Quantum Diagonalization Method in the Tavis-Cummings Model

To obtain the explicit form of evolution operator in the Tavis-Cummings model we must calculate the term ${e}^{-itg(S_{+}\otimes a+S_{-}\otimes a^{\dagger})}$ explicitly which is very hard. In this paper we try to make the quantum matrix $A\equiv S_{+}\otimes a+S_{-}\otimes a^{\dagger}$ diagonal to calculate ${e}^{-itgA}$ and, moreover, to know a deep structure of the model. For the case of one, two and three atoms we give such a diagonalization which is first nontrivial examples as far as we know, and reproduce the calculations of ${e}^{-itgA}$ given in quant-ph/0404034. We also give a hint to an application to a noncommutative differential geometry. However, a quantum diagonalization is not unique and is affected by some ambiguity arising from the noncommutativity of operators in quantum physics. Our method may open a new point of view in Mathematical Physics or Quantum Physics.Comment: Latex files, 21 pages; minor changes. To appear in International Journal of Geometric Methods in Modern Physic

Explicit Form of the Evolution Operator of Tavis-Cummings Model : Three and Four Atoms Cases

In this letter the explicit form of evolution operator of the Tavis-Cummings model with three and four atoms is given. This is an important progress in quantum optics or mathematical physics.Comment: Latex file, 10 pages. We combined quant-ph/0404034(the three atoms case) and quant-ph/0406184(the four atoms case) into an article. to appear in International Journal of Geometric Methods in Modern Physic

Comparative genomics of Glandirana rugosa using unsupervised AI reveals a high CG frequency

The Japanese wrinkled frog (Glandirana rugosa) is unique in having both XX-XY and ZZ-ZW types of sex chromosomes within the species. The genome sequencing and comparative genomics with other frogs should be important to understand mechanisms of turnover of sex chromosomes within one species or during a short period. In this study, we analyzed the newly sequenced genome of G. rugosa using a batch-learning self-organizing map which is unsupervised artificial intelligence for oligonucleotide compositions. To clarify genome characteristics of G. rugosa, we compared its short oligonucleotide compositions in all 1-Mb genomic fragments with those of other six frog species (Pyxicephalus adspersus, Rhinella marina, Spea multiplicata, Leptobrachium leishanense, Xenopus laevis, and Xenopus tropicalis). In G. rugosa, we found an Mb-level large size of repeat sequences having a high identity with the W chromosome of the African bullfrog (P. adspersus). Our study concluded that G. rugosa has unique genome characteristics with a high CG frequency, and its genome is assumed to heterochromatinize a large size of genome via methylataion of CG

Cavity QED and Quantum Computation in the Weak Coupling Regime

In this paper we consider a model of quantum computation based on n atoms of laser-cooled and trapped linearly in a cavity and realize it as the n atoms Tavis-Cummings Hamiltonian interacting with n external (laser) fields. We solve the Schr{\" o}dinger equation of the model in the case of n=2 and construct the controlled NOT gate by making use of a resonance condition and rotating wave approximation associated to it. Our method is not heuristic but completely mathematical, and the significant feature is a consistent use of Rabi oscillations. We also present an idea of the construction of three controlled NOT gates in the case of n=3 which gives the controlled-controlled NOT gate.Comment: Latex file, 22 pages, revised version. To appear in Journal of Optics B : Quantum and Semiclassical Optic