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Journal of Optoelectronics·laser

Nonclassical properties of superposition of vacuum state and singlephoton state in laser process

LU Dao-min

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

Master equations of density operators can be concisely solved by virtue of thermo entangled state representation and the technique of integration within an ordered product of operators.The solution of master equations of density operators is given.We get the Wigner function evolution formula in phase space and photon number distribution formula of the state,which is a superposition of vacuum state and single-photon state initially in laser process.By numerical calculation we plot its Wigner function and photon number distribution evolution curves,when cavity gain constant and cavity loss constant are both equal to certain values.The effect of decoherence on nonclassical property of the state is discussed by comparing negative area size and the depth of negativity of Wigner function.Numerical results show that the negativity area size and the depth of negativity of its Wigner function decrease and then vanish with dissipation.In addition,we calculate the variation of negative volume of Wigner function with dissipation time.We find that it decreases with dissipation time increasing.These results show that the nonclassical properties of the state are weakened and then disappear with dissipation time increasing.

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Master equations of density operators can be concisely solved by virtue of thermo entangled state representation and the technique of integration within an ordered product of operators.The solution of master equations of density operators is given.We get the Wigner function evolution formula in phase space and photon number distribution formula of the state,which is a superposition of vacuum state and single-photon state initially in laser process.By numerical calculation we plot its Wigner function and photon number distribution evolution curves,when cavity gain constant and cavity loss constant are both equal to certain values.The effect of decoherence on nonclassical property of the state is discussed by comparing negative area size and the depth of negativity of Wigner function.Numerical results show that the negativity area size and the depth of negativity of its Wigner function decrease and then vanish with dissipation.In addition,we calculate the variation of negative volume of Wigner function with dissipation time.We find that it decreases with dissipation time increasing.These results show that the nonclassical properties of the state are weakened and then disappear with dissipation time increasing.
The diffusion master equations of density operators under action of linear resonance force were concisely solved by virtue of thermo entangled state representation and the technique of integration within an ordered product of operators.The evolution formula of the field density operator was given,and the Wigner function evolution formula which is in superposition of vacuum state and single-photon state initially was obtained.By numerically calculating the Wigner function was plotted,and the evolution of negative volume of Wigner function with dissipation time was calculated.Through the analysis of the Wigner function,the effect of decoherence on nonclassical property of the state was discussed.Numerical results show that the negativity area size and the depth of negativity of its Wigner function decrease until vanish with dissipation time.In addition,on the other hand,Wigner function can be slipped under the action of linear resonance force.
Photon-added chaotic field is constructed by creation operator roling in chaotic field.Nonclassical property and decoherence of photon-added chaotic field are analysed.Master equations of density operators can be concisely solved by the technique of integration with in an ordered product of operators and virtue of thermo-entangled state representation.We get the evolution formula of the field density operator which is in photon-added chaotic field initially.The evolutions of its Wigner function and the evolutions of Prepresentation are given.The nonclassical property is discussed by calculating its Wigner function in phase space.Numerical results show that the photon-added chaotic field displays nonclassical property initially,and its nonclassical property is weakened with dissipation time increasing.On the other hand,its nonclassical property is also weakened with added photon number increasing.
The Wigner functions of the Fock states and their superposition states have negative value clearly. We focus on discussing the time evolution of the Fock states and their superposition states by the Wigner function under the coherent drive (pumping laser) and dissipation channels (cavity radiation). The results show that the negative region of their Wigner function gradually diminishes as the time kt or the gain coefficient g increasing. In addition, the disappearing time is related to the value of g - k. The loss of non-classical features becomes slower when g increases with the k > g; there is the "frozen zone" when k = g; then the loss of non-classical features becomes faster when g increases with k < g.
The quantum properties of weak cohetent state in terms of squeezing effect and antibunching effect were investigated in the diffusion.Master equation of density operator in the diffusion process can be concisely solved by virtue of thermo-entangled state representation and the technique of integration within an ordered product of operators,which contains normal ordering,antinormal ordering and Weyl ordering.The solution of master equation of density operator in diffusion process was given by Kraus operator.The evolution formula of the field density operator which is in weak coherent state initially was get.Its squeezing effect and antibunching are investigated by the numerical method.The effect of decoherence on its nonclassical property is discussed.Numerical results show that compression depth is weakened and the compression range decreases with diffusion time increasing.On the other hand,the light field displays antibunching effect in the early diffusion.When the diffusion time is greater than a certain value,its antibunching effect disappears.
We investigate the time evolution of a quantum state in the laser channel with cavity gain coefficient g and loss coefficient κ by virtue of the thermo entangled state representation. This is a new approach for solving master equations. We exactly calculate the evolving result of the photon-added coherent state (PACS) governed by the master equation describing the laser process, and the normal ordered form of the density operator in the laser channel is derived, based on which we calculate the Wigner function analytically and graphically. The corresponding law of the PACS evolution in the laser channel is evaluated.
We investigate systematically the evolution of the number state in a laser process by deriving the analytic expression of the density operator and putting it into a normal ordered form. The eigenvalue of the density operator is related to Jacobi polynomials. Then we derive the expression for the mean photon number, the second degree of coherence, the entropy, Wigner function and the photoncount distribution. The nonclassicality is discussed by virtue of the negativity of Wigner function. It is found that the Wigner function is always negative for t < t0, which is independent on the parameter m. On the other hand, the condition for the second degree of coherence larger than 1 is dependent on the parameter m.