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From the citation:

In 1987, Anne L’Huillier discovered that many different overtones of light arose when she transmitted infrared laser light through a noble gas. Each overtone is a light wave with a given number of cycles for each cycle in the laser light. They are caused by the laser light interacting with atoms in the gas; it gives some electrons extra energy that is then emitted as light. Anne L’Huillier has continued to explore this phenomenon, laying the ground for subsequent breakthroughs.

In 2001, Pierre Agostini succeeded in producing and investigating a series of consecutive light pulses, in which each pulse lasted just 250 attoseconds. At the same time, Ferenc Krausz was working with another type of experiment, one that made it possible to isolate a single light pulse that lasted 650 attoseconds.

The laureates’ contributions have enabled the investigation of processes that are so rapid they were previously impossible to follow.

This sounds like we've succeeded in making very short-duration light pulses (similar to individual photons?). Why is that a big deal? What can we do with short-duration light pulses that we can't do with long-duration ones?

As a wild guess maybe this has something to do with the double-slit experiment (for which individual photons are illustrative), or maybe with standard Cesium clocks (since those have very rapid processes)?

I'm not familiar with this subfield of physics, so I would appreciate a general explanation.

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Very short pulses of light can be used to study very short lived processes. Electron transitions are the prime example. Electrons are the basis of all chemistry.

Normally a chemical reaction is described by the input chemicals and output chemicals. What goes on during the reaction is not mentioned. But understanding it can be very important for controlling the reaction or creating different reactions. Or just understanding what happened.

There are very short lived, unstable, highly reactive fragments during a reaction. Light can excite electrons in them. The frequencies absorbed by this tell you about the electronic configurations. Short pulses allow you to excite fragments at different stages of a reaction.

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