In this paper, we analyze, under realistic experimental conditions, entanglement and quantum discord in a two-mode Gaussian state [Formula: see text] coupled to a thermal reservoir. The mode [Formula: see text]([Formula: see text]) is generated during the first(second) transition of a nondegenerate three-level laser. The gain medium of the laser is a set of three-level atoms in a cascade configuration. The atoms are prepared initially in a superposition of the upper and lower levels. In the good cavity-limit, applying the master equation we obtain the covariance matrix of the state [Formula: see text] at steady-state. We use the entanglement of formation and the Gaussian quantum discord to quantify entanglement and quantum correlations beyond entanglement, respectively. The two indicators of nonclassicality are defined by means of the von Neumann entropy, and obtained as functions of the parameters characterizing the physical and environmental parameters of the state [Formula: see text], i.e. atomic coherence, dissipation and thermal photon number. As results, we find that maximum entanglement and discord could be achieved by adjusting the degree of atomic coherence. In contrary to the expectation based on the assumption that entanglement is a part of quantum discord, it is found that the latter can be less than the former. Under thermal noise effect, we find that quantum discord measured when the state [Formula: see text] exhibits entanglement diminishes drastically, while that measured when the [Formula: see text] is separable displays a relatively robust behavior seeming to be captured over a wide range of temperature. Our results assert that nondegenerate three-level lasers may play a crucial role in the implementation of quantum processing tasks, particularly those who do not need entangled states.
In this paper, we analyze, under realistic experimental conditions, entanglement and quantum discord in a two-mode Gaussian state [Formula: see text] coupled to a thermal reservoir. The mode [Formula: see text]([Formula: see text]) is generated during the first(second) transition of a nondegenerate three-level laser. The gain medium of the laser is a set of three-level atoms in a cascade configuration. The atoms are prepared initially in a superposition of the upper and lower levels. In the good cavity-limit, applying the master equation we obtain the covariance matrix of the state [Formula: see text] at steady-state. We use the entanglement of formation and the Gaussian quantum discord to quantify entanglement and quantum correlations beyond entanglement, respectively. The two indicators of nonclassicality are defined by means of the von Neumann entropy, and obtained as functions of the parameters characterizing the physical and environmental parameters of the state [Formula: see text], i.e. atomic coherence, dissipation and thermal photon number. As results, we find that maximum entanglement and discord could be achieved by adjusting the degree of atomic coherence. In contrary to the expectation based on the assumption that entanglement is a part of quantum discord, it is found that the latter can be less than the former. Under thermal noise effect, we find that quantum discord measured when the state [Formula: see text] exhibits entanglement diminishes drastically, while that measured when the [Formula: see text] is separable displays a relatively robust behavior seeming to be captured over a wide range of temperature. Our results assert that nondegenerate three-level lasers may play a crucial role in the implementation of quantum processing tasks, particularly those who do not need entangled states.
Squeezing and entanglement of a two-mode cascade laser, produced by a three-level atom which is initially prepared by a coherent superposition of the top and bottom levels then injected into a cavity coupled to a two-mode squeezed vacuum reservoir is discussed. I obtain stochastic differential equations associated with the normal ordering using the pertinent master equation. Making use of the solutions of the resulting differential equations, we determined the mean photon number for the cavity mode and their correlation, EPR variables, smallest eigenvalue of the symplectic matrix, intensity difference fluctuation, and photon number correlation. It is found that the squeezed vacuum reservoir increases the degree of the statistical and nonclassical features of light produced by the system. Furthermore, using the criteria developed by logarithm negativity and Hillery-Zubairy criteria, the quantum entanglement of the cavity mode is quantified. It is found that the degree of the entanglement for the system under consideration increases with the squeezing parameter of the squeezed vacuum reservoir.
The quantum properties of a non-degenerate three-level laser with the parametric amplifier and coupled to a thermal reservoir are thoroughly analyzed with the use of the pertinent master equation and stochastic differential equations associated with the normal ordering. Applying solutions of resulting differential equations, quadrature variance, the mean and variance of photon number, the photon number correlation are calculated. However, the two-mode driving light has no effect on the squeezing properties of the cavity modes. Employing the same solutions, one can also obtain anti normally ordered characteristic function defined in the Heisenberg picture. For a linear gain coefficient of (A = 100), for a cavity damping constant of K= 0:8, μ = 0.16 and for thermal reservoir nth = 0, the maximum intra cavity photon entanglement is found at steady state and at threshold to be 70%.
Nowadays, it is widely acknowledged that information can serve as a thermodynamic fuel capable of powering the extraction of useful work through measurements and feedback control. Moreover, it has been demonstrated that the work extractable from a correlated bipartite state can effectively distinguish entangled states from separable ones. In this context, we introduce an operational criterion denoted as [Formula: see text] to witness the presence of entanglement in a two-mode Gaussian state [Formula: see text], based on the amount of work that can be extracted from a thermal bath using a Szilard-like engine. In this setup, the state [Formula: see text] acts as the working medium of the engine, where modes [Formula: see text] and [Formula: see text] are generated during the first and second transitions of a nondegenerate three-level laser, and are coupled to a shared two-mode thermal bath. Our results reveal that the proposed criterion [Formula: see text] vanishes when [Formula: see text] is a product state. Furthermore, [Formula: see text] reaches its maximum value when [Formula: see text] is coupled to a vacuum bath, but it diminishes under the influence of thermal noise. Notably, the degree of entanglement detected by [Formula: see text] can be tuned via the atomic coherence of the laser. Finally, a comparison of [Formula: see text] with a reliable measure of entanglement such as logarithmic negativity, demonstrates perfect agreement in identifying the presence of entanglement in [Formula: see text].
The quantum properties of a non-degenerate three-level laser with the parametric amplifier and coupled to a thermal reservoir are thoroughly analyzed with the use of the pertinent master equation and stochastic differential equations associated with the normal ordering. Applying solutions of resulting differential equations, quadrature variance, the mean and variance of photon number, the photon number correlation are calculated. However, the two-mode driving light has no effect on the squeezing properties of the cavity modes. Employing the same solutions, one can also obtain anti normally ordered characteristic function defined in the Heisenberg picture. For a linear gain coefficient of (A = 100), for a cavity damping constant of K= 0:8, µ = 0 and for thermal reservoir th = 0, the maximum intra cavity photon entanglement is found at steady state and at threshold to be 60%.
Quantum correlations play a fundamental role in quantum information science. Within bipartite mixed states, they can arise in different incarnations, i.e. Bell nonlocality, steering, and entanglement. Besides being of fundamental interest, they can all be exploited to attain enhancements in quantum information processing tasks over classical methods. Here, in a two-mode Gaussian state [Formula: see text], where the mode [Formula: see text]([Formula: see text]) is generated during the first(second) transition of a correlated-emission laser, we perform a comparative study between the three forms of quantum correlations in the presence of dissipation and thermal noise. We use the master equation of the state [Formula: see text] to obtain the first and second moments of the laser modes variables in the steady state regime. Under realistic experimental conditions, we show that Bell nonlocality could be exhibited by the state [Formula: see text] only when the two laser modes [Formula: see text] and [Formula: see text] are weakly entangled, in contrast, it disappears when they are strongly entangled. Especially, we find that Bell nonlocality is strongly sensitive to thermal noise. Also, we show that the state [Formula: see text] can display one-way and two-way steering in a wide range of operating parameters. In particular, we demonstrate that one-way steering can be detected solely in the direction [Formula: see text]. Against thermal noise, entanglement is found to be more robust than steering, which is in turn found to be more robust than Bell nonlocality. The obtained results are helpful in understanding the behavior of quantum nonlocality in dissipative-noisy environments, and may find potential applications for quantum information tasks.
Quantum correlations beyond quantum entanglement represent vital resources in quantum information processing as well as in quantum computation. In fact, both quantum entanglement and quantum correlation are the same when the quantum system is described by pure states. However, this is not exactly the case when general mixed states are considered. In order to clarify this, a simple model has been proposed for the production and quantification of these quantum correlations between two mechanical resonators that are macroscopic in two Fabry–Pérot cavities optomechanical coupled by the photon hopping process. In this model, we analyze and investigate the quantification of the quantum correlation beyond the entanglement between the mechanical modes. We determine the global covariance matrix of the model from which we derive the expression of the entropy of formation ([Formula: see text]) as well as the Gaussian quantum discord ([Formula: see text]), which quantify the amount of quantum entanglement and quantum correlations, respectively. The analysis based on these two quantum correlations quantifiers shows that quantum discord is more appropriate to characterize the quantum correlations between the mechanical modes in an optomechanical quantum system in the presence of robust photon hopping.