By introducing a fictitious mode to be a counterpart mode of the system mode under review we introduce the entangled state representation (η|, which can arrange master equations of density operators p(t) in quant...By introducing a fictitious mode to be a counterpart mode of the system mode under review we introduce the entangled state representation (η|, which can arrange master equations of density operators p(t) in quantum statistics as state-vector evolution equations due to the elegant properties of (η|. In this way many master equations (respectively describing damping oscillator, laser, phase sensitive, and phase diffusion processes with different initial density operators) can be concisely solved. Specially, for a damping process characteristic of the decay constant k we find that the matrix element of p(t) at time t in 〈η| representation is proportional to that of the initial po in the decayed entangled state (ηe^-kt| representation, accompanying with a Gaussian damping factor. Thus we have a new insight about the nature of the dissipative process. We also set up the so-called thermo-entangled state representation of density operators, ρ = f(d^2η/π)(η|ρ〉D(η), which is different from all the previous known representations.展开更多
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 utiliz...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 dp/dt = -κ[a+ap -a+pa -apa+ + paa+]. The physical difference between this diffusion equation and the better-known amplitude damping master equation is pointed out.展开更多
This paper solves the newly constructed nonlinear master equation dρ/dt = κ[2f (N) aρ (1/f (N - 1))a^+ -a^+aρ- ρa^+a], where f(N) is an operator-valued function of N = a^+a, for describing amplitude d...This paper solves the newly constructed nonlinear master equation dρ/dt = κ[2f (N) aρ (1/f (N - 1))a^+ -a^+aρ- ρa^+a], where f(N) is an operator-valued function of N = a^+a, for describing amplitude damping channel, and derives the infinite operator sum representation of quasi-Kraus operators for the density operator. It also shows that in this nonlinear process the initial pure number state density operator will evolve into the binomial field (a mixed state) when f (N) = 1√N + 1.展开更多
By virtue of the well-behaved properties of the bipartite entangled states representation, this paper analyse and solves some master equations for generalized phase diffusion models, which seems concise and effective....By virtue of the well-behaved properties of the bipartite entangled states representation, this paper analyse and solves some master equations for generalized phase diffusion models, which seems concise and effective. This method can also be applied to solve other master equations.展开更多
By means of both the separation of the perturbation in accordance with characteristic parnmeters and the Kramers Moyal-expansion of the master equation, it is shown that the time derivative of the partial excess quant...By means of both the separation of the perturbation in accordance with characteristic parnmeters and the Kramers Moyal-expansion of the master equation, it is shown that the time derivative of the partial excess quantity of stochastic entropy due to the deviation from the most probable path is related to the responsibility of a system to the external macroscopic perturbations. This evolution rate of the partial excess stochastic entropy is equivalent to the partlal excess stochastic entropy production, as well as the stochastic excess entropy production rate based on the stochastic potential npproach. It appears also as an eqivalent quantity of the Gibbs excess entropy production for the Polsson distribution. The macroscopic stability of chemical reaction systems is dominnted by this new stochastic quantity when the local equilibrium thermodynamics is broken down .展开更多
We extend the approach of solving master equations for density matrices by projecting it onto the thermal entangled state representation(Hong-Yi Fan and Jun-Hua Chen,J.Phys.A35(2002)6873)to two-mode case.In this appro...We extend the approach of solving master equations for density matrices by projecting it onto the thermal entangled state representation(Hong-Yi Fan and Jun-Hua Chen,J.Phys.A35(2002)6873)to two-mode case.In this approach the two-photon master equations can be directly and conveniently converted into c-number partial differential equations.As an example,we solve the typical master equation for two-photon process in some limiting cases.展开更多
For the first time we derive the evolution law of the negative binomial state In) (nI in an ampli-tude dissipative channel with a damping constant to. We find that after passing through the channel, the final state ...For the first time we derive the evolution law of the negative binomial state In) (nI in an ampli-tude dissipative channel with a damping constant to. We find that after passing through the channel, the final state is still a negative binomial state, however the parameter γ evolves into The decay law of theaverage photon number is also obtained.展开更多
By introducing thermo-entangled state representation Ⅰη〉, which can map master equations of density operator in quantum statistics as state-vector evolution equations, and using "dissipative interaction picture" ...By introducing thermo-entangled state representation Ⅰη〉, which can map master equations of density operator in quantum statistics as state-vector evolution equations, and using "dissipative interaction picture" we solve the master equation of Jaynes-Cummings model with cavity damping. In addition we derive the Wigner function for density operator when the atom is initially in the up state Ⅰ↑〉 and the cavity mode is in coherent state.展开更多
The dynamical behavior of a photon-added thermal state(PATS) in a thermal reservoir is investigated by virtue of Wigner function(WF) and Wigner logarithmic negativity(WLN), where this propagation model is abstracted a...The dynamical behavior of a photon-added thermal state(PATS) in a thermal reservoir is investigated by virtue of Wigner function(WF) and Wigner logarithmic negativity(WLN), where this propagation model is abstracted as an input–output problem in a thermal-loss channel. The density operator of the output optical field at arbitrary time can be expressed in the integration form of the characteristics function of the input optical field. The exact analytical expression of WF is given, which is closely related to the Laguerre polynomial and is dependent on the evolution time and other interaction parameters(related with the initial field and the reservoir). Based on the WLN, we observe the dynamical evolution of the PATS in the thermal reservoir. It is shown that the thermal noise will make the PATS lose the non-Gaussianity.展开更多
In this paper, we analytically solve the master equation for Jaynes-Cummings model in the dispersive regime including phase damping and the field is assumed to be initially in a superposition of coherent states. Using...In this paper, we analytically solve the master equation for Jaynes-Cummings model in the dispersive regime including phase damping and the field is assumed to be initially in a superposition of coherent states. Using an established entanglement measure based on the negativity of the eigenvalues of the partially transposed density matrix we find a very strong sensitivity of the maximally generated entanglement to the amount of phase damping. Qualitatively this behavior is also reflected in alternative entanglement measures, but the quantitative agreement between different measures depends on the chosen noise model The phase decoherence for this model results in monotonic increase in the total entropy while the atomic sub-entropy keeps its periodic behaviour without any effect.展开更多
基金supported by President Foundation of Chinese Academy of Sciences and National Natural Science Foundation of China under Grant Nos. 10775097 and 10874174
文摘By introducing a fictitious mode to be a counterpart mode of the system mode under review we introduce the entangled state representation (η|, which can arrange master equations of density operators p(t) in quantum statistics as state-vector evolution equations due to the elegant properties of (η|. In this way many master equations (respectively describing damping oscillator, laser, phase sensitive, and phase diffusion processes with different initial density operators) can be concisely solved. Specially, for a damping process characteristic of the decay constant k we find that the matrix element of p(t) at time t in 〈η| representation is proportional to that of the initial po in the decayed entangled state (ηe^-kt| representation, accompanying with a Gaussian damping factor. Thus we have a new insight about the nature of the dissipative process. We also set up the so-called thermo-entangled state representation of density operators, ρ = f(d^2η/π)(η|ρ〉D(η), which is different from all the previous known representations.
基金Project supported by the National Basic Research Program of China(Grant No.2012CB922103)the National Natural Science Foundation of China(GrantNos.11175113 and 11274104)the Natural Science Foundation of Hubei Province of China(Grant No.2011CDA021)
文摘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 dp/dt = -κ[a+ap -a+pa -apa+ + paa+]. The physical difference between this diffusion equation and the better-known amplitude damping master equation is pointed out.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10775097 and 10874174)the Research Foundation of the Education Department of Jiangxi Province of China (Grant No. GJJ10097)
文摘This paper solves the newly constructed nonlinear master equation dρ/dt = κ[2f (N) aρ (1/f (N - 1))a^+ -a^+aρ- ρa^+a], where f(N) is an operator-valued function of N = a^+a, for describing amplitude damping channel, and derives the infinite operator sum representation of quasi-Kraus operators for the density operator. It also shows that in this nonlinear process the initial pure number state density operator will evolve into the binomial field (a mixed state) when f (N) = 1√N + 1.
基金supported by the Natural Science Foundation of Heze University of Shandong Province,China (Grant No XY07WL01)the University Experimental Technology Foundation of Shandong Province,China (Grant No S04W138)
文摘By virtue of the well-behaved properties of the bipartite entangled states representation, this paper analyse and solves some master equations for generalized phase diffusion models, which seems concise and effective. This method can also be applied to solve other master equations.
基金This research work is supported by the National Natural Science Foundation of China.
文摘By means of both the separation of the perturbation in accordance with characteristic parnmeters and the Kramers Moyal-expansion of the master equation, it is shown that the time derivative of the partial excess quantity of stochastic entropy due to the deviation from the most probable path is related to the responsibility of a system to the external macroscopic perturbations. This evolution rate of the partial excess stochastic entropy is equivalent to the partlal excess stochastic entropy production, as well as the stochastic excess entropy production rate based on the stochastic potential npproach. It appears also as an eqivalent quantity of the Gibbs excess entropy production for the Polsson distribution. The macroscopic stability of chemical reaction systems is dominnted by this new stochastic quantity when the local equilibrium thermodynamics is broken down .
基金The project supported by National Natural Science Foundation of China under Grant No.10175057the President Foundation of the Chinese Academy of Sciences
文摘We extend the approach of solving master equations for density matrices by projecting it onto the thermal entangled state representation(Hong-Yi Fan and Jun-Hua Chen,J.Phys.A35(2002)6873)to two-mode case.In this approach the two-photon master equations can be directly and conveniently converted into c-number partial differential equations.As an example,we solve the typical master equation for two-photon process in some limiting cases.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11175113 and 112470009)
文摘For the first time we derive the evolution law of the negative binomial state In) (nI in an ampli-tude dissipative channel with a damping constant to. We find that after passing through the channel, the final state is still a negative binomial state, however the parameter γ evolves into The decay law of theaverage photon number is also obtained.
文摘By introducing thermo-entangled state representation Ⅰη〉, which can map master equations of density operator in quantum statistics as state-vector evolution equations, and using "dissipative interaction picture" we solve the master equation of Jaynes-Cummings model with cavity damping. In addition we derive the Wigner function for density operator when the atom is initially in the up state Ⅰ↑〉 and the cavity mode is in coherent state.
基金Project supported by the National Natural Science Foundation of China(Grant No.11665013)
文摘The dynamical behavior of a photon-added thermal state(PATS) in a thermal reservoir is investigated by virtue of Wigner function(WF) and Wigner logarithmic negativity(WLN), where this propagation model is abstracted as an input–output problem in a thermal-loss channel. The density operator of the output optical field at arbitrary time can be expressed in the integration form of the characteristics function of the input optical field. The exact analytical expression of WF is given, which is closely related to the Laguerre polynomial and is dependent on the evolution time and other interaction parameters(related with the initial field and the reservoir). Based on the WLN, we observe the dynamical evolution of the PATS in the thermal reservoir. It is shown that the thermal noise will make the PATS lose the non-Gaussianity.
文摘In this paper, we analytically solve the master equation for Jaynes-Cummings model in the dispersive regime including phase damping and the field is assumed to be initially in a superposition of coherent states. Using an established entanglement measure based on the negativity of the eigenvalues of the partially transposed density matrix we find a very strong sensitivity of the maximally generated entanglement to the amount of phase damping. Qualitatively this behavior is also reflected in alternative entanglement measures, but the quantitative agreement between different measures depends on the chosen noise model The phase decoherence for this model results in monotonic increase in the total entropy while the atomic sub-entropy keeps its periodic behaviour without any effect.