current and future quantum technologies. These systems also provide opportunities for exploring fundamentally new regimes in quantum optics. In order to fully realize the potential of these systems, many figures of merit need to be improved, for example by increasing the stability and coherent lifetimes of these systems. Following the notable improvements using measurement-based feedback, time-delayed coherent optical feedback has been proposed as one such method of stabilizing and improving these systems. Furthermore, modelling coherent feedback itself presents an interesting fundamental problem due to its non-Markovian nature. In this thesis, we use quantum trajectory (QT) theory to derive two models for simulating cavity quantum electrodynamic (cavity-QED) systems with time-delayed coherent feedback. First, an explanation of QT theory is given and the related time discretized waveguide (TDW) model is derived. Next we present a model for feedback using the frequency modes of the waveguide and results are presented in the ``one photon in the loop" approximation. We demonstrate how the photon lifetime can be improved in typical cavity-QED with coherent feedback and we explore some nonlinear effects. We then expand the system to allow for two photons in the feedback loop which requires us to use the TDW model. Lastly, this new approach is used to model two two-level systems coupled via a waveguide and connected to a feedback loop. These findings have implications on improving quantum optic systems by creating a new degree of control, as well as for modelling non-Markovian features in quantum optics.
We describe an efficient approach to modeling cavity quantum electrodynamics (QED) with a time-delayed coherent feedback using quantum trajectory simulations. An analytical set of equations is derived to exploit the advantages of trajectories in the presence of the non-Markovian dynamics, where adjustments to the standard stochastic dynamics are discussed. In the weak excitation regime, we first verify that our approach recovers known results obtained with other simulation methods and demonstrate how a coherent feedback loop can increase the photon lifetime in typical cavity-QED systems. We also highlight the underlying stochastic dynamics. We then explore the nonlinear few-photon regime of cavity QED, under the restriction of at most one photon at a time in the feedback loop. In particular, we show how feedback affects the cavity photoluminescence (populations versus laser detuning) and describe how one must account for conditioning in the presence of feedback; specifically, the system observables must be conditioned on no photon detections at the feedback output channel occurring.
The model of light-matter interaction in quantum electrodynamics typically relies on the Markovian approximation, which assumes that the system's future evolution depends solely on its current state, effectively treating it as a ``memoryless" process. However, this approximation is not valid in scenarios when retardation effects are significant. These memory and retardation effects have the potential to improve existing quantum technologies (e.g., large-scale quantum networks, quantum information processing) and unlock new phenomena for future applications. In this work, we show theory and experiments of a time-delayed coherent feedback system using a transmon artificial atom (treated as a qubit) embedded in a superconducting circuit waveguide, in both linear and nonlinear excitation regimes. By using a feedback loop with a delay time comparable to the qubit relaxation time, pronounced non-Markovian effects appear in the dynamics of the qubit evolution. We also show how the resonance fluorescence spectrum, including elastic and inelastic scattering (such as the well-known Mollow triplet), can be significantly modified through the interaction between the qubit and feedback loop to show genuine non-Markovian and quantum nonlinear phenomena that cannot be explained with instantaneous coupling parameters. This work presents the first experimental report of Mollow triplets in the non-Markovian regime.
We present two different methods for modeling non-Markovian quantum light-matter interactions in waveguide QED systems, using matrix product states (MPSs) and a space-discretized waveguide (SDW) model.After describing the general theory and implementation of both approaches, we compare and contrast these methods directly on three topical problems of interest in waveguide-QED, including (i) a two-level system (TLS) coupled to an infinite (one-dimensional) waveguide, (ii) a TLS coupled to a terminated waveguide with a time-delayed coherent feedback, and (iii) two spatially separated TLSs coupled within an infinite waveguide.Both approaches are shown to efficiently describe multiphoton nonlinear dynamics in highly non-Markovian regimes, and we highlight the advantages and disadvantages of these methods for modeling waveguide QED interactions, including their implementation in PYTHON, computational run times, and ease of conceptual understanding.We explore both vacuum dynamics as well as regimes of strong optical pumping, where a weak excitation approximation cannot be applied.The MPS approach scales better when modeling multiphoton dynamics and long delay times and explicitly includes non-Markovian memory effects.In contrast, the SDW model accounts for non-Markovian effects through space discretization and solves Markovian equations of motion, yet rigorously includes the effects of retardation.The SDW model, based on an extension of recent collisional pictures in quantum optics, is solved through quantum trajectory techniques and can more easily add in additional dissipation processes, including off-chip decay and TLS pure dephasing.The impact of these processes is shown directly on feedback-induced population trapping and TLS entanglement between spatially separated TLSs.