| Quantum optics is a new discipline which comes into being in the cross development of quantum mechanics and classical optics,making it an important part of modern optics.Beginning in the middle and late twentieth century,it is only 60 years old so far.Its founding mark is the experiment by Hanbury Brown-Twiss,which is about the intensity correlation of the light field and the quantum explanation to it,and the study of the quantum statistics of the laser.As is known,the phase correlation of the light field shows the wave characteristics,and the correlation of the intensity shows the quantum statistical properties of the photon.The object of the study of quantum optics is the quantum statistical properties of the light field and the microscopic process of the interaction between field and object as well as the exploration of new quantum light fields.It can be said that the quantum statistical theory of the light field is the core theory of quantum optics.Because most of the systems in nature are in the thermal environment,the process of excitation and reactivation of the system is bound to be influenced by the energy exchange between the system and the thermal environment.The existence of the environment can provide both a certain amount of excitation quantum and the dissipation of the system.According to the knowledge of quantum mechanics,the quantum state of the thermal dynamic equilibrium can usually be represented by the density matrix of the mixed state in the non zero temperature condition.The expected value of a physical quantity of a quantum system is equal to the trace of the matrix and product,but the real value of a quantum system is equal to that of the product.But in practice,the calculation and operation of this method are more complicated and difficult.To study the physical systems in the thermal environment in a more convenient way,in 1975 physicists Takahashi and Umezawa jointly put forward the theory of thermal field dynamics,in which a "virtual" degree of freedom is introduced and the concept of thermal vacuum state is proposed.They have converted the calculation of the expected value of the mixed state of the subsystem to the calculation of the expected value of the equivalent pure state in the non zero temperature condition.The cost is that the degree of freedom of the quantum system will double.But their thermal field dynamics theory of the subsystem is also deficient,which only gives the thermal vacuum state corresponding to the chaotic field and the method is only in the initial stage.On the basis of the existing partial trace theory of predecessors,here a new method for the construction of thermal vacuum state is proposed,which can construct a corresponding thermal vacuum state for complex quantum systems using the technique of integration within an ordered product of operators(abbreviated IWOP technique).Its advantages are:1)The calculation of the ensemble average of the quantity can be converted into the calculation of the expected value under the pure state,which greatly simplifies the calculation of the expectation of quantum statistics.It can make it more convenient for us to study the non-classical properties of the new light field.and the evolution of the quantum channel.2)The entangled state of the quantum system and the thermal environment can be present in the thermal vacuum.It is convenient for us to further the study on the evolution of the system in various quantum channels(such as laser,attenuation etc).3)the entropy and entropy change of the quantum system can be easily calculated in the thermal vacuum state.4)The introduction of the thermal vacuum state is beneficial to the discovery of the new light field in theory.In order to understand the essence of light,we need to construct a new light field and analyze its new properties.For example,the laser field constructed in the 1960s is a new light source compared to chaotic light,which belongs to the coherent state.The study of the properties of the coherent state makes it possible for us to realize that the coherence of the light and the Poisson distribution.Compressed light field contrusted in the 1970s illustrates the anti bunching effect,the subpoisson distribution and other non classical characteristics.It is obvious that the construction of different new light fields is beneficial to explore the nature of light,which is of great physical significance.Here a number of new quantum mechanical light fields are constructed,and their thermal vacuum states are simulated to trace the main non classical characteristics of light by using the method of density matrix.The main contents of this article are as follows1.The Weyl transformation and the Weyl correspondence are introduced,including the Weyl sequence form of the Wigner operator.By using the Weyl ordering from of the coherent state |z??z|=2:e-2(a+-=*)(a-:):,the Weyl-Wigner classical correspondence of the phase operator of the optical field is found.2.A Gaussian-enhanced chaotic light field is constructed,and the thermal vacuum state is obtained through the partial trace and IWOP technique.It is convenient for us to study the statistical properties of the Gaussian-enhanced chaotic light field,and calculate the photon number distribution,the quantum fluctuation and the second-order degree of coherence.3.A single-mode photon-addition for the two-mode squeezed state is constructed,that is Clb*/S2(?)|00?.S2(?)= exp[?(a*b*-ab)]is the two-mode compression operator;Cl is the normalization constant.The quantum statistical properties of the new light field is discussed.The result show that the light field exhibits bunching effect.4.Based on the Kraus operator corresponding to amplitude damping,the evolution law of a DTS has been obtained as an intermediate state between thermal and coherent in this channel.It clearly finds that the initial DTS still remain mixed and thermal with the exponential decay after interacting with amplitude damping.Photon number decay and Wigner function evolution in this channel are directly related to the mixedness M of a Gaussian noise and the displacement d in the phase space,however the entropy evolution only depends on the noise mixedness M.5.By using the hot entangled state method,the main equation on how the damping harmonic oscillator is affected by the linear resonance force in the compressed heat reservoir is solved,and the analytic evolution form in the infinite Kraus operator and the density operator in the representation is found out.The damping and thermal noise can destroy the coherence of the initial coherent state and convert it into a complex mixed state.6.The thermal vacuum state corresponding to the quantized mesoscopic RLC circuit is obtained.The ensemble average energy stored in the element and the element consumed in the element are calculated respectively by applying the state.A new method of calculating the quantum entropy at the finite temperature S =-K??(?)|In ?|?(?)?is proposed to replace the traditional formula S =-kTr[?In ?]and the entropy on the element of the mesoscopic circuit is found out. |
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