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Optics Express

Macroscopic entanglement in optomechanical system induced by non-Markovian environment

Xinyu Zhao

Published Sep 25, 2019• 25 citations
Publisher

Abstract

In this paper, the non-Markovian dynamics of an optomechanical system is analyzed by using the non-Markovian quantum state diffusion (NMQSD) method. An exact solution is obtained for the system composed of a Fabry-Pérot (F-P) cavity with two movable mirrors without the linearization of the Hamiltonian. Based on the solution, we find that the memory effect of the non-Markovian environment can be used to generate macroscopic entanglement between two mirrors. In order to achieve the maximum entanglement generation, the non-Markovian properties of the environment have to be chosen carefully depending on the properties of the system. Then, we also show that the coherence (superposition) in the initial state may produce entanglement in the evolution. At last, we show the entanglement sudden death and revival significantly depend on the strength of the memory effect, and the entanglement revival can be only observed in non-Markovian case. Our treatment, as an example, paves a way to exactly solve a large category of optomechanical systems without the linearization of the Hamiltonian.

DOI
10.1364/oe.27.029082

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In this paper, the non-Markovian dynamics of an optomechanical system is analyzed by using the non-Markovian quantum state diffusion (NMQSD) method. An exact solution is obtained for the system composed of a Fabry-Pérot (F-P) cavity with two movable mirrors without the linearization of the Hamiltonian. Based on the solution, we find that the memory effect of the non-Markovian environment can be used to generate macroscopic entanglement between two mirrors. In order to achieve the maximum entanglement generation, the non-Markovian properties of the environment have to be chosen carefully depending on the properties of the system. Then, we also show that the coherence (superposition) in the initial state may produce entanglement in the evolution. At last, we show the entanglement sudden death and revival significantly depend on the strength of the memory effect, and the entanglement revival can be only observed in non-Markovian case. Our treatment, as an example, paves a way to exactly solve a large category of optomechanical systems without the linearization of the Hamiltonian.
We study optomechanical entanglement between an optical cavity field and a movable mirror coupled to a non-Markovian environment. The non-Markovian quantum-state diffusion approach and the non-Markovian master equation are shown to be useful in investigating entanglement generation between the cavity field and the movable mirror. The simple model presented in this paper demonstrates several interesting properties of optomechanical entanglement that are associated with environment memory effects. It is evident that the effective environment central frequency can be used to modulate the optomechanical entanglement. In addition, we show that the maximum entanglement may be achieved by properly choosing the effective detuning, which is significantly dependent on the strength of the memory effect of the environment.
Abstract In this paper, we analyze the macroscopic entanglement generation between two movable mirrors in an optomechanical system beyond the Markov approximation. We derive a non-Markovian master equation for the optomechanical system and analyze the entanglement generation based on the numerical simulation. It is found that the maximum entanglement can be achieved by utilizing both the optomechanical coupling and the non-Markovian properties of the bath. In particular, we show the contribution from the system-bath coupling has a positive impact only if the bath is non-Markovian. Besides, the symmetric properties of the optomechanical system as well as the initial state are crucial to the entanglement generation. The results presented in the paper illustrate that the impact of the non-Markovian bath is an important factor in the entanglement generation in the optomechanical system.
We investigate dynamics of an optomechanical system under the non-Markovian environment. In the weak optomechanical single-photon coupling regime, we provide an analytical approach fully taking into account the non-Markovian memory effects. When the cavity-bath coupling strength crosses a certain threshold, an oscillating memory state for the classical cavity field is formed. Due to the existence of the non-decay optical bound state, a nonequilibrium optomechanical thermal entanglement is preserved even without external driving laser. Our results provide a potential usage to generate and protect entanglement via non-Markovian environment.
We investigate the non-Markovian effects on the entanglement transfer to the distant non-interacting atom qubits, which are embedded in a coupled superconducting resonator. The master equation governing the dynamics of the system is derived by the non-Markovian quantum state diffusion (NMQSD) method. Based on the solution, we show that the memory effect of the environment can lead to higher entanglement revival and make the entanglement last for a longer time. That is to say, the non-Markovian environment can enhance the entanglement transfer. It is also found that the maximum entanglement transferred to distant atoms can be modified by appropriately selecting the frequency of the modulated inter-cavity coupling. Moreover, with the initial anti-correlated state, the entanglement between the cavity fields can be almost completely transferred to the separated atoms. Lastly, we show that the memory effect has a significant impact on the generation of entanglement from the initial non-entangled states.
We investigate qubit entanglement dynamics in a two-qubit cavity system with stochastically fluctuating coupling strength, comparing white noise (Markovian) and Ornstein-Uhlenbeck noise (non-Markovian) processes. We analytically solve the system dynamics for both Fock and coherent cavity states and systematically characterize how initial qubit configurations affect entanglement generation and preservation. Our results reveal distinct dynamical regimes: in the Fock-state cavity, initial states in the single-excitation subspace generate robust qubit entanglement in decoherence-free subspaces, while initially entangled states in the double-excitation subspace exhibit inevitable decay without protective symmetries. For coherent cavities, we identify a critical photon-number threshold in the intermediate coherent-state amplitude regime where dynamics transition from low-frequency to high-frequency entanglement oscillations, while universal entanglement loss occurs at large amplitudes. Remarkable resilience against entanglement sudden death emerges under strong non-Markovian noise with long correlation times, where repeated revivals occur. These findings establish cavity photon statistics and environmental memory time as key control parameters for engineering qubit entanglement dynamics in qubit-cavity systems, revealing how system-environment correlations govern quantum information preservation.
The piezoelectric optomechanical devices supply a promising experimental platform to realize the coherent and effective control and measurement of optical circuits working in Terahertz (THz) frequencies via superconducting electron devices typically working in Radio (MHz) frequencies. However, quantum fluctuations are unavoidable when the size of mechanical oscillators enter into the nanoscale. The consequences of the noisy environment are still challenging due to the lack of analytical tools. In this paper, a semi-classical and full-quantum model of piezoelectric optomechanical systems coupled to a noisy bosonic quantum environment are introduced and solved in terms of quantum-state diffusion (QSD) trajectories in the non-Markovian regime. We show that the noisy environment, particularly the central frequency of the environment, can enhance the entanglement generation between optical cavities and LC circuits in some parameter regimes. Moreover, we observe the critical points in the coefficient functions, which can lead the different behaviors in the system. Besides, we also witness the entanglement transfers between macroscopic objects due to the memory effect of the environment. Our work can be applied in the fields of electric/ optical switches, and long-distance distribution in a large-scale quantum network.