By introducing the s-parameterized generalized Wigner operator into phase-space quantum mechanics we invent the technique of integration within s-ordered product of operators (which considers normally ordered, antino...By introducing the s-parameterized generalized Wigner operator into phase-space quantum mechanics we invent the technique of integration within s-ordered product of operators (which considers normally ordered, antinormally ordered and Weyl ordered product of operators as its special cases). The s-ordered operator expansion (denoted by s…s ) formula of density operators is derived, which isρ=2/1-s∫d^2β/π〈-β|ρ|β〉sexp{2/s-1(s|β|^2-β*α+βa-αα)}s The s-parameterized quantization scheme is thus completely established.展开更多
A general framework applicable to deriving the s-ordered operator expansions is presented in this paper.We firstly deduce the s-ordered operator expansion formula of density operator ρ a?,a and introduce the techniqu...A general framework applicable to deriving the s-ordered operator expansions is presented in this paper.We firstly deduce the s-ordered operator expansion formula of density operator ρ a?,a and introduce the technique of integration within the sordered product of operators (IWSOP).Based on the deduction and the technique,we derive the s-ordered expansions of operators (μX + νP)n and Hn (μX + νP) (linear combinations of the coordinate operator X and the momentum operator P,Hn (x) is Hermite polynomial),respectively,and discuss some special cases of s=1,0,-1.Some new useful operator identities are obtained as well.展开更多
Nonclassical states play a crucial role in both theoretical and experimental investigations of quantum optics, and there is a wide interest in characterization and quantification of nonclassicality. By exploiting the ...Nonclassical states play a crucial role in both theoretical and experimental investigations of quantum optics, and there is a wide interest in characterization and quantification of nonclassicality. By exploiting the freedom of the parameter s in the s-ordered phase-space distribution introduced by Cahill and Glauber [Phys. Rev. 177, 1882(1969)], we develop a method to reveal and quantify optical nonclassicality via the divided difference of the s-ordered phase-space distribution. Our approach yields naturally a family of quantifiers of optical nonclassicality, which have many desirable properties such as convexity and monotonicity under the Gaussian noise channels. The quantifiers are illustrated by evaluating nonclassicality of several typical states. Two simple and convenient criteria for nonclassicality are established, which in particular certify all nonclassical Gaussian states.展开更多
In reference to the Weyl ordering xmpn→ (1/2)m ∑l=0m (ml)Xm-lPnXl , where X and P are coordinate and momentum operator, respectively, this paper examines operators' s-parameterized ordering and its classical co...In reference to the Weyl ordering xmpn→ (1/2)m ∑l=0m (ml)Xm-lPnXl , where X and P are coordinate and momentum operator, respectively, this paper examines operators' s-parameterized ordering and its classical correspondence, finds the fundamental function-operator correspondence (1-s/2)(n+m)/2Hm,n(/2/1-sα,/2/1-sα)→αman and its complementary relation anam→(-i)n+m(1-s/2)(m+n)/2:Hm,n(i√2/1-sa,i√2/1-sa),where Hrn,n is the two-variable Hermite polynomial, a, at are bosonic annihilation and creation operators respectively, s is a complex parameter. The s'-ordered operator power-series expansion of s-ordered operator atraan in terms of the two-variable Hermite polynomial is also derived. Application of operators' s-ordering formula in studying displaced- squeezed chaotic field is discussed.展开更多
Based on the theory of integration within s-ordering of operators and the bipartite entangled state representation we introduce s-parameterized Weyl-Wigner correspondence in the entangled form. Some of its application...Based on the theory of integration within s-ordering of operators and the bipartite entangled state representation we introduce s-parameterized Weyl-Wigner correspondence in the entangled form. Some of its applications in quantum optics theory are presented as well.展开更多
Using the newly introduced general ordering theorem by Sh/ihandeh and Bazrafkan, we derive and generalize some quantum optical identities and give their applications.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10775097 and 10874174)
文摘By introducing the s-parameterized generalized Wigner operator into phase-space quantum mechanics we invent the technique of integration within s-ordered product of operators (which considers normally ordered, antinormally ordered and Weyl ordered product of operators as its special cases). The s-ordered operator expansion (denoted by s…s ) formula of density operators is derived, which isρ=2/1-s∫d^2β/π〈-β|ρ|β〉sexp{2/s-1(s|β|^2-β*α+βa-αα)}s The s-parameterized quantization scheme is thus completely established.
基金the support from the National Natural Science Foundation of China (Grant Nos. 10775097 and 10874174)the Specialized Research Fund for the Doctoral Program of Higher Education(Grant No. 20070358009)
文摘A general framework applicable to deriving the s-ordered operator expansions is presented in this paper.We firstly deduce the s-ordered operator expansion formula of density operator ρ a?,a and introduce the technique of integration within the sordered product of operators (IWSOP).Based on the deduction and the technique,we derive the s-ordered expansions of operators (μX + νP)n and Hn (μX + νP) (linear combinations of the coordinate operator X and the momentum operator P,Hn (x) is Hermite polynomial),respectively,and discuss some special cases of s=1,0,-1.Some new useful operator identities are obtained as well.
基金supported by the National Natural Science Foundation of China(Grant Nos.11975026,and 12125402)National Key R&D Program of China(Grant No.2020YFA0712700)+2 种基金China Postdoctoral Science Foundation(Grant No.2021M690414)Beijing Postdoctoral Research Foundation(Grant No.2021ZZ091)Beijing Natural Science Foundation(Grant No.Z190005)。
文摘Nonclassical states play a crucial role in both theoretical and experimental investigations of quantum optics, and there is a wide interest in characterization and quantification of nonclassicality. By exploiting the freedom of the parameter s in the s-ordered phase-space distribution introduced by Cahill and Glauber [Phys. Rev. 177, 1882(1969)], we develop a method to reveal and quantify optical nonclassicality via the divided difference of the s-ordered phase-space distribution. Our approach yields naturally a family of quantifiers of optical nonclassicality, which have many desirable properties such as convexity and monotonicity under the Gaussian noise channels. The quantifiers are illustrated by evaluating nonclassicality of several typical states. Two simple and convenient criteria for nonclassicality are established, which in particular certify all nonclassical Gaussian states.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10775097 and 10874174)
文摘In reference to the Weyl ordering xmpn→ (1/2)m ∑l=0m (ml)Xm-lPnXl , where X and P are coordinate and momentum operator, respectively, this paper examines operators' s-parameterized ordering and its classical correspondence, finds the fundamental function-operator correspondence (1-s/2)(n+m)/2Hm,n(/2/1-sα,/2/1-sα)→αman and its complementary relation anam→(-i)n+m(1-s/2)(m+n)/2:Hm,n(i√2/1-sa,i√2/1-sa),where Hrn,n is the two-variable Hermite polynomial, a, at are bosonic annihilation and creation operators respectively, s is a complex parameter. The s'-ordered operator power-series expansion of s-ordered operator atraan in terms of the two-variable Hermite polynomial is also derived. Application of operators' s-ordering formula in studying displaced- squeezed chaotic field is discussed.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.10775097 and 10874174)the President Foundation of the Chinese Academy of Sciences
文摘Based on the theory of integration within s-ordering of operators and the bipartite entangled state representation we introduce s-parameterized Weyl-Wigner correspondence in the entangled form. Some of its applications in quantum optics theory are presented as well.
基金Project supported by the Imam Khomeini International University,I. R. Iran (Grant Nos. 751075-91 and 383042-91)
文摘Using the newly introduced general ordering theorem by Sh/ihandeh and Bazrafkan, we derive and generalize some quantum optical identities and give their applications.