Confirming Expectations

A good experiment definitively distinguishes between alternative hypotheses. But things get tricky when a well established standard view is pitted against ill-defined alternatives.

My Focus story today describes measurements of density fluctuations in ultra-cold gases. Several experimental groups have been capturing and cooling bunches of about a thousand atoms above "atom chips" to study such things as Bose-Einstein condensates. In this case, Julien Armijo, a former member of a group at the Insitute d'Optique in Palaiseau, attributes some of the density fluctuation to quantum zero-point excitation of sound waves in the atomic cloud.

For an isolated oscillator, the signature of zero-point motion is conceptually straightforward: below a certain temperature the motions no longer decrease with temperature. What's left are the intrinsic quantum-mechanical oscillations, and the freezing temperature corresponds to the minimum quantum of energy needed to excite the oscillator. The obvious "null hypothesis" to be excluded would therefore be that the fluctuations continue to decrease toward zero with further cooling.

For the atomic cloud, however, the situation is much more subtle, because the sound waves have a continuous spectrum that extends to zero energy. This means that there are always some waves--the ones with the longest wavelength--that are excited no matter how low the temperature.

A further complication is that different wavelengths vary in their effect on the density fluctuations. A sophisticated theory says that the quantum contribution from the longest wavelengths does not add to the density fluctuations at all. In fact, this theory says that, at very long wavelengths, the fluctuations go away at zero temperature--exactly what one would expect if there were no quantum fluctuations!

As it turns out, though, the experiment measures fluctuations in individual pixels that are a few microns on a side, which corresponds to including waves with wavelengths on the same scale. The theory says that these waves will cause a measurable density fluctuation even at zero temperature.

But the same theory says that at nonzero temperatures, including shorter wavelengths will decrease the contribution of thermal excitations by exactly the same amount. The two terms get bigger as the pixels get smaller, but since they cancel anyway that doesn't affect the prediction.

This is messier than just looking for fluctuations that don't freeze out, isn't it?

It's rather difficult to choose a good null hypothesis where there are no zero-point motions. After all, everyone believes that, physically, the quantum fluctuations should be there, although different theoretical treatments may make slightly different predictions. So there is no particularly obvious way to choose a model where the quantum fluctuations are absent.

Armijo measures fluctuations that don't change with effective pixel size, just as the complete theory predicts. Of course, the measurements also agree with a theory that omits the size dependence of both the quantum and the thermal contributions. What they don't agree with, he emphasizes, is a model that includes only the thermal corrections, since these are no longer cancelled by the quantum term. It's not clear that anyone thinks this would be a credible model that needs to be excluded. (Setting Plank's constant to zero, a common way to "turn off" quantum effects, seems to make both corrections go away.)

What is clear is that the claim that this is a "direct observation of quantum phonon fluctuations" needs to be parsed quite carefully.