Multidimensional Coherent Spectroscopy (MDCS)

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Multidimensional coherent spectroscopy (MDCS) is a technique that unfolds the optical response of a mixed
substance in two or more spectral dimensions. MDCS reveals the correlations between features to separate the signatures of each individual substance from the mixture. This separation is analogous to analyzing overlapped fingerprints to pick out each unique fingerprint or signature.

In the top figure we illustrate the difference in information provided by MDCS versus typical optical spectroscopy. On the left we plot six absorption dips one might measure with the linear absorption or photoluminescence. Unlike these methods, which measure a mixture of constituents as a forest of overlapping features, MDCS measures the correlations between individual substances leading to unique signature mapping of each component. Using the MDCS methodology immediately determines the signatures of all of individual substances in the sample, which can be compared to a database of substance signatures for easy and rapid identification of the sample components.

This idea of isolating the spectra of substances in a mixture applies to all types of materials. It is well known that optical spectra of nanostructures (e. g.  quantum wells in a laser diode and monolayer materials) are dominated by spatial inhomogeneity. MDCS is also useful for separating the homogeneous spectra of an inhomogeneous distribution. In the adjacent MDCS spectrum, the top-left feature is elongated along the diagonal, which  results from spatial inhomogeneity. Despite this inhomogeneity, MDCS is able to measure the homogeneous linewidth.

MDCS is a third-order nonlinear spectroscopy, which is the lowest order of nonlinear spectroscopy for centrosymmetric material, i. e. all materials have a third order response. What makes MDCS so much more powerful than linear spectroscopy techniques is that the use of multiple light-matter interactions is particularly well suited for measuring the intrinsic properties of an optical resonance.

One MDCS application, called the photon-echo sequence, is shown in the adjacent cartoon. If a largely inhomogeneous distribution of optical resonances is measured with a linear spectroscopy technique, the inhomogeneous broadening will dominate the spectrum. By using a photon-echo MDCS pulse sequence, it is possible measure the intrinsic properties of each frequency group including homogeneous dephasing and coupling.

There are yet other techniques for measuring other complex material properties, all of which are possible with the same hardware and require only small software/electronics reconfiguration. One of these other useful MDCS pulse sequences is the two-quantum technique, which is a background-free measurement of many-body effects.

Multidimensional spectrum of semiconductor quantum well
Multidimensional spectrum of two resonances in a semiconductor nanostructure. Reprinted with permission from J. Phys. Chem. B 115, 18, 5365-5371. Copyright 2011 American Chemical Society.
A photon echo experiment can be related to runners around a track. A first pulse gets the runners started around the track, during which time they will dephase. A second pulse tells the runners to turn around. If the runners all maintain their pace, they will all recross the start line at the same time.
One commonly used MDCS pulse sequence is called the photon echo sequence. The underlying technique is illustrated above where pulses are used to drive the system "start" and "turn around" actions. If the intrinsic rates of the system components (tortoise and hare) remain the same, it will take them both equally long to run out as it does to run back. If those rates change for any reason, those changes are measured. Cartoon reprinted from Berlex Imaging.

Applications and Links

Multidimensional coherent spectroscopy (MDCS), the optical analog of NMR, has found its way into several scientific fields. The research community currently applies MDCS to semiconductors, molecules, drug-protein interactions, living bacteria, atoms, and even oil painting degradation. Here we list many of these applications with some links to the original work. Most of these researchers are physicists and chemists that have invested tremendous time and effort into building the setups they use to achieve their results.

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