Measurement of a Quadrupole Transition Moment by Interference of Quadrupole and dc-Field-Induced Sum-Frequency Generation

We show that, by measuring the interference between quadrupole and dc-field-induced sum-frequency generation, both the magnitude and the sign of a quadrupole matrix element can be obtained relative to the dipole matrix elements in atomic transitions. We use the measurement of $〈3s\left|z^2\right|4d〉$ of sodium to demonstrate the technique.