The Raman response in the antiferromagnetic 2-leg S = 1/2 Heisenberg ladder is calculated for various couplings by continuous unitary transformations. For leg couplings above 80% of the rung coupling a characteristic 2-peak structure occurs with a point of zero intensity within the continuum. Experimental data for CaV2O5 and LayCa14−yCu24O41 are analyzed and the coupling constants are determined. Evidence is found that the Heisenberg model is not sufficient to describe cuprate ladders. We argue that a cyclic exchange term is the appropriate extension.PACS numbers: 75.40. Gb, 75.50.Ee, 75.10.Jm Strongly correlated electron systems in low dimensions are of fundamental interest due to their fascinating properties resulting from strong quantum fluctuations [1][2][3]. Important experimental insight is gained from spectroscopic measurements of such systems. The spectral densities measured yield information on the kinetics and on the interaction of the elementary excitations as well as on the matrix elements involved. Thus quantitative theoretical calculations of spectral densities are a major task in condensed matter physics. We use optimally chosen continuous unitary transformations (CUT) to map complex many-body problems to a tractable few-body problems [4]. This clear concept serves as a perfect basis to compute spectral densities of strongly correlated systems thus establishing a quantitative contact between theory and experiment [5].We will focus on optical investigations, in particular on the Raman response, of antiferromagnetic 2-leg Heisenberg ladders realizing quasi one-dimensional (1D) strongly correlated systems. There are several experimental realizations of spin ladders like CaV 2 O 5 , SrCu 2 O 3 and La y Ca 14−y Cu 24 O 41 rendering direct comparison between theory and experiment possible [7][8][9][10][11].Raman scattering measures excitations with zero change of spin and momentum. Starting at T = 0 from the S = 0 ground state the singlet excitations at zero momentum are probed. The Raman response in spin ladders was recently calculated by first order perturbation theory for spin ladders [12] and by exact diagonalization [13]. In this work, we present detailed predictions obtained from CUTs using rung triplets as elementary excitations. Our results are not resolution limited because neither finite size effects occur nor artificial broadenings are necessary.The Hamiltonian for the 2-leg Heisenberg ladder readswhere J > 0 and J ⊥ > 0 are the leg and rung couplings; the subscript i denotes the rungs and 1, 2 the two legs. At T = 0 the Raman response I(ω) is given by the retarded resolventThe observables R rung (R leg ) for magnetic light scattering in rung-rung (leg-leg) polarization read in leading order [14,15]The factors A leg 0and A rung 0 depend on the underlying microscopic electronic model. It is beyond the scope of the present work to compute them. Equally, we do not consider resonating Raman excitation processes. Results will be given in units of the factors squared.Technically, we employ a CUT...