On the Dynamics of a Quantum Coherent Feedback Network of Cavity-mediated Double Quantum Dot Qubits

The purpose of this paper is to present a comprehensive study of a coherent feedback network where the main component consists of two distant double quantum dot (DQD) qubits which are directly coupled to a cavity. This main component has recently been physically realized (van Woerkom et al., Microwave photon-mediated interactions between semiconductor qubits, Physical Review X, 8(4):041018, 2018). The feedback loop is closed by cascading this main component with a beamsplitter. The dynamics of this coherent feedback network is studied from three perspectives. First, an analytic form of the output single-photon state of the network driven by a single-photon state is derived. In contrast to the experimental observations made in the above paper where a laser is used as input, new interesting physical phenomena are revealed by means of single-photon input. Second, excitation probabilities of DQD qubits are computed when the network is driven by a single-photon input state. Finally, if the input is vacuum but one of the two DQD qubits is initialized in its excited state, the explicit expression of the steady-state joint system-field state is derived, which shows that the output single-photon field and the two DQD qubits can form an entangled state if the transition frequencies of two DQD qubits are equal. This analytical expression can be used to interpret experimental results in the existing literature.