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Advances in physics theories and applications

Quantum Entanglement of Twin Light Beams

Assaye Gedifew Yismaw

Published Jan 1, 2018• 0 citations
OpenAlex

Abstract

A detailed quantum entanglement of twin light beams with the same and different frequencies produced by the process of parametric oscillation has been presented.We have described the process of the parametric oscillation with first-order Hamiltonian regardless of whether the twin light beams have the same or different frequencies.According to our study we have the quadrature variance decreases with the amplitude of pump mode and it approaches to the value of the quadrature variance of a two-mode vacuum state as cavity damping constant approaches to 1.In addition to this the degree of entanglement of the cavity modes for the system under consideration increase with the amplitude of the pump mode and decrease with the cavity damping constant, which implies that the degree of entanglement of twin light beams decreases as quadrature variances approaches to that of a two-mode vacuum state.

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A detailed quantum entanglement of twin light beams with the same and different frequencies produced by the process of parametric oscillation has been presented.We have described the process of the parametric oscillation with first-order Hamiltonian regardless of whether the twin light beams have the same or different frequencies.According to our study we have the quadrature variance decreases with the amplitude of pump mode and it approaches to the value of the quadrature variance of a two-mode vacuum state as cavity damping constant approaches to 1.In addition to this the degree of entanglement of the cavity modes for the system under consideration increase with the amplitude of the pump mode and decrease with the cavity damping constant, which implies that the degree of entanglement of twin light beams decreases as quadrature variances approaches to that of a two-mode vacuum state.
A detailed photon statistics of twin light beams with the same and different frequencies produced by the process of parametric oscillation has been presented. We have described the process of the parametric oscillation with first-order Hamiltonian regardless of whether the twin light beams have the same or different frequencies. According to our study we have observed that the mean photon number of the cavity mode decreases with the cavity damping constant increase, which implies that the more photons are escaped from the cavity for the large damping constant and the mean photon number of residue pump mode increases with the amplitude of pump mode.
In this paper we have studied the squeezing and entanglement properties of the cavity light generated by a three-level laser. In this quantum optical system, N three-level atoms available in an open cavity, coupled to a two-mode vacuum reservoir, are pumped to the top level by means of electron bombardment at constant rate. Applying the solutions of the equations of evolution for the expectation values of the atomic operators and the quantum Langevin equations for the cavity mode operators, we have calculated the mean, variance of the photon number, the quadrature squeezing, entanglement amplification as well as the normalized second-order correlation function for the cavity light. In addition, we have shown that the presence of the spontaneous emission process leads to a decrease in the mean and variance of the photon number. We have observed that the two-mode cavity light is in a squeezed state and the squeezing occurs in the minus quadrature. In addition, we have found that the effect of the vacuum reservoir noise is to increase the photon-number variance and to decrease the quadrature squeezing of the cavity light. However, the vacuum reservoir noise does not have any effect on the mean photon number. Moreover, the maximum quadrature squeezing of the light generated by the laser, operating far below threshold, is found to be below the vacuum-state level. In addition, our result indicates that the quadrature squeezing is greater for than that for for 0.01 < < 0.35 and is smaller for than that for for 0.35 < < 1. We have also noted that the squeezing and entanglement in the two-mode light are directly related. As a result, an increase in the degree of squeezing directly leads to an increase in the degree of entanglement and vice versa. This shows that, whenever there is squeezing in the two-mode light, there exists an entanglement in the system.
We present the first measurement of squeezed-state entanglement between the twin beams produced in an optical parametric oscillator operating above threshold. In addition to the usual squeezing in the intensity difference between the twin beams, we have measured squeezing in the sum of phase quadratures. Our scheme enables us to measure such phase anticorrelations between fields of different frequencies. In the present measurements, wavelengths differ by approximately 1 nm. Entanglement is demonstrated according to the Duan et al. criterion [Phys. Rev. Lett. 84, 2722 (2000)] Delta2p- + Delta2q+ = 1.41(2) < 2. This experiment opens the way for new potential applications such as the transfer of quantum information between different parts of the electromagnetic spectrum.
The squeezing, entanglement, and statistical properties of light produced by lambda-type three-level laser coupled to squeezed vacuum reservoir have been studied. We have determined the quadrature variances mean as well as variance photon number photon for cavity modes with the aid of the solutions of c-number Langevin equations associated with the normal order. The results show that the light produced by the system under consideration in squeezed state. The squeezed vacuum reservoir enhances both the quadrature squeezing and mean photon numbers. In addition, the mean photon number of mode b is greater than that of a if more atoms injected with state |a>. We have calculated the quadrature variances of the cavity modes, the result shows that the light produced by the system under consideration is in squeezed state and the squeezing occurs in the minus quadrature. The result also shows that the effect of the squeezed vacuum reservoir is not only enhancing the degree of squeezing for the light modes but also to generate the photons for the system under consideration. The system produce entangled two mode light that increase with η and linear gain coefficient but decrease with squeezing parameters. The correlation function of the two modes decreases as η, the linear gain coefficient and increase with squeezing parameter.
We investigate the statistical and quadrature squeezings, as well as the entanglement properties, of a two-mode light generated by non-degenerate parametric oscillations coupled to a two-mode squeezed vacuum reservoir, by employing the solutions of the quantum Langevin equations. It is found that the two-mode light shows the two-mode squeezing and entanglement for all values of the time. Moreover, it is observed that the squeezed vacuum reservoir and the growing amplitude of the pump mode enhance the degrees of two-mode squeezing and entanglement. We have also shown that the amounts of squeezing and entanglement are significant in a region, where the mean photon number is higher, and the photon number correlation is lower.
With the aid of the solutions of the Quantum Langevin equations, we have calculated the Q-functions for the two-mode coherent and subharmonic cavity light beams. We have then determined the Q-function for the superposed two-mode coherent and subharmonic cavity light beams. With the help of the pertinent Q-functions for cavity light beams, we determined the photon statistics, quadrature statistics, and entanglement. we have obtained that the superposed two-mode coherent and subharmonic cavity light beams are in a squeezed state and the squeezing occurs in the plus quadrature. Besides, our analysis shows that at steady state and at threshold, the superposed two-mode coherent and subharmonic light beams have a maximum squeezing of 25%25\%25% below the two-mode vacuum-state level. We have also clearly shown that the superposed two-mode light beam is entangled at steady-state and threshold and the entanglement turned out to be observed in the highly correlated squeezed photons with 75%75\%75% degree of entanglement.