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Ethiopian Journal of Education and Sciences

Theory of Quantum Entanglement of Intra-Cavity Photons Produced by a Non-Degenerate Parametric Oscillator (Ndpo): Semi-Classical Approach

Tamirat Abebe, Nebiyu Gemechu, Milkessa Gebeyehu

Published Jul 15, 2019• 0 citations
OpenAlex

Abstract

The von-Neumann entropy (VNE), usually expressed in terms of the density operator, is the mathematical tool to measure the degree of entanglement of a bi-partite system. Applying the solutions of the quantum Langevin equations, the anti-normally ordered characteristic function of the intra-cavity photons produced by a non-degenerate parametric oscillator could be calculated. With the help of the resulting characteristic function, the Q- function which is then used to calculate the entanglement of the intracavity photons using VNE is determined. Moreover, the photon number distribution, the mean photon number, the normalized second order correlation function, the intensity difference, and quadrature variance for the intra-cavity photons produced by a nondegenerate parametric oscillator coupled to a two-mode squeezed vacuum reservoir is determined. It was found that when the squeeze parameter increases the entanglement also increases. These show that the entropy entanglement has a direct relation with squeezing.Keywords:Entanglement, Mean photon number, Parametric down conversion, Q-function

Related papers

Theory of Quantum Entanglement of Intra-Cavity Photons Produced by a Non-Degenerate Parametric Oscillator (Ndpo):

Tamirat Abebe, Nebiyu Gemechu, Milkessa Gebeyehu

The von-Neumann entropy (VNE), usually expressed in terms of the density operator, isthe mathematical tool to measure the degree of entanglement of a bi-partite system.Applying the solutions of the quantum Langevin equations, the anti-normally orderedcharacteristic function of the intra-cavity photons produced by a non-degenerateparametric oscillator could be calculated. With the help of the resulting characteristicfunction, the Q- function which is then used to calculate the entanglement of the intra-cavity photons using VNE is determined. Moreover, the photon number distribution, themean photon number, the normalized second order correlation function, the intensitydifference, and quadrature variance for the intra-cavity photons produced by a non-degenerate parametric oscillator coupled to a two-mode squeezed vacuum reservoir isdetermined. It was found that when the squeeze parameter increases the entanglement alsoincreases. These show that the entropy entanglement has a direct relation with squeezing.

•Jan 1, 2019•0 citations

Semiclassical entanglement analyses in a non-degenerate parametric oscillator (NDPO)

Daniel B. Erenso, Joshua Dodson, K. Fesseha

The entanglement of the intracavity photons in subthreshold NDPO coupled to a squeezed vacuum is studied using the von-neumann entropy (VNE). The VNE is calculated in terms of the Q-function representation for the density operator.

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Entanglement Correlation from a Non-degenerate Three-Level Laser with a Parametric Amplifier and Coupled to Vacuum Reservoir

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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%.

Indian Journal of Advanced Physics•Oct 16, 2023•3 citations

Light Entanglement from a Non-Degenerate Three-Level Laser with a Parametric Amplifier and Coupled to a Thermal Reservoir

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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%.

Journal of Electrical and Electronic Engineering•Jun 5, 2023•0 citations

Entangled Photon Generation From a Three-Level Laser with a Parametric Amplifier and Coupled to a Thermal Reservoir

Negasa Belay

In this article we study squeezing and statistical properties of light producing by a non-degenerate three-level laser with the parametric amplifier and coupled to a thermal reservoir. With the aid of master equation, we obtain stochastic differential equations. Applying solutions of resulting differential equations, we calculate quadrature variance, the mean and variance of photon number, the photon number correlation. However, the two-mode driving light has no effect on the squeezing properties of the cavity modes. On the other hand, parametric amplifier and thermal reservoir increase the mean and variance of photon number. Furthermore, employing the same solutions, we 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 ¯ nth = 0 ,the maximum intra cavity photon entanglement is found at steady state and at threshold to be 60%.

Indian Journal of Advanced Physics•Apr 15, 2023•0 citations

Entangled Photon Generation from a Three-Level Laser with a Parametric Amplifier and Coupled to a Thermal Reservoir

Negasa Belay

In this article the investigation of squeezing and statistical properties of light resulting by a non-degenerate three-level laser with the parametric amplifier and coupled to a thermal reservoir have been occurred. With the aid of master equation, stochastic differential equations were obtained. 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. On the other hand, parametric amplifier and thermal reservoir increase the mean and variance of photon number. Furthermore, employing the same solutions, we 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%.

Universal Journal of Physics Research•Feb 9, 2023•1 citation
The von-Neumann entropy (VNE), usually expressed in terms of the density operator, is the mathematical tool to measure the degree of entanglement of a bi-partite system. Applying the solutions of the quantum Langevin equations, the anti-normally ordered characteristic function of the intra-cavity photons produced by a non-degenerate parametric oscillator could be calculated. With the help of the resulting characteristic function, the Q- function which is then used to calculate the entanglement of the intracavity photons using VNE is determined. Moreover, the photon number distribution, the mean photon number, the normalized second order correlation function, the intensity difference, and quadrature variance for the intra-cavity photons produced by a nondegenerate parametric oscillator coupled to a two-mode squeezed vacuum reservoir is determined. It was found that when the squeeze parameter increases the entanglement also increases. These show that the entropy entanglement has a direct relation with squeezing.Keywords:Entanglement, Mean photon number, Parametric down conversion, Q-function
The von-Neumann entropy (VNE), usually expressed in terms of the density operator, isthe mathematical tool to measure the degree of entanglement of a bi-partite system.Applying the solutions of the quantum Langevin equations, the anti-normally orderedcharacteristic function of the intra-cavity photons produced by a non-degenerateparametric oscillator could be calculated. With the help of the resulting characteristicfunction, the Q- function which is then used to calculate the entanglement of the intra-cavity photons using VNE is determined. Moreover, the photon number distribution, themean photon number, the normalized second order correlation function, the intensitydifference, and quadrature variance for the intra-cavity photons produced by a non-degenerate parametric oscillator coupled to a two-mode squeezed vacuum reservoir isdetermined. It was found that when the squeeze parameter increases the entanglement alsoincreases. These show that the entropy entanglement has a direct relation with squeezing.
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%.
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%.
In this article we study squeezing and statistical properties of light producing by a non-degenerate three-level laser with the parametric amplifier and coupled to a thermal reservoir. With the aid of master equation, we obtain stochastic differential equations. Applying solutions of resulting differential equations, we calculate quadrature variance, the mean and variance of photon number, the photon number correlation. However, the two-mode driving light has no effect on the squeezing properties of the cavity modes. On the other hand, parametric amplifier and thermal reservoir increase the mean and variance of photon number. Furthermore, employing the same solutions, we 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 ¯ nth = 0 ,the maximum intra cavity photon entanglement is found at steady state and at threshold to be 60%.
In this article the investigation of squeezing and statistical properties of light resulting by a non-degenerate three-level laser with the parametric amplifier and coupled to a thermal reservoir have been occurred. With the aid of master equation, stochastic differential equations were obtained. 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. On the other hand, parametric amplifier and thermal reservoir increase the mean and variance of photon number. Furthermore, employing the same solutions, we 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%.