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Alexandria Engineering Journal

Conditions for experimental detection of one-way quantum steering in a three-mode optomechanical system

Lihui Sun, Jiadong Shi, Kaikai Zhang, Wen-ju Gu, Z. Ficek, Wenwen Yang

Published Mar 28, 2022• 4 citations
Publisher

Abstract

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.

DOI
10.1016/j.aej.2022.03.028

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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 We consider a three-mode system and show how steering correlations can be created between two modes of the system using the fast dissipation of the third mode. These correlations result in a directional form of entanglement, called quantum or Einstein–Podolsky–Rosen steering. We illustrate this on examples of the interactions among damped radiation modes in an optomechanical three-mode system. By assuming that one of the modes undergoes fast dissipation, we show that the coupling of that mode to one or two other modes of the system may result in one- or two-way quantum steering. Explicit analytical results are given for the steering parameters. We find that two modes coupled by the parametric-type interaction and damped with the same rates can be entangled but cannot exhibit quantum steering. When, in addition, one of the modes is coupled to a fast damped mode, steering correlations are created and the modes then exhibit one-way steering. The creation of the steering correlations is interpreted in the context of the variances of the quadrature components of the modes that the steering correlations result from an asymmetry in the variances of the quadrature components of the modes induced by the auxiliary mode. It is found that the fluctuations act directionally that quantum steering may occur only when the variance of the steering mode is larger that the variance of the steered mode. The scheme is shown to be quite robust against the thermal excitation of the modes if the fluctuations of the steering mode are larger than the fluctuations of the steered mode.
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.
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.
Einstein-Podolsky-Rosen (EPR) steering is a quantum nonlocal effect that characterizes the ability to remotely control quantum states of one system via local measurements on another distant system entangled with the controlled one. Entanglement swapping is an effective way to realize distant entanglement, which is useful for building quantum networks. Previous studies show that the presence of entanglement of subsystems in mixed states is merely necessary for achieving entanglement swapping. In this paper, we find that for Gaussian entanglement swapping with two pairs of entangled modes ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{j}$ and ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{b}}_{j}\phantom{\rule{4pt}{0ex}}(j=1,2)$, the existence of directional EPR steering from the modes ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{b}}_{j}$ under homodyne detection to the other modes ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{j}$ is a sufficient and necessary condition for achieving swapped entanglement between modes ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{1}$ and ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{2}$, and moreover this achievement is independent of the reverse steering from modes ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{j}$ to ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{b}}_{j}$. We further reveal that this is because the steering in that direction enables the amplitude and phase squeezing of the two composite modes of modes ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{1}$ and ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{2}$ via homodyne detection, which is necessary and sufficient for swapped entanglement. As a concrete example, we next investigate light-mechanical steering in a dispersively or dissipatively coupled optomechanical system, and we consider the generation of entanglement between two distant optomechanical oscillators via entanglement swapping by utilizing steering. It is interesting to find that even without the constraint that the cavity linewidth should be smaller than the mechanical frequency, robust mechanical entanglement can be obtained in the steady-state regime.
Multipartite quantum entanglement is a key resource for ensuring security in quantum network. We show that by using a unified parameter in terms of reduced noise variances one can determine different types of tripartite entanglement of a given state generated in a hybrid optomechanical system, where an atomic ensemble is located inside a single-mode cavity with a movable mirror, with different thresholds for each type. In particular, the special quantum states which allow both entanglement and steering genuinely shared among atom-light-mirror modes can be observed, even though there is no direct interaction between the mirror and the atomic ensemble. We further show the robustness against mechanical thermal noise and damping, the relaxation time of atomic ensemble, as well as the effect of gain factors involved in the criteria. Our analysis provides an experimentally achievable method to determine the type of tripartite quantum correlation in a way.
Quantum steering refers to the apparent possibility of exploiting nonseparable quantum correlations to remotely influence the quantum state of an observer via local measurements. Different from entanglement and Bell nonlocality, quantum steering exhibits an inherent asymmetric property, which makes it relevant for many asymmetric quantum information processing tasks. Here, we study Gaussian quantum steering between two mechanical modes in an optomechanical ring cavity. Using experimentally feasible parameters, we show that the state of the two considered modes can exhibit two-way steering and even one-way steering. Instead of using unbalanced losses or noises, we propose a simple practical way to control the direction of one-way steering. A comparative study between the steering and entanglement of the studied modes shows that both steering and entanglement undergo a sudden death-like behavior. In particular, steering is found more fragile against thermal noise remaining constantly upper-bounded by entanglement. The proposed scheme may be meaningful for one-sided device-independent quantum key distribution, where the security of such protocol depends fundamentally on the direction of steering.