Monogamy of quantum steering in exciton--cavity optomechanical system

Abstract

In this work, we study a theoretical scheme to investigate the monogamy of quantum steering in a hybrid exciton--cavity optomechanical (EOM) system. Within the Gaussian-state formalism, we quantify the steerability among the exciton, photon, and mechanical modes in both the steady-state and dynamical regimes. We establish and verify CKW-type monogamy inequalities for Gaussian steering and demonstrate that the distribution of bipartite steering among the three modes can be controlled through the system parameters. We further examine the influence of thermal noise and temporal evolution on the steering properties and the corresponding monogamy relations. Our results show that increasing the temperature generally suppresses the strength of Gaussian steering and modifies the degree of steering sharing imposed by the CKW-type monogamy relations. In contrast, in the dynamical regime, the steerability can increase with evolution time over suitable temporal windows, indicating that the transient dynamics can be exploited to enhance quantum correlations. These results highlight the potential of hybrid exciton--optomechanical platforms for controllable quantum correlations and provide a promising route toward the generation and manipulation of multipartite quantum resources.

The paper examines how Gaussian quantum steering is distributed among exciton, cavity-photon, and mechanical modes in a driven hybrid optomechanical system, focusing on thermal effects, transient evolution, and CKW-type monogamy relations. The model combines a linear exciton–photon interaction with radiation-pressure coupling between the cavity and a mechanical oscillator. Under strong coherent driving, the quantum Langevin equations are linearized around classical steady-state amplitudes. Steady-state and time-dependent covariance matrices are then obtained using a Lyapunov equation. Directional Gaussian steerability is calculated from symplectic eigenvalues of conditional covariance matrices, and previously formulated monogamy inequalities are checked numerically: $\mathcal G^{c\to ab}\geq\mathcal G^{c\to a}+\mathcal G^{c\to b}$ and the corresponding inequality for joint steering of one mode. The simulations use a mechanical frequency of $20\,\mathrm{GHz}$, mechanical damping of $1\,\mathrm{MHz}$, cavity and exciton decay rates of $1\,\mathrm{GHz}$ and $100\,\mathrm{MHz}$, and exciton–photon coupling of $0.9\,\mathrm{GHz}$. At opposite exciton and cavity detunings matched to the mechanical frequency, increasing temperature suppresses steering. Collective steering persists over a wider temperature range than the corresponding pairwise steering, while photon-to-exciton steering is negligible for the selected parameters. Transient steering is reported to appear after approximately $5\,\mathrm{ns}$. The examined collective and pairwise quantities satisfy the monogamy inequalities. The analysis is restricted to the linearized Gaussian description and selected numerical parameters; it does not establish a new general monogamy theorem or provide an experimental demonstration.