翻訳と辞書 Words near each other ・ Rotating gas-check ・ Rotating line camera ・ Rotating locomotion in living systems ・ Rotating Machine Company ・ Rotating magnetic field ・ Rotating pocket heater ・ Rotating radio transient ・ Rotating reference frame ・ Rotating Regional Primary System ・ Rotating Reserve ・ Rotating ring-disk electrode ・ Rotating savings and credit association ・ Rotating spheres ・ Rotating tank ・ Rotating unbalance ・ Rotating wave approximation ・ Rotating wheel space station ・ Rotating-Polarization Coherent anti-Stokes Raman spectroscopy ・ Rotation ・ Rotation (aeronautics) ・ Rotation (album) ・ Rotation (disambiguation) ・ Rotation (film) ・ Rotation (Joe McPhee album) ・ Rotation (mathematics) ・ Rotation (music) ・ Rotation (pool) ・ Rotation around a fixed axis ・ Rotation Curation ・ Rotation flap Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Rotating wave approximation ： ウィキペディア英語版 Rotating wave approximation The rotating wave approximation is an approximation used in atom optics and magnetic resonance. In this approximation, terms in a Hamiltonian which oscillate rapidly are neglected. This is a valid approximation when the applied electromagnetic radiation is near resonance with an atomic transition, and the intensity is low. Explicitly, terms in the Hamiltonians which oscillate with frequencies $\backslash omega\_L+\backslash omega\_0$ are neglected, while terms which oscillate with frequencies $\backslash omega\_L-\backslash omega\_0$ are kept, where $\backslash omega\_L$ is the light frequency and $\backslash omega\_0$ is a transition frequency. The name of the approximation stems from the form of the Hamiltonian in the interaction picture, as shown below. By switching to this picture the evolution of an atom due to the corresponding atomic Hamiltonian is absorbed into the system ket, leaving only the evolution due to the interaction of the atom with the light field to consider. It is in this picture that the rapidly oscillating terms mentioned previously can be neglected. Since in some sense the interaction picture can be thought of as rotating with the system ket only that part of the electromagnetic wave that approximately co-rotates is kept; the counter-rotating component is discarded. == Mathematical formulation == For simplicity consider a two-level atomic system with ground and excited states $|\backslash text\backslash rangle$ and $|\backslash text\backslash rangle$, respectively (using the Dirac bracket notation). Let the energy difference between the states be $\backslash hbar\backslash omega\_0$ so that $\backslash omega\_0$ is the transition frequency of the system. Then the unperturbed Hamiltonian of the atom can be written as : $H\_0=\backslash hbar\backslash omega\_0|\backslash text\backslash rangle\backslash langle\backslash text|$. Suppose the atom experiences an external classical electric field of frequency $\backslash omega\_L$, given by $\backslash vec(t)\; =\; \backslash vec\_0\; e^\; +\backslash vec\_0^$ * e^, e.g. a plane wave propagating in space. Then under the dipole approximation the interaction Hamiltonian between the atom and the electric field can be expressed as : $H\_1=-\backslash vec\backslash cdot\backslash vec$, where $\backslash vec$ is the dipole moment operator of the atom. The total Hamiltonian for the atom-light system is therefore $H=H\_0+H\_1.$ The atom does not have a dipole moment when it is in an energy eigenstate, so $\backslash langle\backslash text|\backslash vec|\backslash text\backslash rangle=\backslash langle\backslash text|\backslash vec|\backslash text\backslash rangle=0.$ This means that defining $\backslash vec\_|\backslash vec|\backslash text\backslash rangle$ allows the dipole operator to be written as : $\backslash vec=\backslash vec\_\backslash rangle\backslash langle\backslash text|+\backslash vec\_\backslash rangle\backslash langle\backslash text|$ (with $^$ * denoting the complex conjugate). The interaction Hamiltonian can then be shown to be (see the Derivation section below) : $H\_1\; =\; -\backslash hbar\backslash left(\backslash Omega\; e^+\backslash tildee^\backslash right)|\backslash text\backslash rangle\backslash langle\backslash text|$ -\hbar\left(\tilde^ *e^+\Omega^ *e^\right)|\text\rangle\langle\text| where $\backslash Omega=\backslash hbar^\backslash vec\_\backslash text\backslash cdot\backslash vec\_0$ is the Rabi frequency and $\backslash tilde:=\backslash hbar^\backslash vec\_\backslash text\backslash cdot\backslash vec\_0^$ * is the counter-rotating frequency. To see why the $\backslash tilde$ terms are called `counter-rotating' consider a unitary transformation to the interaction or Dirac picture where the transformed Hamiltonian $H\_$ is given by : $H\_=-\backslash hbar\backslash left(\backslash Omega\; e^+\backslash tildee^\backslash right)|\backslash text\backslash rangle\backslash langle\backslash text|$ -\hbar\left(\tilde^ *e^+\Omega^ *e^\right)|\text\rangle\langle\text|, where $\backslash Delta:=\backslash omega\_L-\backslash omega\_0$ is the detuning between the light field and the atom. 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「Rotating wave approximation」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.