Expectation Value Theorem for Thermo Vacuum States of Optical Chaotic Field and Negative-Binomial Field

For the density operator (mixed state) describing chaotic light and negative-binomial field there exist the corresponding thermal vacuum state (pure state) in the real-fictitious space. Using the method of integration within ordered product of operators we find the expectation value theorem in these two thermo vacuum states respectively. The thermal average theorem of translation operator is also deduced. Application of the new thermo vacuum state in calculating photon number disturibution and fluctuation and thermal average is presented.     

Evolution of the single-mode squeezed vacuum state in amplitude dissipative channel

Using the way of deriving infinitive sum representation of density operator as a solution to the master equation describing the amplitude dissipative channel by virtue of the entangled state representation, we show manifestly how the initial density operator of a single-mode squeezed vacuum state evolves into a definite mixed state which turns out to be a squeezed chaotic state with decreasing-squeezing and deeoherence. We investigate average photon number, photon statistics distributions for this mixed state.     

相位扩散通道中密度算符相关态的时间演化

利用热纠缠态的性质,对具有代表性的相位扩散主方程进行求解,得到关于密度算符的算符和表示形式,分析不同初始态下的密度算符的时间演化结果,发现在相位扩散通道下当初始态为粒子数态或热态时密度算符保持恒定,而当初始态为相干态时系统在发生相扩散的同时始终保持相干态特性不变.     

Explicit solution of diffusion master equation under the action of linear resonance force via the thermal entangled state representation

Using the well-behaved features of the thermal entangled state representation, we solve the diffusion master equation under the action of a linear resonance force, and then obtain the infinitive operator-sum representation of the density operator. This approach may also be effective for treating other master equations. Moreover, we find that the initial pure coherent state evolves into a mixed thermal state after passing through the diffusion process under the action of the linear resonance force.     

Relations Between Characteristic Function, Positive P-Representation and Coherent Thermal State

We employ the coherent thermal states (a kind of entangled states) in thermal field dynamics to establish a complete entangled state formalism expressing pseudo-classical representations of density operator for light field.Especially, the relationship between the coherent thermal state and the characteristic function and the positive P representation in quantum optics theory are obtained.     

Relations Between Characteristic Function,Positive P-Representation and Coherent Thermal State

We employ the coherent thermal states (a kind of entangled states) in thermal field dynamics to establish a complete entangled state formalism expressing pseudo-classical representations of density operator for light field. Especially, the relationship between the coherent thermal state and the characteristic function and the positive P representation in quantum optics theory are obtained.     

Thermal Squeezed State Representation of Scalar Field and Energy Density in Semiclassical Theory of Gravity

The semiclassical theory of gravity is studied in terms of representation of scalar field in thermal coherent state and thermal squeezed state formalisms. For the FRW cosmological model with a minimal scalar field, the semiclassical Einstein equation reduces to zero-point energy term plus a finite temperature term and classical term in thermal coherent state. In thermal squeezed vacuum state it reduces to quantum term in addition to the finite temperature term and zero-point energy term. The present study can account for nonclassical state and finite temperature effect contributions to energy density in semiclassical theory of gravity.     

Analysis of the master equation for the Dicke model in squeezed vacua

The master equation for the reduced atomic density operator for the Dicke model (N_a 2-level atoms on the same single site) interacting with a broad-band squeezed vacuum state field is derived using operator reaction field theory. The analysis through reaction field theory is presented first of all for the normal vacuum and then for the squeezed vacuum, both within the Markov and Born approximations. In the case of the squeezed vacuum field a statistical decorrelation between matter and field variables is also necessarily adopted in order to close the system of equations: this is also the case for the broad-band black-body field, and the theory contrasts with that which employs projection operator techniques and uses weak coupling. Models involving a both axially symmetrical and wholly isotropic distribution of the squeezed vacuum modes are compared.     

Time-Evolution of Photon-Number Distribution and Density Operator of Squeezed Thermal State in the Thermal Environment

By virtue of the thermal entangled state representation, we analytically study time-dependent evolution of photon-number distribution and density operator of squeezed thermal state (STS) in the thermal environment. It is found that the initial density operator of STS still keeps squeezing and thermal within the thermal environment. At long times, such a state decays to thermal, a Gaussian classical state, as a result of decoherence. Moreover, the oscillations of photon-number distribution slowly disappear with increasing t, but the change of oscillations is completely different from that of STS in amplitude dissipative channel.     

New Approach for Solving the Lindblad Equation of the Density Operator for a Harmonic Oscillator Interacting with an Electromagnetic Field

By virtue of the thermo entangled state (TES) representation whose one mode is a fictitious one accompanying the system mode, this paper presents a novel approach for deriving density operator for a harmonic oscillator interacting with an electromagnetic field. The Fano factor and the Wigner function in evolution process have been derived.     

The geometric phase of a two-level atom in a narrow-bandwidth squeezed vacuum

In this paper, we derive the time dependent solution of the effective master equation for the reduced density matrix operator of a two level atom driven by a coherent laser field and damped by a finite bandwidth squeezed vacuum. The results show that the initial state setting, detuning parameter and Rabi frequency play important roles in the evolution of the system dynamics and geometric phase. We present a useful way for controlling the geometric phase variation for the system under consideration.     

Using a New Disentangling Technique in the Solution of the Master Equation of a Driven Damped Harmonic Oscillator by Thermo Entangled States Representation

In this study we aim to solve the amplitude damping model master equation for a driven damped harmonic oscillator under the action of a classical force with arbitrary time dependence. We use thermo entangled state representation for the density operator, but to avoid a complicated disentangling process in such solutions, we introduce a simple and concise method to extract the density operator from its thermo entangled state representation. Whereas time evolution is a classical process, this method can be effectively used.

     

量子扩散通道中Wigner算符的演化规律

众所周知,量子态的演化可用与其相应的Wigner函数演化来代替.因为量子态的Wigner函数和量子态的密度矩阵一样,都包含了概率分布和相位等信息,因此对量子态的Wigner函数进行研究,可以更加快速有效地获取量子态在演化过程的重要信息.本文从经典扩散方程出发,利用密度算符的P表示,导出了量子态密度算符的扩散方程.进一步通过引入量子算符的Weyl编序记号,给出了其对应的Weyl量子化方案.另外,借助于密度算符的另一相空间表示-Wigner函数,建立了Wigner算符在扩散通道中演化方程,并给出了其Wigner算符解的形式.本文推导出了Wigner算符在量子扩散通道中的演化规律,即演化过程中任意时刻Wigner算符的形式.在此结论的基础上,讨论了相干态经过量子扩散通道的演化情况.     

A Time-Dependent Nonequilibrium Calculational Scheme towards the Study of Temperature Fluctuations

A new perturbative scheme for interacting nonequilibrium thermal quantum fields using thermo field dynamics is outlined by explicitly considering the temporal change of the thermal vacuum as it moves through many inequivalent state vector spaces. One is then naturally led to two sources of time dependence, one from the dynamics and the other from the change of thermal vacuum, which are taken care of by the Hamiltonian and the thermal generator, respectively. To obtain a practical scheme we restrict ourselves by the demand that a spectral representation for the full propagator exists. This leads to a time dependent temperature. The addition of a diagonalization condition for the quasi-particle Hamiltonian provides the master equation for the number density. We show that our formalism is equivalent to an extended form of the path-ordering method. This formalism is a first step towards the study of the origin of heat and temperature in high-energy heavy ion collisions.     

Consistent Histories Approach to the Unruh Effect

Using the history projection operator (HPO) approach to consistent histories we rederive Unruh's result that an observer constantly accelerating through the Minkowski vacuum appears to be immersed in a thermal bath. We show that propositions about any symmetry of a system always form a consistent set and that the probabilities associated with such propositions are decided by their value in the initial state. We use this fact to postulate a condition on the decoherence functional in the HPO setup. Finally we show that the Unruh effect arises from the fact that the initial density matrix corresponding to the inertial vacuum can be written as a thermal density matrix in the Fock basis associated with the accelerating observer.     

Finite temperature vibronic spectra of harmonic surfaces: a time-dependent coupled cluster approach

An algorithm to compute vibronic spectra of harmonic surfaces including Dushinsky rotation and Hertzberg–Teller terms is described. The method, inspired by thermo field dynamics, maps the thermal density matrix onto the vacuum state and uses the time-dependent coupled cluster ansatz to propagate it in time. In the Franck–Condon approximation where the dipole matrix elements are taken to be constants, this reduces to the auto correlation function of the new vacuum. In the Hertzberg–Teller approximation, the full time evolution operator is needed. This too is governed by a closed set of equations. The theoretical development is presented along with an application to anthracene.     

Functional Fokker-Planck treatment of electromagnetic field propagation in a thermal medium

The quantum statistics of continuous space time dependent electromagnetic fields is analyzed by means of functionals. The case of a field propagating in a thermal reservoir serves as a simple example to illustrate the succeeding steps: a masterequation is derived for the density operator which is a functional of the field operators. By means of the coherent state representation for continuous fields the masterequation is transformed into a functional differential equation in the function space, spanned by the coherent state amplitudes. This equation is of the Fokker-Planck type and determines a Gaussian process for a continuum of variables or a field. It is solved by determining the characteristics in function space of the associated equation of motion for the characteristic functional and subsequent functional integration. The solution is used to calculate some correlation functions and the spectral function of the field.     

Wigner function and density operator of the photon-subtracted squeezed thermal state

By using the technique of integration within an ordered product of operators, the normal ordered density operator of the photon-subtracted squeezed thermal state (PSSTS) is derived. Then the corresponding Wigner function is presented by using the coherent state representation of the Wigner operator. The nonclassical properties of the PSSTS are discussed based on the negativity of the Wigner function.     

Density matrix of a quantum field in a particle-creating background

We examine the time evolution of a quantized field in external backgrounds that violate the stability of vacuum (particle-creating backgrounds). Our purpose is to study the exact form of the final quantum state (the density operator at the final instant of time) that has emerged from a given arbitrary initial state (from a given arbitrary density operator at the initial time instant) in the course of evolution. We find a generating functional that allows one to obtain density operators for an arbitrary initial state. Averaging over states of the subsystem of antiparticles (particles), we obtain explicit forms of reduced density operators for the subsystem of particles (antiparticles). Analyzing one-particle correlation functions, we establish a one-to-one correspondence between these functions and the reduced density operators. It is shown that in the general case a presence of bosons (e.g., gluons) in the initial state increases the creation rate of the same type of bosons. We discuss the question (and its relation to the initial stage of quark–gluon plasma formation) whether a thermal form of one-particle distribution can appear even if the final state of the complete system is not in thermal equilibrium. In this respect, we discuss some cases when pair-creation by an electric-like field can mimic the one-particle thermal distribution. We apply our technics to some QFT problems in slowly varying electric-like backgrounds: electric, SU(3) chromoelectric, and metric. In particular, we analyze the time and temperature behavior of the mean numbers of created particles, provided that the effects of switching the external field on and off are negligible. It is demonstrated that at high temperatures and in slowly varying electric fields the rate of particle-creation is essentially time-dependent.     

Evolution of quantum states via Weyl expansion in dissipative channel

Based on the Weyl expansion representation of Wigner operator and its invariant property under similar transformation, we derived the relationship between input state and output state after a unitary transformation including Wigner function and density operator. It is shown that they can be related by a transformation matrix corresponding to the unitary evolution. In addition, for any density operator going through a dissipative channel, the evolution formula of the Wigner function is also derived. As applications, we considered further the two-mode squeezed vacuum as inputs, and obtained the resulted Wigner function and density operator within normal ordering form. Our method is clear and concise, and can be easily extended to deal with other problems involved in quantum metrology, steering, and quantum information with continuous variable.