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Modern Physics Letters A

Study of collective steering behavior in a double cavity optomechanical system

Jamila Hmouch, Noureddine Benrass, Abdelkader Hidki, Mostafa Nassik

Published Sep 24, 2025• 0 citations
Publisher

Abstract

In this paper, we theoretically investigate, in a double cavity system, collective steering, between two mechanical modes and an optical mode, as well as between two optical modes and a mechanical mode. We explore the behavior of collective steering in terms of squeezing light, phonon tunneling force and photon hopping strength. We thus found the optimal choice for the considered parameters to improve collective steering irreducible to individual steering. In parallel, the monogamy of steering was demonstrated via the CKW-type monogamy inequalities. In addition, the study of collective steering behaviors indicates the conditions under which each considered tripartite state generates one-way and two-way steering.

DOI
10.1142/s021773232550169x

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In this paper, we theoretically investigate, in a double cavity system, collective steering, between two mechanical modes and an optical mode, as well as between two optical modes and a mechanical mode. We explore the behavior of collective steering in terms of squeezing light, phonon tunneling force and photon hopping strength. We thus found the optimal choice for the considered parameters to improve collective steering irreducible to individual steering. In parallel, the monogamy of steering was demonstrated via the CKW-type monogamy inequalities. In addition, the study of collective steering behaviors indicates the conditions under which each considered tripartite state generates one-way and two-way steering.
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.
Quantum steering plays a key role for quantum technologies, such as one-way quantum computation and quantum communication. Here, we consider a vector cavity optomechanical scheme to create quantum steering between two orthogonal polarized lights and a mechanical vibration, where cavity modes are driven by short laser pulses. By controlling the polarization behavior of a light field, we not only manipulate the steering of the vibration via polarized light, but also reversibly switch between ordinary tripartite steering and collective steering. In addition, we find that bipartite steering is more sensitive to thermal noise than tripartite steering. As a result, collective steering can be achieved within a larger parameter range. Controllable quantum steering with such a vectorial device may provide effective resources to build up steered networks.
Conditions for experimental detection of asymmetric one-way quantum steering in a three-mode optomechanical system are examined. We consider cases of collective steering in which two modes collectively interact with the third mode, and the case of separate modes steering in which two mutually independent modes interact with the third mode. We find that the occurrence of both collective and separate modes quantum steering results not from an asymmetry between thermal noise of the modes, as it has been realized in linear optics systems, but from an asymmetry between the damping rates of the modes. We show the requirement that the modes are damped with different rates to be the necessary and sufficient condition for collective steering. In the case of separate modes, we find that apart from unequal damping rates, an additional condition is required that the modes are coupled to the third mode with unequal strengths. Thus, the generation of quantum steering between separate modes is more restrictive to the parameters than the collective steering. Determination of conditions for experimental detection of one-way steering in multi-mode system could give a new stimulus to develop secure directional communication networks.
Abstract In this work, we discuss the monogamy property of quantum correlations (entanglement and steering) distributed in a cavity-free optomechanical system. In a tripartite pure Gaussian state, we verify the hierarchy of the studied quantum correlations. We investigate in detail the CKW-type monogamy inequalities, based on Gaussian Rényi-2 entropy entanglement, as well as, Gaussian steering. We quantify genuine tripartite entanglement by using the minimum residual Gaussian entanglement. In addition, we consider the minimum residual Gaussian steering as a quantifier of genuine tripartite steering. Our results indicate that, in the one-mode versus two-mode Gaussian state, the correlations hierarchy was respected; in the considered pure state, the monogamy of entanglement and steering distribution was proven and the studied genuine tripartite correlations have similar time evolution under the same conditions.
The theory of phase control of coherence, entanglement and quantum steering is developed for an optomechanical system composed of a single mode cavity containing a partially transmitting dielectric membrane and driven by short laser pulses. The membrane divides the cavity into two mutually coupled optomechanical cavities resulting in an effective three-mode closed loop system, two field modes of the two cavities and a mechanical mode representing the oscillating membrane. The closed loop in the coupling creates interfering channels which depend on the relative phase of the coupling strengths of the field modes to the mechanical mode. Populations and correlations of the output modes are calculated analytically and show several interesting phase dependent effects such as reversible population transfer from one field mode to the other, creation of collective modes, and induced coherence without induced emission. We find that these effects result from perfect mutual coherence between the field modes which is preserved even if one of the modes is not populated. The inseparability criterion for the output modes is also investigated and we find that entanglement may occur only between the field modes and the mechanical mode. We show that depending on the phase, the field modes can act on the mechanical mode collectively or individually resulting, respectively, in tripartite or bipartite entanglement. In addition, we examine the phase sensitivity of quantum steering of the mechanical mode by the field modes. Deterministic phase transfer of the steering from bipartite to collective is predicted and optimum steering corresponding to perfect EPR state can be achieved. These different types of quantum steering can be distinguished experimentally by measuring the coincidence rate between two detectors adjusted to collect photons of the output cavity modes. In particular, we find that the minima of the interference pattern of the coincidence rate signal the bipartite steering, while the maxima signal the collective steering.
We have investigated the dynamical entanglement and quantum steering in a pulsed hybrid opto-electro-mechanical system. Using the symmetric and asymmetric criteria, the possibilities of bipartite entanglement, one-way steering, two-way steering, and collective tripartite steering have been studied between different output modes. In addition, the influence of the squeezing parameter on the amount of tripartite steering measurement is also examined. The results show that a higher electro-mechanical coupling rate leads to stronger tripartite steering. The microwave cavity mode can enhance the output quantum steering and remotely steers the optical cavity. Thus, the slower mode can steer the faster mode. Such hybrid systems can serve as frequency converters between microwave and optical domains and can have a profound impact on building quantum networks of microwave-operated superconducting quantum computers.