jdrov

However, it is a seemingly miraculous trick of spin systems that we are able to use pulses to effectively reverse the time evolution of the system and produce echoes. When looking at one new pulse sequence which had many pulses, the discoverer of the spin echo (Erwin Hahn) said "With that many pulses I could bring back the Messiah!" [1].

It is very difficult to understand the complex state of the system after many of these interactions, but in our papers we explore how "coherent" the interactions are by "resurrecting" the signal in what are called spin echoes [1]. Simply speaking, after many interactions the "order" of the system lies not in the nuclear spins individually, but in a complex network of interactions among the spins -- this complex order is not observable (and so the signal appears to "decay away" over time).

Using techniques developed in nuclear magnetic resonance (NMR), we are able to put this "order" back into an observable state, and watch it return. It feels like reversing time, I never get used to it!

Sometimes physicists think of phase transitions in terms of "symmetry breaking." Imagine zooming in very close on the molecules in a glass of liquid water, all tumbling quickly into and out of your field of view. The situation is highly "symmetric": if you closed your eyes and I shifted the field of view slightly to the left, you wouldn't know what I'd done when you opened your eyes again.

Now suppose the water freezes into a crystal of ice, so that the molecules are arranged on a regular lattice. If I repeat my "shift-slightly-to-the-left" experiment, you'd be able to tell I moved things. That is, somehow the molecules chose a particular location for the lattice, even though any other location of the lattice could have done just as well. In jargon, we say the water "spontaneously broke the continuous translational symmetry": the defining equations of motion are agnostic about the particular location in space, but the state of the system chose a location anyways.

In our experiment, we do something similar in time rather than space. We drive the system with pulses once every time period "T", so the equations of motion are identical under this "discrete" shift in time. However, the state of the system (in our case, the direction of the nuclear magnetization) only goes back to itself every time 2T, and so "breaks discrete time translational symmetry."

There is one more important feature of the observed signature in this analogy: if you nudge an atom that is in a crystal lattice, it will want to return to its original position. Similarly, the period of the magnetization's direction-reversal is robust to our pulse imperfections, if we allow the quantum interactions long enough to act. So, the "region" of parameter space where you can observe this effect is not confined to perfectly ideal pulses, but is instead robust to our pulse imperfections -- the "robustness" depends on the amount of time we allow the nuclear spin interactions to take place.

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I hope this helps. I recommend the synopses available at prl.aps.org, and searching for the PDF preprints on the Arxiv (not yet quite as good as the published versions), if you don't have Physical Review access.

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