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 — documentation:basics:fluorescence_yield [2016/10/10 09:40] (current) 2016/10/06 20:36 Maurits W. Haverkort created 2016/10/06 20:36 Maurits W. Haverkort created Line 1: Line 1: + {{indexmenu_n>​8}} + ====== Fluorescence yield ====== + ### + Fluorescence spectroscopy is a resonant spectroscopy technique whereby one integrates over the outgoing energies: + $$+ I_{FY} = \frac{\imath}{\pi} \int G^3(\omega_1,​\omega_2) d\omega_2 +$$ + $I_{FY}$ is a real quantity and in that respect different from the response functions ($G^1$ and $G^3$, where the real and imaginary part are related by Kramers Kronig relations). The normalization $\imath/​\pi$ is chosen such that the product with the integral of $G^3$ over $\omega_2$ ($\int 1/(\omega_2 - H_2 + \imath \Gamma/​2)d\omega_2 = -\imath\pi$) yields 1. + $$+ \begin{eqnarray} + I_{FY} &=& \bigg\langle \psi_i \bigg| T_1^{\dagger} \frac{1}{\omega_1 - H_1 - \imath \Gamma/2} T_2^{\dagger}\\ + \nonumber && \quad \quad T_2 \frac{1}{\omega_1 - H_1 + \imath \Gamma/2} T_1 \bigg | \psi_i \bigg\rangle. + \end{eqnarray} +$$ + In Quanty Fluorescence yield spectra are calculated with the function "​CreateFluorescenceYield()"​. Note that the calculation of a Fluorescence yield spectrum is much faster than the calculation of a resonant spectrum and then integrating. Naturally it yields the same answer. + ​ + -- Creating a spectrum from a starting state psi + -- a transition operator, T1, T2, + -- and Hamiltonian H1 + IFY = CreateFluorescenceYield(H1,​ T1, T2, psi) + ​ + ### + + + ===== Index ===== + - [[documentation:​basics:​basis|]] + - [[documentation:​basics:​operators|]] + - [[documentation:​basics:​wave_functions|]] + - [[documentation:​basics:​expectation_values|]] + - [[documentation:​basics:​eigen_states|]] + - [[documentation:​basics:​spectra|]] + - [[documentation:​basics:​resonant_spectra|]] + - Fluorescence yield