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Journal of the Optical Society of America B

Continuous-variable quantum steering in a Raman-driven quantum beat laser

Mahboob Hasan Shah, Haleema Sadia Qureshi, Shakir Ullah, Fazal Ghafoor

Published Mar 31, 2026• 2 citations
Publisher

Abstract

In this work, we investigate continuous-variable (CV) quantum steering in a genuine bimodal active Raman-driven quantum beat laser (RDQBL) system. The lasing medium of the system is coupled to two external classical fields in Raman configuration and to two quantized cavity modes, the latter being initially prepared in arbitrary single-mode Gaussian states. Using the reduced density matrix of the evolved cavity modes, we derive and solve the dynamical equations analytically and numerically. We analyze the time evolution and strength of quantum steering in the two-mode Gaussian states against various system parameters, for instance, the intensity and relative phase of the classical Raman fields, the cavity decay rates, and the non-classicality and purity of the input cavity modes. Our results show that the cavity modes exhibit robust, tunable steerability across a wide range of parameters. We further demonstrate the intrinsic asymmetry of quantum steering, that is, an imbalance in the non-classicality of input modes ( τ 1 ≠ τ 2 ) leads to one-way directional steering. These findings establish the RDQBL system as a promising platform for controllable CV quantum steering with potential applications in secure quantum communication, quantum key distribution (QKD), quantum metrology, and asymmetric quantum networks.

DOI
10.1364/josab.596470

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In this work, we investigate continuous-variable (CV) quantum steering in a genuine bimodal active Raman-driven quantum beat laser (RDQBL) system. The lasing medium of the system is coupled to two external classical fields in Raman configuration and to two quantized cavity modes, the latter being initially prepared in arbitrary single-mode Gaussian states. Using the reduced density matrix of the evolved cavity modes, we derive and solve the dynamical equations analytically and numerically. We analyze the time evolution and strength of quantum steering in the two-mode Gaussian states against various system parameters, for instance, the intensity and relative phase of the classical Raman fields, the cavity decay rates, and the non-classicality and purity of the input cavity modes. Our results show that the cavity modes exhibit robust, tunable steerability across a wide range of parameters. We further demonstrate the intrinsic asymmetry of quantum steering, that is, an imbalance in the non-classicality of input modes ( τ 1 ≠ τ 2 ) leads to one-way directional steering. These findings establish the RDQBL system as a promising platform for controllable CV quantum steering with potential applications in secure quantum communication, quantum key distribution (QKD), quantum metrology, and asymmetric quantum networks.
We study the quantum steering of a two-mode Gaussian state evolved by a simple quantum beat laser with the cavity field being initially in arbitrary two single-mode Gaussian states and the lasing medium being driven by a strong classical field. In presence of the cavity damping, the quantum steering time of the two-mode Gaussian state increases with the relative intensity of the coupling fields, whereas the relative phase switches the steerable states into the non-steerable and vice versa. We further show that the higher the non-classicality of the initial cavity modes, the longer the time of steerability in the two-mode Gaussian state. Nonetheless, the quantum steering is irrespective of the influence from the purity of the initial cavity modes of the laser system.
Quantum steering is an important type of quantum correlation with potential applications in one-sided device-independent (1SDI) quantum information protocols. In this contribution, we explore the time-dependent dynamics of Gaussian quantum steering in coupled lossy optical waveguides using the covariance matrix formalism. Optical dissipation is explicitly incorporated to account for realistic propagation losses in coupled waveguides. We systematically investigate the influence of the optical loss rate, purity, nonclassicality, and squeezing of the input Gaussian states on the generation and evolution of steering. The results demonstrate that increasing nonclassicality and squeezing enhances Gaussian steering, while optical loss and reduced purity progressively suppress it. However, a considerable amount of steering can persist over finite propagation intervals in the presence of optical loss. We further examine that steering is symmetric for input states with identical nonclassicality, while unequal nonclassicalities lead to directional steering asymmetry, offering a way to control the steering direction through input-state engineering. These results demonstrate that coupled optical waveguides can support controllable Gaussian quantum steering under practical loss conditions and offer a promising integrated-photonic platform for asymmetric quantum-information protocols, including 1SDI quantum key distribution (QKD) and quantum communication.
Abstract Quantum discord, an appropriate measure of quantum correlation, is analyzed in a two-mode Gaussian state of the cavity field evolved by a system of quantum beat laser. In the laser system, two arbitrary single-mode Gaussian states of the cavity fields and an external classical field couple to the atomic lasing medium. We calculate the time-dependent expression for the quantum discord both analytically and numerically, by following the reduced density matrix equation of the resulting cavity field. In this framework, we investigate the generation and control of Gaussian quantum discord in the two-mode Gaussian state of the cavity field at the output in terms of the purity and non-classicality of the two input cavity modes, the Rabi frequency of the classical driving field, the relative phase of the coupling parameters, and the damping rates of the cavity modes. The behaviour of quantum discord appears oscillatory due to the quantum beats in the output cavity field developed by the classical driving field in the medium as time passes. Moreover, we find that quantum discord switches on and off while adjusting the relative phase of the coupling parameters. Analysis of the analytical results agrees well with our numerical simulations.
We study the entanglement dynamics of two-mode Gaussian state (TMGS) in a quantum beat laser driven by two classical fields in Raman configuration using Simon's criterion of quantum state separability. The two modes of the cavity field are considered initially in general single-mode Gaussian states. The effect of the non-classicality, purity, and relative phase of the cavity modes on the entanglement phenomenon is studied thoroughly. We show that in the presence of cavity decay rates, the higher the non-classicality of the initial states, the higher is the inseparability of the evolved TMGS of the cavity field. The inseparability, on the other side, is independent of the purity of the initial states. Moreover, the time scale of the entangled state increases with the relative intensity of the driving fields, whereas the relative phase switches the entangled state into the disentangled state of the cavity field and vice versa. The quantum statistics of the mean photons number of the cavity field is analyzed.
Abstract We theoretically investigate the emergence and asymmetry of Gaussian quantum steering and Rényi-2 entanglement in the radiation field of a nondegenerate three-level laser system. The gain medium consists of atoms initially prepared in a coherent superposition of the upper and lower states, interacting with two quantized cavity modes coupled to a common thermal reservoir. Using the steady-state solution of the master equation and the covariance matrix formalism, we compute the Gaussian steerability in both directions and compare it to the Gaussian Rényi-2 entanglement. Our analysis reveals that, under a wide range of parameters—including gain strength, population inversion, and thermal phonon number—the system exhibits generic one-way steering from mode A to mode B , with the reverse direction being inaccessible. This asymmetry is shown to originate from the photon number imbalance between the two modes. We further demonstrate that thermal noise degrades quantum correlations, with steering being more fragile than entanglement. These results provide theoretical support for the implementation of asymmetric quantum information protocols in cavity-based platforms and could be tested with current experimental technologies.
The generation of two-mode Gaussian-type entangled states of the cavity field is studied in a quantum beat laser, where three-level atoms of the VVV-type level configuration are coupled to two quantized modes of the cavity field and two upper levels of the atom are driven by a strongly classical field. According to Simon's criterion that is a necessary and sufficient condition for the inseparability of two-mode Gaussian states with a general form of covariance matrices, we analytically and numerically investigate the influence of phase and Rabi frequency of the classical driving field, cavity loss, and the purity and nonclassicality of the initial state of the cavity field on the entanglement property of the resulting two-mode Gaussian state. In the limit of weak cavity loss and strong driving, we show that the cavity field can be periodically into an ideal two-mode entangled Gaussian-type state.