MULTIPHOTON JAYNES-CUMMINGS MODEL SOLVED VIA SUPERSYMMETRIC UNITARY TRANSFORMATION

For multiphoton Jaynes-Cummings(JC) model Hamiltonian, we find its supersymmetric structure. Based on this, we introduce a supersymmetric unitary transformation to diagonalize the JC Hamiltonian, in so doing, its eigenvalues and eigenfunctions are obtained. The transition process is also calculated.     

用超对称幺正变换解双光子过程的Jaynes-Cummings模型

本文发现了描写双光子过程的Jaynes-Cummings哈密顿量的超对称结构.根据超对称量子力学理论,引入了超对称幺正变换使其哈密顿量对角化.从而,得到了它的本征值、本征态,同时也计算了态的演化和跃迁几率.     

Invariant theory and exact solutions of the time-dependent supersymmetric two-level multiphoton Jaynes－Cummings model

On the basis of the fact that the two-level multiphoton Jaynes－Cummings (TLMJC) model possesses a supersymmetric structure, an invariant is constructed in terms of the supersymmetric generators by working in the sub-Hilbert-space corresponding to a particular eigenvalue of the conserved supersymmetric generators (the time-independent invariant). In this paper, we investigate the invariant-related unitary transformation approach to exact solutions of the time-dependent TLMJC model.     

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.     

Solving Multiphoton Jaynes–Cummings Model with Field Nonlinearity by Supersymmetric Unitary Transformation

We introduce a supersymmetric unitary transformation, to diagonalize the multiphoton Jaynes–Cummings model Hamiltonian based on supersymmetric quantum mechanics theory, that includes any forms of intensity-dependent coupling and field nonlinearity. On doing so, we obtain its eigenvalue and eigenstates, and the time evolution of state vector.     

Solving Two Kinds of JC Models Relating to Two-Photon Process by Supersymmetric Transformation

We propose two kinds of new Jaynes Cummings models relating to two-photon process by using the supersymmetric unitary transformation. The corresponding energy eigenvalues and eigenvectors are obtained.     

Solving Two Kinds of JC Models Relating to Two-Photon Process by Supersymmetric Transformation

We propose two kinds of new Jaynes Cummings models relating to two-photon process by using the supersymmetric unitary transformation. The corresponding energy eigenvalues and eigenvectors are obtained.     

Supersymmetric structures of Dirac oscillators in commutative and noncommutative spaces

The supersymmetric properties of a charged planar Dirac oscillator coupling to a uniform perpendicular magnetic field are studied. We find that there is an N=2 supersymmetric structure in both commutative and noncommutative cases. We construct the generators of the supersymmetric algebras explicitly and show that the generators of the supersymmetric algebras can be mapped onto ones which only contain the left or right-handed chiral phonons by unitary transformations.     

Linearised version of B.R.S. transformations: Renormalisation of massive QED in the Veltman gauge

A linearised (supersymmetric) version of the Becchi-Rouet-Stora (B.R.S.) transformation is used to prove the renormalisibility of QED with a massive photon in a generalized Veltman gauge. In particular, it is shown in a very simple way that in ignoring couplings with matter fields, the remaining model is unitary.     

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 transfor mation 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.