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arXiv:1803.05630 · Automatica

On the dynamics of two photons interacting with a two-qubit coherent feedback network

Guofeng Zhang, Yu Pan

Published Apr 7, 2020• 15 citations
arXivHTMLPDF
DOI
10.1016/j.automatica.2020.108978

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The purpose of this paper is to study the dynamics of a quantum coherent feedback network composed of two two-level systems (qubits) driven by two counter-propagating photons. The coherent feedback network is a marginally stable system, and the spectral entanglement of photons could be enhanced as a consequence of the continuing two-photon interaction inside the feedback loop. By means of quantum stochastic calculus and the input-output framework, the analytic form of the steady-state output field states are derived in the Heisenberg picture for the first time. Based on the analytic form, significant enhancement of photon-photon interaction can be observed. In particular, we demonstrate that the famous Hong-Ou-Mandel effect can be created using this coherent feedback structure. The proposed framework is also applicable in the single-photon scenario.
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 based on waveguide quantum electrodynamics plays important roles in quantum devices design and quantum information processing. In this paper, we study the coherent dynamics of the quantum network composed of two separated resonators coupling to a waveguide. Using the dynamical feedback equation in Markovian regime, we obtain the analytical solutions to the output states for the two photons incident from the same or different directions of the waveguide. The two- photon scattering properties are analyzed based on the analytical expressions. It is found that the output states of the two photons can be controlled well by the phase induced by the single photon propagating between the two separated resonators. The results given in this paper are helpful in designing quantum devices at few-photon level.