On the Entangled Fractional Fourier Transform in Tripartite Entangled State Representation

Based on the newly constructed two mutually conjugate 3-mode entangled states of continuum variablesin three-mode Fock space we introduce entangled fractional Fourier transform (EFFT) for the tripartite entangled staterepresentations, which are not a direct product of three 1-dimensional FFTs. The eigenmodes of EFFT are obtained,which is different from the usual Hermite polynomials. The EFFT of the three-mode squeezed state is derived.     

One- and Two-Mode Combination Squeezing Operator for Two Harmonic Oscillators with Coordinate-Momentum Coupling

By virtue of the technique of integration within an ordered product of operators, we derive the normal ordering expansion of a one- and two-mode combination squeezing operator for two harmonic oscillators with coordinatemomentum coupling. It turns out that this squeezing operator just diagonalizes the Hamiltonian H = p21/2m1 m1ω21x21/2 p22/2m2 m2ω22x22/2 - λx2p1, so its ground state is a one- and two-mode combination squeezed state.Quantum fluctuation in the ground state is calculated.     

A convenient and efficient H2SO4-promoted regioselective monobromination of phenol derivatives using N-bromosuccinimide

Abstract

A convenient, rapid H₂SO₄-promoted regioselective monobromination reaction with N-bromosuccinimide was developed. The desired para-monobrominated or ortho-monobrominated products of phenol derivatives were obtained in good to excellent yields with high selectivity. Regioselective chlorination and iodination were also achieved in the presence of H₂SO₄ using N-chlorosuccinimide and N-iodosuccinimide, respectively.     

Evolution of Number State to Density Operator of Binomial Distribution in the Amplitude Dissipative Channel

We show that passing through the amplitude dissipative channel the initial pure number state density operator is evolved into the density operator of binomial distribution （a mixed state）, and the binomial distribution parameter is just equal to e^-2kt, where k is the dissipative parameter of the channel. We solve the corresponding master equation to obtain the operator-sum representation of the density operator by virtue of the entangled state representation, which seems to be a convenient approach.     

Marginal Distributions of Wigner Function in a Mesoscopic L-C Circuit at Finite Temperature and Thermal Wigner Operator

Wigner function in phase space has its physical meaning as marginal probability distribution in coordinate space and momentum space respectively, here we endow the Wigner function with a new physical meaning, i.e., its marginal distributions’ statistical average for q ²/(2C) and p ²/(2L) are the energy stored in capacity and in inductance of a mesoscopic L-C circuit at finite temperature, respectively. PACS numbers: 03.65.-w, 73.21.-b     

Fresnel-Transform＇s Quantum Correspondence and Quantum Optical ABCD Law

Corresponding to the Fresnel transform there exists a unitary operator in quantum optics theory, which could be known the Fresnel operator （FO）. We show that the multiplication rule of the FO naturally leads to the quantum optical ABCD law. The canonical operator methods as mapping of ray-transfer ABCD matrix is explicitly shown by the normally ordered expansion of the FO through the coherent state representation and the technique of integration within an ordered product of operators. We show that time evolution of the damping oscillator embodies the quantum optical ABCD law.     

Quantum superposition of localized and delocalized phases of photons

Based on a variant of 2-site Jaynes–Cummings–Hubbard model constructed using superconducting circuits, we propose a method to coherently superpose the localized and delocalized phases of microwave photons, which makes it possible to engineer the collective features of multiple photons in the quantum way using an individual two-level system. Our proposed architecture is also a promising candidate for implementing distributed quantum computation since it is capable of coupling remote qubits in separate resonators in a controllable way.     

The Generalized Thermo Jaynes–Cummings Model and?Its Energy Spectrum

By analyzing the characteristics of thermo field dynamics, we present a new generalized thermo Jaynes-Cummings (TJC) model at finite temperature including the thermal effects and expatiate on its physical explanation. By virtue of Lewis-Riesenfeld invariant method, we obtain its exact eigenenergy spectrum and the explicit expressions for the evolution operator of the wavefunctions. In addition, we evaluate various expectation values of physical quantities and find the pseudo-invariant eigen-operator for the generalized TJC Hamiltonian.     

On Mutual Transform Between Number-Difference State and Phase State Corresponding to Operational Phase Operator

In the mutual transform between the number-difference state and the phase state corresponding to the operational phase operator we find that there exists an end-point ambiguousness. This problem can be avoided by Lighthill＇s method.