# 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.

Example.Quanty
-- Creating a spectrum from a starting state psi
-- a transition operator, T1, T2,
-- and Hamiltonian H1
IFY = CreateFluorescenceYield(H1, T1, T2, psi)