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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Maxwell-Bloch equations ： ウィキペディア英語版 Maxwell-Bloch equations The Maxwell-Bloch equations, also called the optical Bloch equations, were first derived by Tito Arecchi and Rodolfo Bonifacio of Milan, Italy.〔F. T. Arecchi and R. Bonifacio, 'Theory of Optical Maser Amplifiers', IEEE J. Quantum Electron. 1, pp169-178 (1965).〕 They describe the dynamics of a two-state quantum system interacting with the electromagnetic mode of an optical resonator. They are analogous to (but not at all equivalent to) the Bloch equations which describe the motion of the nuclear magnetic moment in an electromagnetic field. The equations can be derived either semiclassically or with the field fully quantized when certain approximations are made. ==Semi-classical formulation== The derivation of the semi-classical optical Bloch equations is nearly identical to solving the two-state quantum system (see the discussion there). However, usually one casts these equations into a density matrix form. The system we are dealing with can be described by the wave function: :$\backslash psi\; =\; c\_g\backslash psi\_g\; +\; c\_e\backslash psi\_e$ :$\backslash left|c\_g\backslash right|^2\; +\; \backslash left|c\_e\backslash right|^2\; =\; 1$ The density matrix is : * & c_e c_^ * \\ c_g c_^ * & c_g c_^ * \end (other conventions are possible; this follows the derivation in Metcalf (1999)).〔Metcalf, Harold. ''Laser Cooling and Trapping'' Springer 1999 pg. 24-〕 One can now solve the Heisenberg equation of motion, or translate the results from solving the Schrödinger equation into density matrix form. One arrives at the following equations, including spontaneous emission: :$\backslash frac\; =\; \backslash gamma\; \backslash rho\_\; +\; \backslash frac(\backslash Omega^$ * \bar \rho_ - \Omega\bar \rho_) :$\backslash frac\; =\; -\backslash gamma\; \backslash rho\_\; +\; \backslash frac(\backslash Omega\; \backslash bar\; \backslash rho\_\; -\; \backslash Omega^$ *\bar \rho_) :$\backslash frac\; =\; -\backslash left(\; \backslash frac\; +\; i\backslash delta\; \backslash right)\; \backslash bar\; \backslash rho\_\; +\; \backslash frac\backslash Omega^$ *(\rho_ - \rho_) :$\backslash frac\; =\; -\; \backslash left(\; \backslash frac\; -\; i\backslash delta\; \backslash right)\; \backslash bar\; \backslash rho\_\; +\; \backslash frac\backslash Omega(\backslash rho\_\; -\; \backslash rho\_)$ In the derivation of these formulae it was explicitly assumed that spontaneous emission is described by an exponential decay of the coefficient $\backslash rho\_(t)$ with decay constant $\backslash frac$. $\backslash Omega$ is the (generalized) Rabi frequency, which is :$\backslash Omega\; =\; \backslash sqrt$ where $\backslash delta\; =\; \backslash omega\; -\; \backslash omega\_$ is the detuning and measures how far the light frequency, $\backslash omega$, is from the transition, $\backslash omega\_$. $\backslash chi\_\; =\; \backslash cdot\backslash vec\_0\; \backslash over\; \backslash hbar\}$ where $\backslash scriptstyle\}$ is the transition dipole moment for the $\backslash scriptstyle$ transition and $\backslash scriptstyleE\_0\}$ is the vector electric field amplitude including the polarization. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Maxwell-Bloch equations」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.