Using the coherent state representation of Wigner operator and the technique of integration within an ordered product （IWOP） of operators, this paper derives the Wigner functions for the photon-depleted even and odd...Using the coherent state representation of Wigner operator and the technique of integration within an ordered product （IWOP） of operators, this paper derives the Wigner functions for the photon-depleted even and odd coherent states （PDEOCSs）. Moreover, in terms of the Wigner functions with respect to the complex parameter a the nonclassical properties of the PDEOCSs are discussed. The results show that the nonclassicality for the state ｜β, m〉o （or ｜β,m〉e） is more pronounced when m is even （or odd）. According to the marginal distributions of the Wigner functions, the physical meaning of the Wigner functions is given. Further, the tomograms of the PDEOCSs are calculated with the aid of newly introduced intermediate coordinate-momentum representation in quantum optics.展开更多
In deformation quantization, static Wigner functions obey functional ,-genvalue equation, which is equivalent to time-independent Schrodinger equation in Hilbert space operator formalism of quantum mechanics. This equ...In deformation quantization, static Wigner functions obey functional ,-genvalue equation, which is equivalent to time-independent Schrodinger equation in Hilbert space operator formalism of quantum mechanics. This equivalence is proved mostly for Hamiltonian with form H^ = （1/2）p^2 ＋ V（x^） [D. Fairlie, Proc. Camb. Phil. Soc. 60 （1964） 581]. In this note we generalize this proof to a very general Hamiltonian H^（x^,p^） and give examples to support it.展开更多
Using the coherent state representation of Wigner operator and the technique of integration within an ordered product （IWOP） of operators, the Wigner functions of the even and odd binomial states （EOBSs） are obtai...Using the coherent state representation of Wigner operator and the technique of integration within an ordered product （IWOP） of operators, the Wigner functions of the even and odd binomial states （EOBSs） are obtained. The physical meaning of the Wigner functions for the EOBSs is given by means of their marginal distributions. Moreover, the tomograms of the EOBSs are calculated by virtue of intermediate coordinate-momentum representation in quantum optics.展开更多
Quantization of damped systems usually gives rise to complex spectra and corresponding resonant states, which do not belong to the Hilbert space. Therefore, the standard form of calculating Wigner function （WF） does...Quantization of damped systems usually gives rise to complex spectra and corresponding resonant states, which do not belong to the Hilbert space. Therefore, the standard form of calculating Wigner function （WF） does not work for these systems. In this paper we show that in order to let WF satisfy a ,-genvalue equation for the damped systems, one must modify its standard form slightly, and this modification exactly coincides with the results derived from a ＊-Exponential expansion in deformation quantization.展开更多
The major difficulty for the Feynman Path Integral Monte Carlo (PIMC) simulations of the quantum systems of particles is the so called “sign problem”, arising due to the fast oscillations of the path integral integr...The major difficulty for the Feynman Path Integral Monte Carlo (PIMC) simulations of the quantum systems of particles is the so called “sign problem”, arising due to the fast oscillations of the path integral integrand depending on the complex-valued action. Our aim is to find universal techniques being able to solve this problem. The new method combines the basic ideas of the Metropolis and Hasting algorithms and is based on the Picard-Lefschetz theory and complex-valued version of Morse theory. The basic idea is to choose the Lefschetz thimbles as manifolds approaching the saddle point of the integrand. On this thimble the imaginary part of the complex-valued action remains constant. As a result the integrand on each thimble does not oscillate, so the “sign problem” disappears and the integral can be calculated much more effectively. The developed approach allows also finding saddle points in the complexified space of path integral integration. Some simple test calculations and comparisons with available analytical results have been carried out.展开更多
Based on the integral representation of the Bessel functions and the generating function of the Tricomi function, an analytical expression of the Wigner distribution function （WDF） for a coherent or partially cohere...Based on the integral representation of the Bessel functions and the generating function of the Tricomi function, an analytical expression of the Wigner distribution function （WDF） for a coherent or partially coherent Bessel Gaussian beam is presented. The reduced two-dimensional WDFs are also demonstrated graphically, which reveals the dependence of the reduced WDFs on the beam parameters.展开更多
We find a new x-parameter squeezed coherent state （p, q）κ representation, which possesses well-behaved features, i.e., its Wigner function＇s marginal distribution in the ＂q-direction＂ and in the ＂p-direction＂ ...We find a new x-parameter squeezed coherent state （p, q）κ representation, which possesses well-behaved features, i.e., its Wigner function＇s marginal distribution in the ＂q-direction＂ and in the ＂p-direction＂ is the Gauss/an form exp（-κ（q＇ - q）2}, and exp{（p＇ - p）2/κ}, respectively. Based on this, the Husimi function of（p, q）κ is also obtained, which is a Gauss/an broaden version of the Wigner function. The （P, q）κ state provides a good representative space for studying various properties ot the Husimi operator.展开更多
In this paper, we study the Wigner function of coherent state of N components, especially two components and three components. This function consists of two terms： the Gaussian term and the interference term with the...In this paper, we study the Wigner function of coherent state of N components, especially two components and three components. This function consists of two terms： the Gaussian term and the interference term with the negativity. The first term comprises N Gaussian surfaces evenly centred on a circle of radius ｜β｜ = ｜α｜ with a separate angle of 2π/N, and the second term is composed of 1/2N（N - 1） Gaussian-cosine surfaces evenly centred in a circular region of radius ｜β｜ 〈 ｜α｜. Here, a is the eigenvalue of the annihilation operator α, and β is a variable in some complex space in which the Wigner function is defined. We have proved that the essential condition to eliminate the negativity of the Wigner function is that the mean photon count of the coherent state is equal to that of the Glouber coherent state.展开更多
By using the explicit form of the entangled Wigner operator and the entangled state representation we derive the relationship between wave function and corresponding Wigner function for bipartite entangled systems. Th...By using the explicit form of the entangled Wigner operator and the entangled state representation we derive the relationship between wave function and corresponding Wigner function for bipartite entangled systems. The technique of integration within an ordered product （IWOP） of operators is employed in our discussions.展开更多
We show that the Wigner function (an ensemble average of the density operator ρ, Δ is the Wigner operator) can be expressed as a matrix element of ρ in the entangled pure states. In doing so, converting from quant...We show that the Wigner function (an ensemble average of the density operator ρ, Δ is the Wigner operator) can be expressed as a matrix element of ρ in the entangled pure states. In doing so, converting from quantum master equations to time-evolution equation of the Wigner functions seems direct and concise. The entangled states are defined in the enlarged Fock space with a fictitious freedom.展开更多
Based on the Wigner function in local equilibrium, we derive hydrodynamical quantities for a system of polarized spin-1/2 particles: the particle number current density, the energy-momentum tensor, the spin tensor, an...Based on the Wigner function in local equilibrium, we derive hydrodynamical quantities for a system of polarized spin-1/2 particles: the particle number current density, the energy-momentum tensor, the spin tensor, and the dipole moment tensor. Compared with ideal hydrodynamics without spin, additional terms at the first and second orders in the Knudsen number Κ_(n) and the average spin polarization Χ_(s) have been derived. The Wigner function can be expressed in terms of matrix-valued distributions, whose equilibrium forms are characterized by thermodynamical parameters in quantum statistics. The equations of motion for these parameters are derived by conservation laws at the leading and next-to-leading order Κ_(n) and Χ_(s).展开更多
Using the coherent state representation of Wigner operator and the technique of integration within an ordered product （IWOP） of operators, this paper derives the Wigner function for the Hermite polynomial state （HP...Using the coherent state representation of Wigner operator and the technique of integration within an ordered product （IWOP） of operators, this paper derives the Wigner function for the Hermite polynomial state （HPS）. The tomogram of the HPS is calculated with the aid of newly introduced intermediate coordinate-momentum representation in quantum optics.展开更多
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 fun...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.展开更多
By using the technique of integration within an ordered product （IWOP） of operator we derive Wigner function of density operator for negative binomial distribution of radiation field in the mixed state case, then we...By using the technique of integration within an ordered product （IWOP） of operator we derive Wigner function of density operator for negative binomial distribution of radiation field in the mixed state case, then we derive the Wigner function of squeezed number state, which yields negative binomial distribution by virtue of the entangled state representation and the entangled Wigner operator.展开更多
This paper proves a new theorem on the relationship between optical field Wigner function＇s two-parameter Radon transform and optical Fresnel transform of the field, i.e., when an input field ψ （x＇） propagates th...This paper proves a new theorem on the relationship between optical field Wigner function＇s two-parameter Radon transform and optical Fresnel transform of the field, i.e., when an input field ψ （x＇） propagates through an optical [D （-B） （-C） A] system, the energy density of the output field is equal to the Radon transform of the Wigner function of the input field, where the Radon transform parameters are D, B. It prove this theorem in both spatial-domain and frequency-domain, in the latter case the Radon transform parameters are A, C.展开更多
This paper discusses some statistical properties of the superposition of two coherent states with a vacuum state, such as sub-Poissonian photon statistics and negativity of the Wigner function. Phase probability distr...This paper discusses some statistical properties of the superposition of two coherent states with a vacuum state, such as sub-Poissonian photon statistics and negativity of the Wigner function. Phase probability distribution and phase variance are calculated. Special cases of the constructed superposition states are presented. The results show that depending on the vacuum state coefficient γ and the coherent state coefficient a, it can generate a variety of nonclassical states.展开更多
In this paper we address the possibility of using the Wigner function to capture the quantum entanglement present in a multi-qubit system. For that purpose, we calculate both the degree of entanglement and the Wigner ...In this paper we address the possibility of using the Wigner function to capture the quantum entanglement present in a multi-qubit system. For that purpose, we calculate both the degree of entanglement and the Wigner function for mixed tripartite squeezed states of Greenberger–Horne–Zeilinger(GHZ) type then we compare their behaviors. We show that the role of Wigner function in detecting and quantifying bipartite quantum correlation [Int. J. Mod. Phys. B30(2016) 1650187] may be generalized to the multipartite case.展开更多
First we calculate the Wigner phase-space distribution function for the Klein-Gordan Landau problem ona commmutative space.Then we study the modifications introduced by the coordinate-coordinate noncommuting andmoment...First we calculate the Wigner phase-space distribution function for the Klein-Gordan Landau problem ona commmutative space.Then we study the modifications introduced by the coordinate-coordinate noncommuting andmomentum-momentum noncommuting, namely, by using a generalized Bopp’s shift method we construct the Wignerfunction for the Klein-Gordan Landau problem both on a noncommutative space (NCS) and a noncommutative phasespace (NCPS).展开更多
For investigating dynamic evolution of a mass-varying harmonic oscillator we constitute a ket-bra integrationoperator in coherent state representation and then perform this integral by virtue of the technique of integ...For investigating dynamic evolution of a mass-varying harmonic oscillator we constitute a ket-bra integrationoperator in coherent state representation and then perform this integral by virtue of the technique of integration withinan ordered product of operators.The normally ordered time evolution operator is thus obtained.We then derive theWigner function of u(t)|n>,where |n> is a Fock state,which exhibits a generalized squeezing,the squeezing effect isrelated to the varying mass with time.展开更多
We calculate Wigner function, tomogram of the pair coherent state by using its Sehmidt decomposition in the coherent state representation. It turns out that the Wigner function can be seen as the quantum entanglement ...We calculate Wigner function, tomogram of the pair coherent state by using its Sehmidt decomposition in the coherent state representation. It turns out that the Wigner function can be seen as the quantum entanglement （QE） between two two-variable Hermite polynomials （TVHP） and the tomogram is further simplified as QE of two single-variable Hermite polynomials. The Husimi function of pair coherent state is also calculated.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 Y2004A09)
文摘Using the coherent state representation of Wigner operator and the technique of integration within an ordered product （IWOP） of operators, this paper derives the Wigner functions for the photon-depleted even and odd coherent states （PDEOCSs）. Moreover, in terms of the Wigner functions with respect to the complex parameter a the nonclassical properties of the PDEOCSs are discussed. The results show that the nonclassicality for the state ｜β, m〉o （or ｜β,m〉e） is more pronounced when m is even （or odd）. According to the marginal distributions of the Wigner functions, the physical meaning of the Wigner functions is given. Further, the tomograms of the PDEOCSs are calculated with the aid of newly introduced intermediate coordinate-momentum representation in quantum optics.
基金supported by National Natural Science Foundation of China under Grant No.10675106
文摘In deformation quantization, static Wigner functions obey functional ,-genvalue equation, which is equivalent to time-independent Schrodinger equation in Hilbert space operator formalism of quantum mechanics. This equivalence is proved mostly for Hamiltonian with form H^ = （1/2）p^2 ＋ V（x^） [D. Fairlie, Proc. Camb. Phil. Soc. 60 （1964） 581]. In this note we generalize this proof to a very general Hamiltonian H^（x^,p^） and give examples to support it.
基金supported by the National Natural Science Foundation of China (Grant No 10574060)the Natural Science Foundation of Shandong Province, China (Grant No Y2008A23)
文摘Using the coherent state representation of Wigner operator and the technique of integration within an ordered product （IWOP） of operators, the Wigner functions of the even and odd binomial states （EOBSs） are obtained. The physical meaning of the Wigner functions for the EOBSs is given by means of their marginal distributions. Moreover, the tomograms of the EOBSs are calculated by virtue of intermediate coordinate-momentum representation in quantum optics.
基金The project supported by National Natural Science Foundation of China under Grant Nos. 10375056 and 10675106
文摘Quantization of damped systems usually gives rise to complex spectra and corresponding resonant states, which do not belong to the Hilbert space. Therefore, the standard form of calculating Wigner function （WF） does not work for these systems. In this paper we show that in order to let WF satisfy a ,-genvalue equation for the damped systems, one must modify its standard form slightly, and this modification exactly coincides with the results derived from a ＊-Exponential expansion in deformation quantization.
文摘The major difficulty for the Feynman Path Integral Monte Carlo (PIMC) simulations of the quantum systems of particles is the so called “sign problem”, arising due to the fast oscillations of the path integral integrand depending on the complex-valued action. Our aim is to find universal techniques being able to solve this problem. The new method combines the basic ideas of the Metropolis and Hasting algorithms and is based on the Picard-Lefschetz theory and complex-valued version of Morse theory. The basic idea is to choose the Lefschetz thimbles as manifolds approaching the saddle point of the integrand. On this thimble the imaginary part of the complex-valued action remains constant. As a result the integrand on each thimble does not oscillate, so the “sign problem” disappears and the integral can be calculated much more effectively. The developed approach allows also finding saddle points in the complexified space of path integral integration. Some simple test calculations and comparisons with available analytical results have been carried out.
文摘Based on the integral representation of the Bessel functions and the generating function of the Tricomi function, an analytical expression of the Wigner distribution function （WDF） for a coherent or partially coherent Bessel Gaussian beam is presented. The reduced two-dimensional WDFs are also demonstrated graphically, which reveals the dependence of the reduced WDFs on the beam parameters.
基金＊The project supported by the Specialized Research Fund for the Doctorial Progress of.Higher Education of China under Grant No. 20040358019
文摘We find a new x-parameter squeezed coherent state （p, q）κ representation, which possesses well-behaved features, i.e., its Wigner function＇s marginal distribution in the ＂q-direction＂ and in the ＂p-direction＂ is the Gauss/an form exp（-κ（q＇ - q）2}, and exp{（p＇ - p）2/κ}, respectively. Based on this, the Husimi function of（p, q）κ is also obtained, which is a Gauss/an broaden version of the Wigner function. The （P, q）κ state provides a good representative space for studying various properties ot the Husimi operator.
文摘In this paper, we study the Wigner function of coherent state of N components, especially two components and three components. This function consists of two terms： the Gaussian term and the interference term with the negativity. The first term comprises N Gaussian surfaces evenly centred on a circle of radius ｜β｜ = ｜α｜ with a separate angle of 2π/N, and the second term is composed of 1/2N（N - 1） Gaussian-cosine surfaces evenly centred in a circular region of radius ｜β｜ 〈 ｜α｜. Here, a is the eigenvalue of the annihilation operator α, and β is a variable in some complex space in which the Wigner function is defined. We have proved that the essential condition to eliminate the negativity of the Wigner function is that the mean photon count of the coherent state is equal to that of the Glouber coherent state.
基金The project supported by the Natural Science Foundation of Heze University of Shandong Province of China under Grant Nos.XY07WL01 and XY05WL01the University Experimental Technology Foundation of Shandong Province of China under Grant No.S04W138
文摘By using the explicit form of the entangled Wigner operator and the entangled state representation we derive the relationship between wave function and corresponding Wigner function for bipartite entangled systems. The technique of integration within an ordered product （IWOP） of operators is employed in our discussions.
文摘We show that the Wigner function (an ensemble average of the density operator ρ, Δ is the Wigner operator) can be expressed as a matrix element of ρ in the entangled pure states. In doing so, converting from quantum master equations to time-evolution equation of the Wigner functions seems direct and concise. The entangled states are defined in the enlarged Fock space with a fictitious freedom.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 11890713, 11890710, 11947301, 11935007, 11221504,11861131009, 11890714, 11890710, and 12047528)the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No. XDB34030102)。
文摘Based on the Wigner function in local equilibrium, we derive hydrodynamical quantities for a system of polarized spin-1/2 particles: the particle number current density, the energy-momentum tensor, the spin tensor, and the dipole moment tensor. Compared with ideal hydrodynamics without spin, additional terms at the first and second orders in the Knudsen number Κ_(n) and the average spin polarization Χ_(s) have been derived. The Wigner function can be expressed in terms of matrix-valued distributions, whose equilibrium forms are characterized by thermodynamical parameters in quantum statistics. The equations of motion for these parameters are derived by conservation laws at the leading and next-to-leading order Κ_(n) and Χ_(s).
基金Project supported by the National Natural Science Foundation of China （Grant No 10574060） and the Natural Science Foundation of Shandong Province of China （Grant No Y2004A09）.
文摘Using the coherent state representation of Wigner operator and the technique of integration within an ordered product （IWOP） of operators, this paper derives the Wigner function for the Hermite polynomial state （HPS）. The tomogram of the HPS is calculated with the aid of newly introduced intermediate coordinate-momentum representation in quantum optics.
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
文摘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.
基金the Natural Science Foundation of Heze University of Shandong Province of China under Grant Nos.XY07WL01 and XY05WL01the University Experimental Technology Foundation of Shandong Province of China under Grant No.S04W138
文摘By using the technique of integration within an ordered product （IWOP） of operator we derive Wigner function of density operator for negative binomial distribution of radiation field in the mixed state case, then we derive the Wigner function of squeezed number state, which yields negative binomial distribution by virtue of the entangled state representation and the entangled Wigner operator.
基金supported by the National Natural Science Foundation of China (Grant Nos 10775097 and 10874174)
文摘This paper proves a new theorem on the relationship between optical field Wigner function＇s two-parameter Radon transform and optical Fresnel transform of the field, i.e., when an input field ψ （x＇） propagates through an optical [D （-B） （-C） A] system, the energy density of the output field is equal to the Radon transform of the Wigner function of the input field, where the Radon transform parameters are D, B. It prove this theorem in both spatial-domain and frequency-domain, in the latter case the Radon transform parameters are A, C.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10674038 and 10974039)the National Basic Research Program of China (Grant No. 2006CB302901)
文摘This paper discusses some statistical properties of the superposition of two coherent states with a vacuum state, such as sub-Poissonian photon statistics and negativity of the Wigner function. Phase probability distribution and phase variance are calculated. Special cases of the constructed superposition states are presented. The results show that depending on the vacuum state coefficient γ and the coherent state coefficient a, it can generate a variety of nonclassical states.
文摘In this paper we address the possibility of using the Wigner function to capture the quantum entanglement present in a multi-qubit system. For that purpose, we calculate both the degree of entanglement and the Wigner function for mixed tripartite squeezed states of Greenberger–Horne–Zeilinger(GHZ) type then we compare their behaviors. We show that the role of Wigner function in detecting and quantifying bipartite quantum correlation [Int. J. Mod. Phys. B30(2016) 1650187] may be generalized to the multipartite case.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10965006 and 10875035
文摘First we calculate the Wigner phase-space distribution function for the Klein-Gordan Landau problem ona commmutative space.Then we study the modifications introduced by the coordinate-coordinate noncommuting andmomentum-momentum noncommuting, namely, by using a generalized Bopp’s shift method we construct the Wignerfunction for the Klein-Gordan Landau problem both on a noncommutative space (NCS) and a noncommutative phasespace (NCPS).
基金Supported by National Natural Science Foundation of China under Grant No.10874174
文摘For investigating dynamic evolution of a mass-varying harmonic oscillator we constitute a ket-bra integrationoperator in coherent state representation and then perform this integral by virtue of the technique of integration withinan ordered product of operators.The normally ordered time evolution operator is thus obtained.We then derive theWigner function of u(t)|n>,where |n> is a Fock state,which exhibits a generalized squeezing,the squeezing effect isrelated to the varying mass with time.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10775097 and 10874174the Research Foundation of the Education Department of Jiangxi Province
文摘We calculate Wigner function, tomogram of the pair coherent state by using its Sehmidt decomposition in the coherent state representation. It turns out that the Wigner function can be seen as the quantum entanglement （QE） between two two-variable Hermite polynomials （TVHP） and the tomogram is further simplified as QE of two single-variable Hermite polynomials. The Husimi function of pair coherent state is also calculated.
