In this paper we find that a set of energy eigenstates of a two-dimensional anisotropic harmonic potential in a uniform magnetic field is classified as the atomic coherent states ｜τ） in terms of the spin values of ...In this paper we find that a set of energy eigenstates of a two-dimensional anisotropic harmonic potential in a uniform magnetic field is classified as the atomic coherent states ｜τ） in terms of the spin values of j in the Schwinger bosonic realization. The correctness of the above conclusions can be verified by virtue of the entangled state 〈η｜ representation of the state ｜τ）.展开更多
We discuss quantum fluctuation in excited states （named thermo number states） of mesoscopic LC circuits at a finite temperature. By introducing the coherent thermo state into the thermo field dynamics pioneered by U...We discuss quantum fluctuation in excited states （named thermo number states） of mesoscopic LC circuits at a finite temperature. By introducing the coherent thermo state into the thermo field dynamics pioneered by Umezawa and using the natural representation of thermo squeezing operator we can concisely derive the fluctuation. The result shows that the noise becomes larger when either temperature or the excitation number increases.展开更多
We study how can an angular momentum coherent state |τ> keeps its form-invariant during time evolution governed by the Hamiltonian H = f(t)J++ f^*(t)J-+ g(t)Jz. We discuss this topic in the context of boson realiz...We study how can an angular momentum coherent state |τ> keeps its form-invariant during time evolution governed by the Hamiltonian H = f(t)J++ f^*(t)J-+ g(t)Jz. We discuss this topic in the context of boson realization of |τ>. By employing the entangled state representation |ζ> and deriving a new binomial theorem involving two-subscript Hermite polynomials, we derive the wave function <ζ|τ>, which turns out to be a single-subscript Hermite polynomial. Based on this result the maintenance of angular momentum coherent state during time evolution is examined, and the value of τ(t) is totally determined by the parameters involved in the Hamiltonian.展开更多
Based on the Einstein, Podolsky, and Rosen （EPR） entangled state representation, this paper introduces the wave function for the squeezed atomic coherent state （SACS）, which turns out to be just proportional to a ...Based on the Einstein, Podolsky, and Rosen （EPR） entangled state representation, this paper introduces the wave function for the squeezed atomic coherent state （SACS）, which turns out to be just proportional to a single-variable ordinary Hermite polynomial of order 2j. As important applications of the wave function, the Wigner function of the SACS and its marginal distribution are obtained and the eigenproblems of some Hamiltonians for the generalized angular momentum system are solved.展开更多
This paper introduces the generalized excited pair coherent state （GEPCS）. Using the entangled state 〈η〉 representation of Wigner operator, it obtains the Wigner function for the GEPCS. In the ρ-γ phase space, ...This paper introduces the generalized excited pair coherent state （GEPCS）. Using the entangled state 〈η〉 representation of Wigner operator, it obtains the Wigner function for the GEPCS. In the ρ-γ phase space, the variations of the Wigner function distributions with the parameters q, α, k and l are discussed. The tomogram of the GEPCS is calculated with the help of the Radon transform between the Wigner operator and the projection operator of the entangled state ｜η1, η2, τ1, τ2｜. The entangled states ｜η〉 and ｜η1, η2, τ1, τ2〉 provide two good representative space for studying the Wigner functions and tomograms of various two-mode correlated quantum states.展开更多
This paper constructs a new type of finite-dimensional thermal coherent states （FDTCS）, which differs from the proceeding thermal coherent state in construction, as realisations of SU（2） Lie algebra. Using the tec...This paper constructs a new type of finite-dimensional thermal coherent states （FDTCS）, which differs from the proceeding thermal coherent state in construction, as realisations of SU（2） Lie algebra. Using the technique of integration within an ordered product of operator, it investigates the orthonormality and completeness relation of the FDTCS. Based on the thermal Wigner operator in the thermal entangled state representation, the Wigner function of the FDTCS is obtained. The nonclassical properties of the FDTCS are discussed in terms of the negativity of its Wigner function.展开更多
Based on the newly developed coherent-entangled state representation,we propose the so-called Fresnel-Weyl complementary transformation operator.The new operator plays the roles of both Fresnel transformation（for（a ...Based on the newly developed coherent-entangled state representation,we propose the so-called Fresnel-Weyl complementary transformation operator.The new operator plays the roles of both Fresnel transformation（for（a 1 a 2）/√ 2） and the Weyl transformation（for（a 1 ＋ a 2）/√ 2）.Physically,（a 1 a 2）/√ 2 and（a 1 ＋ a 2）/√ 2 could be a symmetric beamsplitter＇s two output fields for the incoming fields a 1 and a 2.We show that the two transformations are concisely expressed in the coherent-entangled state representation as a projective operator in the integration form.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 10574060)the Natural Science Foundation of Shandong Province of China (Grant No. Y2008A23)the Shandong Provincal Higher Educational Science and Technology Program of China (Grant Nos. J09LA07 and J10LA15)
文摘In this paper we find that a set of energy eigenstates of a two-dimensional anisotropic harmonic potential in a uniform magnetic field is classified as the atomic coherent states ｜τ） in terms of the spin values of j in the Schwinger bosonic realization. The correctness of the above conclusions can be verified by virtue of the entangled state 〈η｜ representation of the state ｜τ）.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10574060 and 10775097)the Natural Science Foundation of Shandong Province of China (Grant No. Y2008A23)the Shandong Province Higher Educational Science and Technology Program (Grant No. J09LA07)
文摘We discuss quantum fluctuation in excited states （named thermo number states） of mesoscopic LC circuits at a finite temperature. By introducing the coherent thermo state into the thermo field dynamics pioneered by Umezawa and using the natural representation of thermo squeezing operator we can concisely derive the fluctuation. The result shows that the noise becomes larger when either temperature or the excitation number increases.
基金Project supported by the National Natural Science Foundation of China(Grant No.11347026)the Natural Science Foundation of Shandong Province,China(Grant Nos.ZR2016AM03 and ZR2017MA011)
文摘We study how can an angular momentum coherent state |τ> keeps its form-invariant during time evolution governed by the Hamiltonian H = f(t)J++ f^*(t)J-+ g(t)Jz. We discuss this topic in the context of boson realization of |τ>. By employing the entangled state representation |ζ> and deriving a new binomial theorem involving two-subscript Hermite polynomials, we derive the wave function <ζ|τ>, which turns out to be a single-subscript Hermite polynomial. Based on this result the maintenance of angular momentum coherent state during time evolution is examined, and the value of τ(t) is totally determined by the parameters involved in the Hamiltonian.
基金Project supported by the Natural Science Foundation of Shandong Province, China (Grant No. Y2008A23)
文摘Based on the Einstein, Podolsky, and Rosen （EPR） entangled state representation, this paper introduces the wave function for the squeezed atomic coherent state （SACS）, which turns out to be just proportional to a single-variable ordinary Hermite polynomial of order 2j. As important applications of the wave function, the Wigner function of the SACS and its marginal distribution are obtained and the eigenproblems of some Hamiltonians for the generalized angular momentum system are solved.
基金supported by the National Natural Science Foundation of China (Grant No 10574060)the Natural Science Foundation of Shandong Province of China (Grant No Y2004A09)
文摘This paper introduces the generalized excited pair coherent state （GEPCS）. Using the entangled state 〈η〉 representation of Wigner operator, it obtains the Wigner function for the GEPCS. In the ρ-γ phase space, the variations of the Wigner function distributions with the parameters q, α, k and l are discussed. The tomogram of the GEPCS is calculated with the help of the Radon transform between the Wigner operator and the projection operator of the entangled state ｜η1, η2, τ1, τ2｜. The entangled states ｜η〉 and ｜η1, η2, τ1, τ2〉 provide two good representative space for studying the Wigner functions and tomograms of various two-mode correlated quantum states.
基金Project supported by the National Natural Science Foundation of China(Grant No.10574060)the Natural Science Foundation of Shandong Province,China(Grant No.Y2008A23and ZR2010AQ027)the Shandong Province Higher Educational Science and Technology Program,China(Grant Nos.J09LA07and J10LA15).
文摘This paper constructs a new type of finite-dimensional thermal coherent states （FDTCS）, which differs from the proceeding thermal coherent state in construction, as realisations of SU（2） Lie algebra. Using the technique of integration within an ordered product of operator, it investigates the orthonormality and completeness relation of the FDTCS. Based on the thermal Wigner operator in the thermal entangled state representation, the Wigner function of the FDTCS is obtained. The nonclassical properties of the FDTCS are discussed in terms of the negativity of its Wigner function.
基金Project supported by the Doctoral Scientific Research Startup Fund of Anhui University,China (Grant No. 33190059)the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20113401120004)the Open Funds from National Laboratory for Infrared Physics,Chinese Academy of Sciences (Grant No. 201117)
文摘Based on the newly developed coherent-entangled state representation,we propose the so-called Fresnel-Weyl complementary transformation operator.The new operator plays the roles of both Fresnel transformation（for（a 1 a 2）/√ 2） and the Weyl transformation（for（a 1 ＋ a 2）/√ 2）.Physically,（a 1 a 2）/√ 2 and（a 1 ＋ a 2）/√ 2 could be a symmetric beamsplitter＇s two output fields for the incoming fields a 1 and a 2.We show that the two transformations are concisely expressed in the coherent-entangled state representation as a projective operator in the integration form.
