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Physics Letters A

Pairwise entanglement in a three-cavity optomechanical system

Abderrahim Lakhfif, Abdelkader Hidki, Jamal El Qars, Mostafa Nassik

Published Jun 8, 2022• 18 citations
Publisher
DOI
10.1016/j.physleta.2022.128247

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We theoretically investigate the generation of steady-state entanglement in a levitated optomechanical system with a cascade three-level atomic medium and a dielectric nanosphere. There are two cavity modes, driven by two external laser beams with different frequencies, which are responsible for trapping and cooling the nanosphere. Atoms prepared in coherent superposition are injected into the cavity to manipulate the optical fields and the effective optomechanical coupling. We show that the entanglement between the nanosphere and the cavity modes can be enhanced by selecting properly the initial population of the lower atomic level. In particular, when the atoms are prepared at that level, the corresponding optomechanical entanglement increases with the increase of the atom-field coupling strength. We also investigate in detail the influence of the effective cavity field detunings, the atomic detunings, the driving power, and the nanosphere's radius and found that there exist optimal values of the effective cavity field detuning and the driving power that maximize the optomechanical entanglement. By selecting the system's parameters properly, we further demonstrate the generation of genuine tripartite entanglement between three degrees of freedom in the system. The findings here may help flexible control of the steady-state entanglement in hybrid optomechanical systems.
Abstract We propose a model for controlling and enhancing the entanglement between the two cavity fields and mirror with a hybrid optomechanical system consisting of Λ-type three-level 85Rb atomic ensembles driven by two externally modulated laser fields. When one (another) cavity mode is driven at the red (blue) mechanical sideband and both cavity modes are blue-detuned by the mechanical frequency to the respective atomic resonant transitions, the dynamic coupling control of the cavity field and mirror can be realized by periodically modulating the amplitudes of the two incident laser fields. Compared to the unmodulated case, the periodic modulation of the laser fields in a cavity-optomechanical system embedded with a small number of atoms has the capability to enhance the entanglement between the two cavity fields and mirror. This scheme provides a new approach to the generation and control of entanglement in cavity-optomechanical systems.
Quantum entanglement not only plays an important role in the study of the fundamentals of quantum theory, but also is considered as a crucial resource in quantum information science. The generation of macroscopic entanglement involving multiple optical and mechanical modes is a desired task in cavity optomechanics. However, the dark-mode effect is a critical obstacle against the generation of quantum entanglement in multimode optomechanical systems consisting of multiple degenerate or near-degenerate mechanical modes coupled to a common cavity mode. Here we propose an auxiliary-cavity-mode method to enhance optomechanical entanglement in a multimode optomechanical system by breaking the dark-mode effect. We find that the introduction of the auxiliary cavity mode not only assists the entanglement creation between the cavity mode and the mechanical modes, but also improves the immunity of the optomechanical entanglement to the thermal excitations by about three orders of magnitude. We also study the optomechanical entanglement in the network-coupled optomechanical system consisting of two mechanical modes and two cavity modes. By analyzing the correspondence between the optomechanical entanglement and the dark-mode effect, we find that optomechanical entanglement can be largely enhanced once the dark mode is broken. In addition, we study the mechanical entanglement and find that it is negligibly small. We also present some discussions on the experimental implementation with a microwave optomechanical setup, on the relationship between the dark-mode-breaking mechanism and the center-of-mass and relative coordinates, and on the explanation of the important role of the dark-mode breaking in the enhancement of optomechanical entanglement. Our results pave the way towards the preparation of entangled optomechanical networks and noise-resistant quantum resources.