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documentation:basics:fluorescence_yield [2016/10/06 20:36] – created Maurits W. Haverkortdocumentation:basics:fluorescence_yield [2016/10/10 09:40] (current) – external edit 127.0.0.1
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 +{{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.
 +<code Quanty Example.Quanty>
 +-- Creating a spectrum from a starting state psi
 +-- a transition operator, T1, T2,
 +-- and Hamiltonian H1
 +IFY = CreateFluorescenceYield(H1, T1, T2, psi)
 +</code>
 +###
 +
 +
 +===== 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

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