New approach for solving master equation of open atomic system

We describe a new approach called Ket-Bra Entangled State (KBES) Method which enables one convert master equations into Schr\"odinger-like equation. In sharply contrast to the super-operator method, the KBES method is applicable for any master equation of finite-level system in theory, and the calculation can be completed by computer. With this method, we obtain the exact dynamic evolution of a radioactivity damped 2-level atom in time-dependent external field, and a 3-level atom coupled with bath; Moreover, the master equation of N-qubits Heisenberg chain each qubit coupled with a reservoir is also resolved in Sec.III; Besides, the paper briefly discuss the physical implications of the solution.Comment: 7 pages, 5figure

Wigner operator's new transformation in phase space quantum mechanics and its applications

Using operators' Weyl ordering expansion formula (Hong-yi Fan,\emph{\}J. Phys. A 25 (1992) 3443) we find new two-fold integration transformation about the Wigner operator $\Delta(q',p')$ ($q$-number transform) in phase space quantum mechanics, $$\iint_{-\infty}^\infty dp' dq'/\pi \Delta (q',p') e^{-2i(p-p') (q-q')} =\delta (p-P) \delta (q-Q),$$ and its inverse $$\iint_{-\infty}^\infty dq dp \delta (p-P) \delta (q-Q) e^{2i(p-p') (q-q')}=\Delta (q',p'),$$ where $Q,$ $P$ are the coordinate and momentum operators, respectively. We apply it to studying mutual converting formulas among $Q-P$ ordering, $P-Q$ ordering and Weyl ordering of operators. In this way, the contents of phase space quantum mechanics can be enriched.Comment: 11 pages no figur

Remarks on the Bose description of the Pauli spin operators

Using both the fermionic-like and the bosonic-like properties of the Pauli spin operators we discuss the Bose description of the Pauli spin operators firstly proposed by Shigefumi Naka, and derive another new bosonic representation of the Pauli spin operators. The eigenvector of $\sigma_{-}$ in the bosonic representation is a nonlinear coherent state with the eigenvalues being the Grassmann numbers.Comment: 6 page

Relation between Optical Fresnel transformation and quantum tomography in two-mode entangled case

Similar in spirit to the preceding work [Opt. Commun. 282 (2009) 3734] where the relation between optical Fresnel transformation and quantum tomography is revealed, we study this kind of relationship in the two-mode entangled case. We show that under the two-mode Fresnel transformation the bipartite entangled state density |eta><eta|F_2 ^{dag}=|eta>_{r,s}<eta|, which is just the Radon transform of the two-mode Wigner operator (sigma,gama) in entangled form, where F_2 is an two-mode Fresnel operator in quantum optics, and s,r are the complex-value expression of (A, B, C,D). So the probability distribution for the Fresnel quadrature phase is the {tomography (Radon transform of the two-mode Wigner function), correspondingly, {s,r}_=. Similarly, we find a simial conclusion in the `frequency` domain.Comment: 10 page

Quantum mechanical perspectives and generalization of the fractional Fourier Transformation

Fourier and fractional-Fourier transformations are widely used in theoretical physics. In this paper we make quantum perspectives and generalization for the fractional Fourier transformation (FrFT). By virtue of quantum mechanical representation transformation and the method of integration within normal ordered product (IWOP) of operators, we find the key point for composing FrFT, and reveal the structure of FrFT. Following this procedure, a full family of generalized fractional transformations are discovered with the usual FrFT as one special case. The eigen-functions of arbitrary GFrT are derived explicitly

Dynamic Entanglement Evolution of Two-qubit XYZ Spin Chain in Markovian Environment

We propose a new approach called Ket-Bra Entangled State (KBES) Method for converting master equation into Schr\"{o}dinger-like equation. With this method, we investigate decoherence process and entanglement dynamics induced by a $2$-qubit spin chain that each qubit coupled with reservoir. The spin chain is an anisotropy $XYZ$ Heisenberg model in the external magnetic field $B$, the corresponding master equation is solved concisely by KBES method; Furthermore, the effects of anisotropy, temperature, external field and initial state on concurrence dynamics is analyzed in detail for the case that initial state is Extended Wenger-Like(EWL) state. Finally we research the coherence and concurrence of the final state (namely the density operator for time tend to infinite

Entropy evolution law in a laser process

For the first time, we obtain the entropy variation law in a laser process after finding the Kraus operator of the master equation describing the laser process with the use of the entangled state representation. The behavior of entropy is determined by the competition of the gain and damping in the laser process. The photon number evolution formula is also obtained

Density matrix of the superposition of excitation on coherent states with thermal light and its statistical properties

A beam's density matrix that is described by the superposition of excitation on coherent states with thermal noise (SECST) is presented, and its matrix elements in Fock space are calculated. The maximum information transmitted by the SECST beam is derived. It is more than that by coherent light beam and increases as the excitation photon number increases. In addition, the nonclassicality of density matrix is demonstrated by calculating its Wigner function.Comment: 7 pages, 9 figures, revtex

A new quantum mechanical photon counting distribution formula

By virtue of density operator's P-representation in the coherent state representation, we derive a new quantum mechanical photon counting distribution formula. As its application, we find the photon counting distribution for the pure squeezed state relates to the Legendre function, which seems a new result.Comment: 6 pages, 0 figure

New approach for deriving operator identities by alternately using normally, antinormally, and Weyl ordered integration

Dirac's ket-bra formalism is the "language" of quantum mechanics and quantum field theory. In Refs.(Fan et al, Ann. Phys. 321 (2006) 480; 323 (2008) 500) we have reviewed how to apply Newton-Leibniz integration rules to Dirac's ket-bra projectors. In this work by alternately using the technique of integration within normal, antinormal, and Weyl ordering of operators we not only derive some new operator ordering identities, but also deduce some useful integration formulas regarding to Laguerre and Hermite polynomials. This opens a new route of deriving mathematical integration formulas by virtue of the quantum mechanical operator ordering technique.Comment: 6 figures, submitted to Am. J. Phy