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Chinese Physics B

Master equation describing the diffusion process for a coherent state

Tang-Kun Liu, Chuan-Jia Shan, Jibing Liu, Hong-Yi Fan

Published Mar 1, 2014• 8 citations
Publisher

Abstract

The evolution of a pure coherent state into a chaotic state is described very well by a master equation, as is validated via an examination of the coherent state's evolution during the diffusion process, fully utilizing the technique of integration within an ordered product (IWOP) of operators. The same equation also describes a limitation that maintains the coherence in a weak diffusion process, i.e., when the dissipation is very weak and the initial average photon number is large. This equation is dρ/ d t = −κ[ a + a ρ − a + ρ a − a ρ a + + ρ aa + ]. The physical difference between this diffusion equation and the better-known amplitude damping master equation is pointed out.

DOI
10.1088/1674-1056/23/3/030303

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The evolution of a pure coherent state into a chaotic state is described very well by a master equation, as is validated via an examination of the coherent state's evolution during the diffusion process, fully utilizing the technique of integration within an ordered product (IWOP) of operators. The same equation also describes a limitation that maintains the coherence in a weak diffusion process, i.e., when the dissipation is very weak and the initial average photon number is large. This equation is dρ/ d t = −κ[ a + a ρ − a + ρ a − a ρ a + + ρ aa + ]. The physical difference between this diffusion equation and the better-known amplitude damping master equation is pointed out.
Based on the Kraus operator of laser theory which we derived in [2] and by virtue of the technique of integration within ordered product of operators we exactly calculate the evolving result of a chaotic field, governed by the master equation describing the laser process, we find that the initial density operator evolves into a new chaotic field, with where g and κ represent the cavity gain and loss of the laser, respectively. When g = 0, the system reduces to an amplitude dissipative channel, and f' becomes −ln [(e−f − 1) e2κt + 1]. The law of photon number decay in this process is evaluated, and the corresponding Wigner function's evolution is also demonstrated.
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.
In quantum statistics theory, very few systems’ quantum entropy can be evaluated, since the quantum entropy’s formula by von-Neumann is [Formula: see text] where [Formula: see text] is density operator, [Formula: see text] is the Boltzmann constant, and the natural logarithm [Formula: see text] is quite difficult to treat. In this work, we tackle how to derive the entropy evolution of an initial coherent state undergoing a quantum diffusion process. We employ the method of integration within ordered product (IWOP) of operators to derive the final mixed state, which is a displaced chaotic state, and then deduce its entropy.
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.