Song Tong-Qiang

Solving Generalized Non-degenerate Two-Mode Two-Photon Jaynes–Cummings Model by Supersymmetric Unitary Transformation*

Based on supersymmetric quantum mechanics theory, we introduced a supersymmetric unitary transformation to diagonalize the Hamiltonian of non-degenerate two-mode two-photon Jaynes–Cummings models which include any forms of intensity-dependent coupling, field-dependent detuning, and field nonlinearity. Its eigenvalue, eigenstates, and time evolution of state vector are obtained.

Quantum Fluctuation of a Mesoscopic Inductance Coupling Circuit at Finite Temperature

We study the quantization of mesoscopic inductance coupling circuit and discuss its time evolution. By means of the thermal field dynamics theory we study the quantum fluctuation of the system at finite temperature.

Density Matrix and Squeezed Vacuum State for General Coupling Harmonic Oscillator

By taking a unitary transformation approach, we study two harmonic oscillators with both kinetic coupling and coordinate coupling terms, and derive the density matrix of the system. The results show that the ground state of the system is a rotated two single-mode squeezed state.

Entangled Fractional Fourier Transform for the Multipartite Entangled State Representation

We deduce entangled fractional Fourier transformation (EFFT) for the multipartite entangled state representation, which was newly constructed with two mutually conjugate n-mode entangled states of continuum variables in n-mode Fock space. We establish a formalism of EFFT for quantum mechanical wave functions, which provides us a convenient way to derive some wave functions. We find that the eigenmode of EFFT is different from the usual Hermite Polynomials. We also derive the EFFT of the n-mode squeezed state.

Squeezing Transformation of Three-Mode Entangled State

We introduce the three-mode entangled state and set up an experiment to generate it. Then we discuss the three-mode squeezing operator squeezed | p, χ2, χ3 → μ-3/2 | p/μ, χ2/μ, χ3/μ and the optical implement to realize such a squeezed state. We also reveal that c-number asymmetric shrink transform in the three-mode entangled state, i.e. | p, χ2, χ3 → μ-1/2 | p/μ, χ2, χ3 , maps onto a kind of one-sided three-mode squeezing operator exp {iλ/3 (∑i=13 Pi) (∑i=13 Qi) − λ/2}. Using the technique of integration within an ordered product (IWOP) of operators, we derive their normally ordered forms and construct the corresponding squeezed states.

Exact Solution of the Milburn Equation for the Coupled-Channel Cavity QED Model*

We give the exact solution of Milburn equation for a coupled-channel cavity QED model which includes the Stark term and the frequency detuning, and study the influence of the intrinsic decoherence on the atomic inversion of the system.

Phase Properties of Nonlinear Coherent States

Using the Pegg–Barnett formalism we study the phase probability distributions and the squeezing effects of measured phase operators in the nonlinear coherent states introduced by R.L. de Matos Filho and W. Vogel to describe the center-of mass motion of a trapped ion and the q-coherent states. Moreover, we have obtained the completeness relation of nonlinear coherent states and proved that the q-Fock state introduced in many papers is, in fact, the usual Fock state.

Statistical Properties of the Nonlinear SU(1,1) Coherent States*

Using non-Hermitian realizations of SU(1,1) Lie algebra in terms of an f-oscillator, we generalize the notion of nonlinear coherent states to the single-mode and two-mode nonlinear SU(1,1) coherent states. Taking the nonlinearity function , their statistical properties are studied.

Coordinate-Dependent N-Mode Squeezing Transformations

We introduce the coordinate-dependent N-mode squeezing transformation and show that it can be constructed by the combination of two unitary transformations, a coordinate-dependent displacement followed by the standard squeezed transformation. The properties of the corresponding N-mode squeezed states are also discussed.

Coordinate-Dependent Two-Mode Squeezing Transformations and the Corresponding Squeezed States

We introduce the coordinate-dependent one- and two-mode squeezing transformations and discuss the properties of the corresponding one-and two-mode squeezed states. We show that the coordinate-dependent one-and two-mode squeezing transformations can be constructed by the combination of two transformations, a coordinate-dependent displacement followed by the standard squeezed transformation. Such a decomposition turns a nonlinear problem into a linear one because all the calculations involving the nonlinear one- and two-mode squeezed transformation have been shown to be able to reduce to those only concerning the standard one- and two-mode squeezed states.