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Physical Review A

Entangling optical and mechanical cavity modes in an optomechanical crystal nanobeam

Qizhi Cai, Boyu Fan, Yunru Fan, Guangwei Deng, You Wang, Hai‐Zhi Song, Guang‐Can Guo, Qiang Zhou

Published Aug 23, 2023• 8 citations
Publisher

Abstract

A scheme for the generation of steady-state entanglement between optical and mechanical cavity modes in an optomechanical crystal nanobeam is proposed. Based on finite element simulation and the quantum Langevin equation, we explore the evolution of entanglement with optomechanical properties in various device configurations, and demonstrate the ability of optimal entanglement generation in both blue and red detuned optical pumps. The intrinsic relationship between optomechanical cooperativity and entanglement is further clarified for depicting a clear physical picture of optomechanical interaction. Our work expands the understanding of macroscopic quantum mechanics and is an important step for developing novel quantum optomechanical devices.

DOI
10.1103/physreva.108.022419

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A scheme for the generation of steady-state entanglement between optical and mechanical cavity modes in an optomechanical crystal nanobeam is proposed. Based on finite element simulation and the quantum Langevin equation, we explore the evolution of entanglement with optomechanical properties in various device configurations, and demonstrate the ability of optimal entanglement generation in both blue and red detuned optical pumps. The intrinsic relationship between optomechanical cooperativity and entanglement is further clarified for depicting a clear physical picture of optomechanical interaction. Our work expands the understanding of macroscopic quantum mechanics and is an important step for developing novel quantum optomechanical devices.
Abstract Nano-optomechanical systems, capable of supporting enhanced light-matter interactions, have wide applications in studying quantum entanglement and quantum information processors. Yet, preparing optical telecom-band entanglement within a single optomechanical nanobeam remains blank. We propose and design a triply resonant optomechanical nanobeam to generate steady-state entangled propagating optical modes and present its quantum-enhanced performance for teleportation-based quantum state transfer under realistic conditions. Remarkably, the entanglement quantified by logarithmic negativity can obtain E N = 1. Furthermore, with structural imperfections induced by realistic fabrication processes considered, the device still shows great robustness. Together with quantum interfaces between mechanical motion and solid-state qubit processors, the proposed device potentially paves the way for versatile nodes in long-distance quantum networks.
We theoretically demonstrate genuine steady-state tripartite entanglement in a monolithic optomechanical nanobeam integrating one transverse electric (TE) and two transverse magnetic (TM) optical modes coupled to a single mechanical mode. The system achieves strong coupling rates of g1/2π≈6.99×105 Hz for the TE mode, and g2,3/2π≈5.92×104 Hz and 4.91×104 Hz for the TM modes, with a mechanical quality factor Qm≈2.15×109, ensuring thermal stability up to 350 mK. Our analysis reveals that while bipartite entanglement persists across various regimes, genuine tripartite entanglement requires strong coupling, confirming the optimal operating point of our design. Telecom-band compatibility at 1549 nm is achieved through width-dependent tuning. Using finite element simulations and quantum Langevin analysis, we identify parameter regimes where the three optical modes exhibit verifiable tripartite entanglement (Rτmin>0), stable under cryogenic conditions with milliwatt-level pump powers.
We present a detailed study of a double-cavity optomechanical system, focusing on the dynamics of the entanglement between the cavity and mechanical modes, as well as the entanglement between two cavity modes. The discussions are based on a complete quantum approach without the standard practice of fluctuation expansion. The entanglement evolutions for various combinations of two different drives, such as those of the same blue detuning, of the same red detuning, and one red detuning and one blue detuning, are investigated. The relation of the entanglement and the rate of photon hopping between two cavities is also discussed.
The outstanding progress in nanostructure fabrication and cooling technologies allows what was unthinkable a few decades ago: bringing single-mode mechanical vibrations to the quantum regime. The coupling between photon and phonon excitations is a natural source of nonclassical states of light and mechanical vibrations, and its study within the field of cavity optomechanics is developing lightning fast. Photonic crystal cavities are highly integrable architectures that have demonstrated the strongest optomechanical coupling to date and should therefore play a central role for such hybrid quantum-state engineering. In this context, we propose a realistic heralding protocol for the on-chip preparation of remotely entangled mechanical states, relying on the state-of-the-art optomechanical parameters of a silicon-based nanobeam structure. Pulsed sideband excitation of a Stokes process, combined with single-photon detection, allows the writing of a delocalized mechanical Bell state in the system, signatures of which can then be read out in the optical field. A measure of entanglement in this protocol is provided by the visibility of a characteristic quantum interference pattern in the emitted light.
Abstract We investigate the effect of a degenerate optical parametric amplifier (OPA) placed inside an optomechanical cavity on the steady-state entanglement of two cavity modes, which jointly interact with a mechanical resonator. Two cavity modes are, respectively, driven at the red and blue sideband associated with the mechanical resonator, which generates entanglement between them in the limit of resolved sideband. The OPA gives rise to single-mode squeezing of the cavity fields, which results in significant improvement of the two-mode entanglement. It is found that an optimal nonlinear gain of the OPA exists, depending on the system temperatures, which yields the maximum entanglement. The improvement is particularly remarkable for the system at cryogenic temperatures.
The ability to coherently control mechanical systems with optical fields has made great strides over the past decade, and now includes the use of photon counting techniques to detect the nonclassical nature of mechanical states. These techniques may soon be used to perform an optomechanical Bell test, hence highlighting the potential of cavity optomechanics for device-independent quantum information processing. Here, we propose a witness which reveals optomechanical entanglement without any constraint on the global detection efficiencies in a setup allowing one to test a Bell inequality. While our witness relies on a well-defined description and correct experimental calibration of the measurements, it does not need a detailed knowledge of the functioning of the optomechanical system. A feasibility study including dominant sources of noise and loss shows that it can readily be used to reveal optomechanical entanglement in present-day experiments with photonic crystal nanobeam resonators.