By introducing a convenient complex form of the α-th 2-dimensional fractional Fourier transform (CFFT) operation we find that it possesses new eigenmodes which are two-mode Hermite polynomials. We prove the eigenvalu...By introducing a convenient complex form of the α-th 2-dimensional fractional Fourier transform (CFFT) operation we find that it possesses new eigenmodes which are two-mode Hermite polynomials. We prove the eigenvalues of propagation in quadratic graded-index medium over a definite distance are the same as the eigenvalues of the α-th CFFT, which means that our definition of the α-th CFFT is physically meaningful.展开更多
Based on the technique of integration within an ordered product of operators, we derive new bosonicoperators' ordering identities by using entangled state representation and the properties of two-variable Hermite ...Based on the technique of integration within an ordered product of operators, we derive new bosonicoperators' ordering identities by using entangled state representation and the properties of two-variable Hermite poly-nomials H and vice versa. In doing so, some concise normally (antinormally) ordering operator identities, such asa+man =:Hm,n(a+,a):, ana+m = (-i)m+n:Hm,n(ia+,ia): are obtained.展开更多
Starting from the optical fractional Fourier transform (FFT) and using the technique of integration withinan ordered product of operators we establish a formalism of FFT for quantum mechanical wave functions. In doing...Starting from the optical fractional Fourier transform (FFT) and using the technique of integration withinan ordered product of operators we establish a formalism of FFT for quantum mechanical wave functions. In doing so, theessence of FFT can be seen more clearly, and the FFT of some wave functions can be derived more directly and concisely.We also point out that different FFT integral kernels correspond to different quantum mechanical representations. Theyare generalized FFT. The relationship between the FFT and the rotated Wigner operator is studied by virtue of theWeyl ordered form of the Wigner operator.展开更多
By virtue of the neat expression of the two-mode squeezing operator in the Einstein,Podolsky and Rosen entangled state representation,we provide a new approach for discussing the teleportation scheme using optical squ...By virtue of the neat expression of the two-mode squeezing operator in the Einstein,Podolsky and Rosen entangled state representation,we provide a new approach for discussing the teleportation scheme using optical squeezers and photon counting devices.We derive the explicit form of the teleported states,so that the conditional property of teleportation and teleportation fidelity of this protocol can be scen more clcarly.The derivation is concise.展开更多
On the assumption that a Cooper pair acts as a Bose particle and based on the newly established <η|representation, which is the common eigenvector of two particles' relative position and total momentum, we int...On the assumption that a Cooper pair acts as a Bose particle and based on the newly established <η|representation, which is the common eigenvector of two particles' relative position and total momentum, we introduce a mesoscopic Josephson junction Hamiltonian constituted by two-mode Bose phase operator and number-difference operator. The number-difference-phase uncertainty relation can then be set up, which implies the existence of Josephson current.展开更多
文摘By introducing a convenient complex form of the α-th 2-dimensional fractional Fourier transform (CFFT) operation we find that it possesses new eigenmodes which are two-mode Hermite polynomials. We prove the eigenvalues of propagation in quadratic graded-index medium over a definite distance are the same as the eigenvalues of the α-th CFFT, which means that our definition of the α-th CFFT is physically meaningful.
文摘Based on the technique of integration within an ordered product of operators, we derive new bosonicoperators' ordering identities by using entangled state representation and the properties of two-variable Hermite poly-nomials H and vice versa. In doing so, some concise normally (antinormally) ordering operator identities, such asa+man =:Hm,n(a+,a):, ana+m = (-i)m+n:Hm,n(ia+,ia): are obtained.
文摘Starting from the optical fractional Fourier transform (FFT) and using the technique of integration withinan ordered product of operators we establish a formalism of FFT for quantum mechanical wave functions. In doing so, theessence of FFT can be seen more clearly, and the FFT of some wave functions can be derived more directly and concisely.We also point out that different FFT integral kernels correspond to different quantum mechanical representations. Theyare generalized FFT. The relationship between the FFT and the rotated Wigner operator is studied by virtue of theWeyl ordered form of the Wigner operator.
基金the President Foundation of the Chinese Academy of Sciences，National Natural Science Foundation of China
文摘By virtue of the neat expression of the two-mode squeezing operator in the Einstein,Podolsky and Rosen entangled state representation,we provide a new approach for discussing the teleportation scheme using optical squeezers and photon counting devices.We derive the explicit form of the teleported states,so that the conditional property of teleportation and teleportation fidelity of this protocol can be scen more clcarly.The derivation is concise.
文摘On the assumption that a Cooper pair acts as a Bose particle and based on the newly established <η|representation, which is the common eigenvector of two particles' relative position and total momentum, we introduce a mesoscopic Josephson junction Hamiltonian constituted by two-mode Bose phase operator and number-difference operator. The number-difference-phase uncertainty relation can then be set up, which implies the existence of Josephson current.
