Fan Yue

New Bosonic Operator Ordering Identities Gained by the Entangled State Representation and Two-Variable Hermite Polynomials*

Based on the technique of integration within an ordered product of operators, we derive new bosonic operators, ordering identities by using entangled state representation and the properties of two-variable Hermite polynomials , and vice versa. In doing so, some concise normally (antinormally) ordering operator identities, such as : are obtained.

Angular Momentum-Phase Coherent State for an Electron in Uniform Magnetic Field

Based on the newly constructed state |l,r [Fan et al., Chin. Phys. Lett. 16(1999)706], where l is the angular momentum quantum number and r denotes the electrons orbit radius in a uniform magnetic field, we propose a new angular momentum-phase coherent state by introducing a new operator A. A and A? are annihilation and creation operators in the |l,r space, respectively. The coherent state is As eigenket and possesses non-orthonormal and overcomplete properties. It is constructed on the certain superposition of zero-angular momentum states along the radius direction.

New Eigenmodes of Propagation in Quadratic Graded Index Media and Complex Fractional Fourier Transform

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.

New Representation for Squeezing-Rotating Entangled Unitary Transformation

We introduce a new unitary operator which can engender a squeezing and rotating entangled transformation. The operator has a concise expression in a new representation in two-mode Fock space. The normally ordered form of can be derived by using the technique of integration within an ordered product of operators. The fluctuation in quadrature phases for these squeezing-rotating entangled states are analyzed.

Teleportation of a Two-Mode Squeezed State

By virtue of the Einstein-Podolsky-Rosen (EPR) pair eigenstates |η we derive the result of quantum teleportation of a two-mode squeezed state. The calculation can be greatly simplified by using the natural representation of the two-mode squeezing operator in the complete and orthonormal |η representation.

Fractional Fourier Transformation for Quantum Mechanical Wave Functions Studied by Virtue of IWOP Technique

Starting from the optical fractional Fourier transform (FFT) and using the technique of integration within an ordered product of operators we establish a formalism of FFT for quantum mechanical wave functions. In doing so, the essence 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. They are generalized FFT. The relationship between the FFT and the rotated Wigner operator is studied by virtue of the Weyl ordered form of the Wigner operator.

Squeezing and displacing related two-mode squeezed coherent state

A type of special two-mode squeezed coherent state is constructed which is a characteristic of squeezing and displacing related. The new states take simpler and neater form than the usual two-mode squeezed coherent states, and also passes. a completeness relation. It is expected that experimentalists woking on quantum optics should fabricate such a type of squeezed coherent optical field.

``Eigen-Operator" Method of the Square of Schrödinger Operator in Interaction Picture and Its Application in Describing Parametric Amplifiers*

We extend the method of searching ``eigen-operator of the square of the Schrodinger operator to the interaction picture, which not only helps to construct Hamiltonians of two kinds of parametric amplifiers but also leads to a new uncertainty relation regarding to the free Hamiltonian and the interacting Hamiltonian.

Landau Wavefunction Immediately Derived by Virtue of the 〈λ| Representation

We show that by virtue of the 〈λ| representation (Hong-Yi Fan, Phys. Lett. A 126 (1987) 150) the Landau wavefunctions of an electron in a uniform magnetic field can be immediately derived without solving the corresponding Schrodinger equation. It turns out that the differential operation form of the electrons dynamic Hamiltonian, adopted in standard quantum mechanics textbooks, is actually expressed in 〈λ| representation.

Normally Ordered Quantum Gate Operators for Continuum Variables as Images of Classical Transforms

We derive normally ordered quantum gate operators for continuum variables by mapping classical transforms onto Fock space. Successive gate operations can be treated in a unified way that is using the technique of integration within an ordered product of operators.