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ACTA PHOTONICA SINICA

Decoherence of Weak Coherent State in the Diffusion Process

Qiu Chang-don

Published Jan 1, 2015• 0 citations
OpenAlex

Abstract

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.

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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.
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.
We have studied the case in which one mode of the light field in the two-mode squeezed vacuum state evolves in a diffusion channel. By virtue of thermo-entangled state representation and the technique of integration within an ordered product, the evolution formula of the field density operator is given. Its non-classical properties, such as squeezing effect, antibunching effect, the violation of Cauchy–Schwartze inequality and the entanglement property between two modes, are studied. The influences of the squeezing parameter and the dissipation time on the non-classical properties are discussed. The results obtained by the numerical method show that its non-classical properties are all weakened with the dissipation. On the other hand, its squeezing effect and the entanglement property between two modes are strengthened, but its antibunching effect and the violation of Cauchy–Schwartze inequality are weakened with the increase of the squeezing parameter.
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.
By virtue of the properties of thermal entanglement, we succeed to obtain the solution to the representative phase diffusion master equation and give the operator sum representation of density operator. After analyzing the time evolution process of density operator at different initial state, we find out density operators keep invariable with the initial state being Fock state or thermal state. But the system always maintains coherence with phase diffusion when the initial state is coherent state.
We solve various master equations to obtain density operators' infinite operator-sum representation via a new approach, i.e., by virtue of the thermo-entangled state representation that has a fictitious mode as a counterpart mode of the system mode. The corresponding Kraus operators from the point of view of quantum channel are derived, whose normalization conditions are proved. Miscellaneous characters possessed by different quantum channels, such as decoherence, phase diffusion, damping, and amplification, can be shown explicitly in the entangled state representation of the density operators. Squeezing transformation is applied to the density operator for decoherence to generate a master equation for describing the phase sensitive process. Partial trace method for deriving new density operators is also introduced. Throughout our discussion, the technique of integration within an ordered product (IWOP) of operators is fully used.
Abstract Using the operator correspondence of the real and fictious modes in the thermo entangled state representation, we solve the quantum master equation describing the diffusion channel and obtain the Kraus operator-sum representation of its analytical solution. we find that the pure coherent states evolve into the new mixed thermal superposed states in the diffusion channel. Also, we investigate the statistical properties of the initial coherent states and their entropy evolutions in the diffusion channel, and find that the entropy evolutions are only related to the decay time and without the amplitudes of the initial coherent states.