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Jarlskog's Parametrization of Unitary Matrices and Qudit Theory
Kazuyuki Fujii, Kunio Funahashi, Takayuki Kobayashi
In the paper (math-ph/0504049) Jarlskog gave an interesting simple parametrization to unitary matrices, which was essentially the canonical coordinate of the second kind in the Lie…
From Quantum Optics to Non-Commutative Geometry : A Non-Commutative Version of the Hopf Bundle, Veronese Mapping and Spin Representation
Kazuyuki Fujii
In this paper we construct a non-commutative version of the Hopf bundle by making use of Jaynes-Commings model and so-called Quantum Diagonalization Method. The bundle has a kind o…
Jaynes-Cummings Model and a Non-Commutative "Geometry" : A Few Problems Noted
Kazuyuki Fujii
In this paper we point out that the Jaynes-Cummings model without taking a renonance conditon gives a non-commutative version of the simple spin model (including the parameters …
Explicit Form of Solution of Two Atoms Tavis-Cummings Model
Kazuyuki Fujii, Kyoko Higashida, Ryosuke Kato +1
In this paper we consider the two atoms Tavis--Cummings model and give an explicit form to the solution of this model which will play a central role in quantum computation based on…
A Rabi Oscillation in Four and Five Level Systems
Kazuyuki Fujii, Kyoko Higashida, Ryosuke Kato +1
In this paper we consider a general model of an atom with n energy levels interacting with n-1 external (laser) fields which is a natural extension in the two and three level syste…
Quantum Optical Construction of Generalized Pauli and Walsh-Hadamard Matrices in Three Level Systems
Kazuyuki Fujii
A set of generators of generalized Pauli matrices play a crucial role in quantum computation based on n level systems of an atom. In this paper we show how to construct them by mak…