Sum Frequency Generation Spectroscopy of Rydberg States

Abstract

Consider sum frequency generation (SFG) ω3 = 2 ω1 + ω2 in a phase matched metal-noble gas mixture, using two lasers ω1 and ω2, where 2 ω1 is tuned to a two photon transition Ωg2 and ω2 is shifted across Rydberg transitions Ω2n (g groundstate, 2 excited state, n Rydberg state of the metal atom). Then the intensity of the SFG spectrum I3 (ω3)~ |χ(3) (ω3)|2 displays resonances and related antiresonances, separated by (1) which are caused respectively by constructive and destructive interference of resonant and nonresonant parts of the 3. order nonlinear susceptibility χ(3) (ω3 ≃ Ωng) = χR(ω3)+ χNR (3) The products μ2nμng:= xn of the dipole transition matrix elements may then be obtained from a simple measurement of the frequency spacings Δωn at a large number of transitions Ωgn and solving iteratively the coupled equation system (1),(3); neither absolute radiation intensity nor vapour density deter mination is needed.