In similar to the relation between the coherent state and the Bargmann transform, we find a generalized Bargmann transformation naturally accompanying Einstein–Podolsky–Rosen (EPR) entangled state of continuous variables. The new Bargmann transform kernel is introduced which can naturally lead to the entangled state. The generalized Bargmann representation of two-mode Fock state is a two-variable Hermite polynomial.

Via the route of developing Dirac's symbolic method by virtue of the technique of integration within an ordered product (IWOP) of operators we derive various entan-gled state representations, squeezed states, and operator ordering formulae. We show how the entangled states can be applied to many aspects of quantum optics theory. The applications of the entangled states in the interdisciplinary study of quantum optics and Fourier optics are also introduced. All these discussions exhibit the power of Dirac's symbolic method with the aid of the IWOP technique.

finite temperature we construct a new thermal excitation representation |E,g>, which is the common eigenvector of Hamiltonian operator of total system (including the reservoir) and the operator (α(β)−ã†(β))(α†(β)−ã(β)), where α†(β) (ã†(β)) creates a quantum of energy hω(β) (−hω(β)), respectively, β=ãh/kT, k is the Boltzmann constant. The explicit from of |E,g> is derived by virtue of the common eigenvector α(β)− ã†(β) and α†(β)− ã(β). The thermo excitation and de-excitation operations are manifestly displayed in |E,g> representation. As an application, the |E,g> representation of thermal squeezing operator is obtained.

We develop Dirac's representation theory in quantum mechanics by constructing the nonlinear entangled state |η nl and its non-Hermite conjugate state nl η| with continuum variable. By virtue of the technique of integration within an ordered product of operators we show that |η nl and nl η| make up an orthonormal and complete representation. From |η nl we also deduce another kind of entangled states. Application of |η nl in studying two-mode squeezed state is demonstrated.

We propose a concise quantization scheme for mesoscopic electric circuits which is in accord with the discreteness of electric charge. Our scheme is based on finding the correct explicit form of charge ascending and lowering operators. The charge eigenstate are derived from the appropriate entangled state representation. We show how the entangled state representation can play the role of constructing a concise and natural quantization scheme for mesoelectronics.

We propose the conception of invariant 'eigen-operator' of the square of the Schr

We employ the EPR eigenstate representation |η and the operational phase operator to propose a protocol of quantum dense coding. The |η state provides a convenient way to realize quantum dense coding when the quantum channel is a twomode squeezed state, because the two-mode squeezing operator has a natural representation in the η|representation.  2001

We derive the normally ordered expansion formula of bipartite Coulomb potential operator |Rα-Rβ |−1 by virtue of the method of integral within an ordered product of operators and the entangled state representation, where |Rα-Rβ| is the distance between two particles' positions. The new expansion formula provides convenience for calculating its coherent states'matrix elements. The normally ordered expansion of |Rα −Rβ|k, k≥2, is also deduced.

We present a general unified approach for arranging quantum operators of optical fields into ordered products (normal ordering, antinormal ordering, Weyl ordering (or symmetric ordering)) by fashioning Dirac's symbolic method and representation theory. We propose the technique of integration within an ordered product (IWOP) of operators to realize our goal. The IWOP makes Dirac's representation theory and the symbolic method more transparent and consequently more easily understood. The beauty of Dirac's symbolic method is further revealed. Various applications of the IWOP technique, such as in developing the entangled state representation theory, nonlinear coherent state theory, Wigner function theory, etc, are presented.

We find that the coherent thermal state |η(H.-y. Fan et al., Phys. Lett. A 246 (1998) 242) can provide a new approach for studying quasi-probability distribution of density operators and their time evolution. This approach is convenient and concise because the |η state possesses well-behaved properties and is based on the thermal field dynamics.