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.
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.
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 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.
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 purpose of this article is to study two-photon dynamics induced by the coherent feedback control of a cavity quantum electrodynamics (cavity-QED) system coupled to a waveguide. In this setup, the two-level system in the cavity can work as a photon source, and the photon emitted into the waveguide can reinteract with the cavity-QED system many times after the transmission and reflection in the waveguide, during which the feedback can tune the number of the photons in and out of the cavity. We analyze the dynamics of two-photon processes in this coherent feedback network in two scenarios: the continuous mode coupling scheme and the discrete periodic mode coupling scheme between the waveguide and cavity. The difference of these coupling schemes is due to their relative scales and the number of semitransparent mirrors for coupling. Specifically, in the continuous mode coupling scheme, the generation of two-photon states is influenced by the length of the feedback loop by the waveguide and the coupling strength between the waveguide and the cavity-QED system. By tuning the length of the waveguide and the coupling strength, we are able to generate two-photon states efficiently. In the discrete periodic mode coupling scheme, the Rabi oscillation in the cavity can be stabilized and there are no notable two-photon states in the waveguide.
This thesis discusses the dynamics of quantum-optical systems located in complex, non-markovian photonic environments, using numerical simulations as well as analytical derivations. The main focus lies on time-delayed quantum-coherent feedback effects of the Pyragas type, in analogy to effects well-known in classical physics. Time-delayed feedback is treated as a specific kind of a non-markovian environment. Additionally, the control of qubit entanglement in optical cavities is studied. The thesis consists of three main parts: After an overview of the important concepts of quantum optics, advanced methods for the description and numerical treatment of time-delayed quantum-coherent feedback are presented. The main focus lies on the development of a pseudomode-based approach, which describes time-delayed feedback as the coupling to a complex network of lossy harmonic oscillators. Additionally, further methods for numerical simplification are presented, in particular nonlinear expectation value dynamics for the treatment of arbitrary non-markovian reservoirs, as well as the use of input-output theory for time-delayed feedback. In the second part, applications of time-delayed feedback to control quantum statistics are discussed. First it is demonstrated that time-delayed feedback can be used to create and sustain entanglement between coupled qubits. This approach will then be extended to larger networks of qubits. Afterwards, feedback control is applied to nonlinear quantum-optical systems: It is shown how to use it for the stabilization of Fock states in a cavity containing a Kerr medium, and this analysis is expanded to a cavity containing a two-level system. Furthermore, it is shown how time-delayed feedback can be used to control and enhance the entanglement of photons emitted in a biexciton cascade. In the third and last part, the non-equilibrium dynamics of qubits coupled to a photonic environment consisting of high-Q cavities subject to periodic driving are discussed. First, the connection between bistability and entanglement in a cavity containing two qubits is analyzed. Next a setup of two coupled cavities, containing a qubit each, is examined. The influence of a third cavity in between the two other cavities, simulating a delay line, is analyzed. Furthermore, a protocol is developed on how to overcome dephasing between the two qubits, using a resonant Raman scattering process. It is shown that this protocol can create and sustain high values of entanglement, and is ready to be extended to systems of more than two qubits.
Quantum Coherent Feedback Control of an N-Level Atom With Multiple Excitations
The purpose of this article is to study the dynamics of a quantum coherent feedback network, where anN-level atom is coupled with a cavity and the cavity is also coupled with a single or multiple parallel waveguides. When the atom is initialized at the highest energy level, it can emit multiple photons into the cavity, and the photons can be further transmitted to the waveguides and reinteract with the cavity quantum electrodynamics (cavity-QED) system. The transmission of photons in the waveguide can construct a feedback channel with a delay determined by the length of the waveguide. We model the dynamics of the atomic and photonic states of the cavity-QED system as a linear control system with delay. By tuning the control parameters such as the coupling strengths among the atom, cavity and waveguide, the eigenstates of the quantum system can be exponentially stable or unstable, and the exponential stability of the linear quantum control system with delay is related with the generation of single- and multiphoton states. Besides, when the cavity-QED system is coupled with multiple parallel waveguides, the emitted photons oscillate among different waveguides and the stability of quantum states is influenced by the feedback loop length and coupling strengths among waveguides.