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Physica Scripta

Asymmetric Markovian control of quantum entanglement

Abolghasem Daeichian, Mehdi Mirzaee

Published Feb 2, 2023• 2 citations
Publisher

Abstract

Abstract Expanding utilization of entangled states in quantum technologies, such as quantum information, is a motivating force of developing new methods for enhancement and stabilization of quantum entanglement. This study focuses on using asymmetric lawsto control the entangled states of a quantum systemconsistingof two atoms, each confined in a cavity.The effect of asymmetry laws has been explored in three different scenarios. First, the effect of an asymmetric drive Hamiltonian on a closed quantum system, in which neither the cavity nor the atoms exhibit losses, is studied. Here, the eigenvalues and eigenstates of the total system Hamiltonian have been obtained and the time evolution of the system state has been derived. Also, the fidelity of the system in terms of the asymmetric drive Hamiltonian has been derived analytically. In the second scenario, the stationary solution of an open quantum system, which includes losses in a master equation approach, is derived and the concurrence is studied in terms of the asymmetric drive Hamiltonian and coupling constant. The last scenario is devoted to applying feedback rulesto an open quantum system where some heuristic feedback control laws have been proposed. The simulation results show the concurrence boosting in a larger range of driving field and feedback strength when applying the introduced feedback rules.

DOI
10.1088/1402-4896/acb85d

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Abstract Expanding utilization of entangled states in quantum technologies, such as quantum information, is a motivating force of developing new methods for enhancement and stabilization of quantum entanglement. This study focuses on using asymmetric lawsto control the entangled states of a quantum systemconsistingof two atoms, each confined in a cavity.The effect of asymmetry laws has been explored in three different scenarios. First, the effect of an asymmetric drive Hamiltonian on a closed quantum system, in which neither the cavity nor the atoms exhibit losses, is studied. Here, the eigenvalues and eigenstates of the total system Hamiltonian have been obtained and the time evolution of the system state has been derived. Also, the fidelity of the system in terms of the asymmetric drive Hamiltonian has been derived analytically. In the second scenario, the stationary solution of an open quantum system, which includes losses in a master equation approach, is derived and the concurrence is studied in terms of the asymmetric drive Hamiltonian and coupling constant. The last scenario is devoted to applying feedback rulesto an open quantum system where some heuristic feedback control laws have been proposed. The simulation results show the concurrence boosting in a larger range of driving field and feedback strength when applying the introduced feedback rules.
We propose a scheme to enhance entanglement and asymmetric steering between two mechanical oscillators in an optomechanical system with coherent feedback control. In the system, an optical cavity interacts with two mechanical oscillators and an auxiliary cavity whose output field is fed back into the input port of the optical cavity via a feedback loop. Due to the coherence between the auxiliary cavity and feedback, we derive the effective decay rate and a nonzero frequency shift of the optical cavity. Consequently, the induced beam-splitter-type and parametric-type interactions between the two mechanical oscillators are modulated, which leads to the enhancement of entanglement and the generation of asymmetric steering even if the two mechanical oscillators possess identical decoherence properties. And the direction of asymmetric steering can be controlled by tuning the jumping phase between two cavities and optimizing the ratio of drive asymmetry. In contrast to the method of adding losses or noises to one subsystem at the cost of reducing steerability, this scheme provides an active way to achieve enhanced asymmetric steering. Furthermore, the steady-state and dynamical entanglement and asymmetric steering can be generated in the unresolved-sideband regime, which is friendly for experimental implementation.
The weak-coupled two-level open quantum system described by non-Markovian time-convolution-less master equation is investigated in this paper. Based on the Lyapunov stability theorem, the system control laws used to transfer state are designed. The characteristics of the purity changes in the non-Markovian open quantum systems are studied. The effectiveness of the control system is ensured by adjusting the parameters of control laws. Three simulation experiments are implemented under the Matlab environment, they are the states transfer from the eigenstate to the superposition state, from the superposition state to the superposition state, and from the mixed state to the superposition state, respectively. Numerical experimental results show that the target state can be reached from different initial states under the action of the control laws designed, and demonstrate the effectiveness of quantum Lyapunov control method proposed.
The problem of optimal control of non-Markovian open quantum system via weak measurement is presented. Based on the non-Markovian master equation, we evaluate exactly the non-Markovian effect on the dynamics of the system of interest interacting with a dissipative reservoir. We find that the non-Markovian reservoir has dual effects on the system: dissipation and backaction. The dissipation exhausts the coherence of the quantum system, whereas the backaction revives it. Moreover, we design the control Hamiltonian with the control laws attained by the stochastic optimal control and the corresponding optimal principle. At last, we considered the exact decoherence dynamics of a qubit in a dissipative reservoir composed of harmonic oscillators, and demonstrated the effectiveness of our optimal control strategy. Simulation results showed that the coherence will completely lost in the absence of control neither in non-Markovian nor Markovian system. However, the optimal feedback control steers it to a stationary stochastic process which fluctuates around the target. In this case the decoherence can be controlled effectively, which indicates that the engineered artificial reservoirs with optimal feedback control may be designed to protect the quantum coherence in quantum information and quantum computation.
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.
We study a hybrid quantum open system consisting of two interacting subsystems formed by one two-level atom (qubit) and one three-level atom (qutrit). The quantum open system is coupled to an external environment (cavity) via the qubit-cavity interaction. It is found that the feedback control on different parts of the system (qubit or qutrit) gives dramatically different asymptotical behaviors of the open system dynamics. We show that the local feedback control mechanism acting on the qutrit subsystem is superior than that on the qubit in the sense of improving the entanglement. Particularly, the qutrit-control scheme may result in an entangled steady state, depending on the initial state.
A system, comprised of a qubit pair coupled to a common cavity, is studied with the aim of establishing qubit entanglement. This study is the sequel of the paper Phys. Rev. A 111, 043705 (2025), where similar model was investigated for an initially vacuum cavity. In the present manuscript the cavity with finite initial occupancy is considered and the effect of asymmetric qubit cavity couplings is investigated. For a closed system scenario, the ratio of the qubit-cavity couplings shows a threshold beyond which no maximally-entangled qubit state is available. The threshold value is shown to depend on the excitation level of the cavity. For a driven-dissipative case steady state entanglement is shown to depend non-monotonically on the qubit drive. Intricate interplay of drive, dissipation, and coupling asymmetry is shown to be pivotal for steady-state entanglement generation.