Cogwheel phase cycling in population-detected optical coherent multidimensional spectroscopy

TL;DR

This paper introduces and evaluates cogwheel phase cycling for population-detected optical multidimensional spectroscopy, demonstrating its efficiency in isolating nonlinear signals with fewer steps than traditional nested phase cycling.

Contribution

It adapts cogwheel phase cycling from NMR to optical spectroscopy, deriving selection rules, optimizing winding numbers, and experimentally comparing its performance to nested phase cycling.

Findings

Cogwheel phase cycling captures nonlinear signals with fewer steps.

Experimental results show effective separation of signals.

The method is more economical than nested phase cycling.

Abstract

An integral procedure in every coherent multidimensional spectroscopy experiment is to suppress undesired background signals. For that purpose, one can employ a particular phase-matching geometry or phase cycling, a procedure that was adapted from nuclear magnetic resonance (NMR) spectroscopy. In optical multidimensional spectroscopy, phase cycling has been usually carried out in a "nested" fashion, where pulse phases are incremented sequentially with linearly spaced increments. Another phase-cycling approach which was developed for NMR spectroscopy is "cogwheel phase cycling," where all pulse phases are varied simultaneously in increments defined by so-called "winding numbers". Here we explore the concept of cogwheel phase cycling in the context of population-based coherent multidimensional spectroscopy. We derive selection rules for resolving and extracting fourth-order and higher-order nonlinear signals by cogwheel phase cycling and describe how to perform a numerical search for the winding numbers for various population-detected 2D spectroscopy experiments. We also provide an expression for a numerical search for nested phase-cycling schemes and predict the most economical schemes of both approaches for a wide range of nonlinear signals. The signal selectivity of the technique is demonstrated experimentally by acquiring rephasing and nonrephasing fourth-order signals of a laser dye by both phase-cycling approaches. We find that individual nonlinear signal contributions are, in most cases, captured with fewer steps by cogwheel phase cycling compared to nested phase cycling.