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International Journal of Theoretical Physics

Observation of Non-Hermitian Quantum Correlation Criterion in Mesoscopic Optomechanical System

Wenlin Li, Feng‐Yang Zhang, Chong Li, He‐Shan Song

Published Nov 12, 2015• 7 citations
Publisher
DOI
10.1007/s10773-015-2849-y

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Multimode cavity optomechanical systems allow light to couple otherwise non-interacting mechanical resonators, enabling non-Hermitian phenomena such as exceptional points, where eigenfrequencies and eigenvectors of coupled modes coalesce. Accessing an exceptional point and its nearby parameter space is a first step towards chiral mode dynamics and topological state transfer. Diamond optomechanical devices support strong coherent optomechanical coupling required to tune resonances to an exceptional point, as well as strain-coupling to spin-defects for hybrid quantum technologies, but have not yet been used for multimode non-Hermitian physics. Here we tune to an exceptional point in a diamond optomechanical crystal, which uses structural symmetry breaking to produce two high-frequency mechanical resonances coupled to an optical cavity. The exceptional point is reached within a stable operating window below the phonon-lasing threshold, and we observe asymmetric redistribution of optomechanical damping and anti-damping between hybridized modes. These results establish diamond optomechanical crystals as a platform for non-Hermitian optomechanics, opening routes to topological mechanical dynamics in hybrid spin-phonon interfaces.
Higher-order exceptional points (EPs) in non-Hermitian systems have attracted great interest due to their advantages in sensitive enhancement and distinct topological features. However, realization of such EPs is still a challenge because more fine-tuning parameters are generically required in quantum systems, compared to the second-order EP (EP2). Here, we propose a non-Hermitian three-mode optomechanical system in the blue-sideband regime for predicting the third-order EP (EP3). By deriving the pseudo-Hermitian condition for the proposed system, one cavity with loss and the other with gain must be required. Then we show that EP3 or EP2 can be observed when the mechanical resonator (MR) is neutral, loss, or gain. For the neutral MR, we find that two degenerate or two nondegenerate EP3s can be predicted by tuning system parameters in the parameter space, while four nondegenerate EP2s can be observed when the system parameters deviate from EP3s, which is distinguished from the previous study in the red-detuned optomechanical system. For the gain (loss) MR, we find that only two degenerate EP3s or EP2s can be predicted by tuning enhanced coupling strength. Our proposal provides a potential way to predict higher-order EPs or multiple EP2s and study multimode quantum squeezing around EPs using blue-detuned non-Hermitian optomechanical systems.
Abstract In this work, we examine the robust continuous variable quantum correlation by analyzing two coupled optomechanical systems. Under the linearization approximation, the steady state correlation is quantified through correlation function of two non-Hermitian operators and we find that quantum correlation is always existence between two optical fields, two-oscillators and optical field-oscillator. Unlike the discrete variable system, we show quantum correlation in our model seems to be independent without any close transfer relationship. We further emphasize the influence of cavity-cavity coupling parameter on the amount of quantum correlations.
We investigate how the exceptional-point structure of a dissipative cavity optomechanical system is inherited by experimentally accessible dynamical, spectral, and quantum-statistical observables. At optical-mechanical resonance, the effective non-Hermitian first-moment dynamics exhibits a second-order exceptional point, where two eigenvalues and their eigenvectors coalesce and the eigenvalue splitting follows the characteristic square-root dependence on perturbations. We show that the same square-root feature also governs transient photon and phonon populations, first-order coherence, spectral poles, and second-order intensity correlations. Below the exceptional point, the dynamics is non-oscillatory, whereas above it damped oscillations emerge together with frequency splitting of the spectral poles. At the exceptional point, the Jordan-block structure produces polynomial-exponential relaxation and a second-order spectral pole. Using the quantum regression theorem and Gaussian moment factorization, we further show that the stationary fluctuations satisfy the Siegert relation linking first- and second-order correlations. Although the zero-delay autocorrelations retain their thermal value, the finite-delay intensity correlations exhibit clear exceptional point signatures. This finding connects non-Hermitian mode coalescence with measurable dynamical and correlation observables in cavity optomechanics.