Pump–Probe Spectroscopy Using the Hadamard Transform

Abstract

A new method of performing pump–probe experiments is proposed and experimentally demonstrated by a proof of concept on the millisecond scale. The idea behind this method is to measure the total probe intensity arising from several time points as a group, instead of measuring each time separately. These measurements are multiplexes that are then transformed into the true signal via multiplication with a binary Hadamard S matrix. Each group of probe pulses is determined by using the pattern of a row of the Hadamard S matrix and the experiment is completed by rotating this pattern by one step for each sample excitation until the original pattern is again produced. Thus to measure n time points, n excitation events are needed and n probe patterns each taken from the n ×  n S matrix. The time resolution is determined by the shortest time between the probe pulses. In principle, this method could be used over all timescales, instead of the conventional pump–probe method which uses delay lines for picosecond and faster time resolution, or fast detectors and oscilloscopes on longer timescales. This new method is particularly suitable for situations where the probe intensity is weak and/or the detector is noisy. When the detector is noisy, there is in principle a signal to noise advantage over conventional pump–probe methods.