Tobias Jenke of Vienna and 11 co-authors from Austria, Germany, and France have performed an interesting experiment with neutrons in the gravitational field (although they have done similar experiments in the past) and their new preprint was just published in the prestigious PRL (Physical Review Letters):
Click to zoom in: outline and results.
What have they done?
Well, they have prepared some very cold neutrons and sent them in between two horizontal mirrors which were separated by \(\Delta z = 30\,\mu{\rm m}\) in altitude. As you know, this is a nice and simple system in undergraduate non-relativistic quantum mechanics, a potential well.
If the walls were infinitely tall and there were no gravity, the energy eigenstates would be\[
\psi_n(z) = C_n \sin \zav{ \frac{\pi n z}{\Delta z} }, \quad n=1,2,3,\dots
\] The spectrum is discrete. If the gravitational field is added, the wave functions are no longer simple sines. Instead, they are combinations of the Airy functions \({\rm Ai}(z)\) of a sort – with the right coefficients and the right boundary conditions to make everything work. It means that the \(n\)-th wave function is more likely to be found near the bottom wall (mirror) and the wave function is more quickly oscillating over there. Note that the unrestricted linear potential has a continuous energy spectrum (just shifting the wave function in the \(z\)-direction adds some energy) while the mirrors make the spectrum discrete.
These states are discrete but they also apply some frequency – in a way that you know from Rabi spectroscopy – I think that they finally tickled the mirrors in some way although they had wanted to use some variable magnetic gradients, too. In fact, it means that the height of the walls (from the mirrors) isn't infinite but a finite and oscillating as \(\cos \omega t \) with some frequency between 50 and 800 Hertz that they may adjust. This extra periodic, time-dependent disturbance may be treated as a perturbation of the original quantum mechanical system that allows the transitions between the energy levels and they measure their probabilities. For example, the transition \(\ket{2}\leftrightarrow \ket{4}\) has been measured for the first time.
Everything agrees with quantum mechanics supplemented with Newton's potential.
It follows that they may eliminate at the 95% confidence level some (previously viable) models for dark matter and dark energy, namely "chameleon fields" (a species of quintessence) and axions with masses between \(10\,\mu{\rm eV}\) and \(1\eV\) – which would add a Yukawa potential with the Yukawa length between \(2\,{\rm cm}\) and \(0.2\,\mu{\rm m}\) as long as the coupling constant is greater than something like \(g_s g_p \geq 4\times 10^{-16}\).
Some people have proposed that these animals are in between the mirrors everywhere around us and they are responsible for the accelerated expansion of the Universe.
Note that the axions would mediate new Yukawa-like spin-dependent forces between the neutron inside the mirrors and nucleons in between the walls. The Yukawa wavelength is directly linked to the distance between the mirrors. I find it plausible that such axions may exist but the "unnaturally" tiny interaction constants that are required by the experiments make them less likely. The chameleon scenario would produce some additional potential as well and it is excluded for certain ranges of parameters, too.
This GRS (gravity resonance spectroscopy) approach is a powerful way to test models of very light and weakly interacting fields and particles and extra contributions to Newton's gravitational force. There is some overlap with the experiments that have tested old large dimensions (via modifications of Newton's inverse-square law: I think that if BICEP2 is right, old large dimensions are wrong and no corrections to Newton's law will ever be found in this way) but they are not really the same. GRS discussed here uses the quantum wave functions so it may feel certain things more finely than the very fine, but still classical mechanical experiments that have measured gravity beneath one millimeter.
GRS much like other precision experiments rely on resonances and exact frequencies – experimenters get very far with frequency measurements, indeed.
Gravity Resonance Spectroscopy Constrains Dark Energy and Dark Matter Scenarios (arXiv, PRL)Recall that neutrons' wave functions in the Earth's gravitational field have previously been mentioned on this blog as a way to debunk the "gravity as an entropic force": LM, Archil Kobakhidze.
Semi-popular: APS, ArsTechnica, Huff. Post
Click to zoom in: outline and results.
What have they done?
Well, they have prepared some very cold neutrons and sent them in between two horizontal mirrors which were separated by \(\Delta z = 30\,\mu{\rm m}\) in altitude. As you know, this is a nice and simple system in undergraduate non-relativistic quantum mechanics, a potential well.
If the walls were infinitely tall and there were no gravity, the energy eigenstates would be\[
\psi_n(z) = C_n \sin \zav{ \frac{\pi n z}{\Delta z} }, \quad n=1,2,3,\dots
\] The spectrum is discrete. If the gravitational field is added, the wave functions are no longer simple sines. Instead, they are combinations of the Airy functions \({\rm Ai}(z)\) of a sort – with the right coefficients and the right boundary conditions to make everything work. It means that the \(n\)-th wave function is more likely to be found near the bottom wall (mirror) and the wave function is more quickly oscillating over there. Note that the unrestricted linear potential has a continuous energy spectrum (just shifting the wave function in the \(z\)-direction adds some energy) while the mirrors make the spectrum discrete.
These states are discrete but they also apply some frequency – in a way that you know from Rabi spectroscopy – I think that they finally tickled the mirrors in some way although they had wanted to use some variable magnetic gradients, too. In fact, it means that the height of the walls (from the mirrors) isn't infinite but a finite and oscillating as \(\cos \omega t \) with some frequency between 50 and 800 Hertz that they may adjust. This extra periodic, time-dependent disturbance may be treated as a perturbation of the original quantum mechanical system that allows the transitions between the energy levels and they measure their probabilities. For example, the transition \(\ket{2}\leftrightarrow \ket{4}\) has been measured for the first time.
Everything agrees with quantum mechanics supplemented with Newton's potential.
It follows that they may eliminate at the 95% confidence level some (previously viable) models for dark matter and dark energy, namely "chameleon fields" (a species of quintessence) and axions with masses between \(10\,\mu{\rm eV}\) and \(1\eV\) – which would add a Yukawa potential with the Yukawa length between \(2\,{\rm cm}\) and \(0.2\,\mu{\rm m}\) as long as the coupling constant is greater than something like \(g_s g_p \geq 4\times 10^{-16}\).
Some people have proposed that these animals are in between the mirrors everywhere around us and they are responsible for the accelerated expansion of the Universe.
Note that the axions would mediate new Yukawa-like spin-dependent forces between the neutron inside the mirrors and nucleons in between the walls. The Yukawa wavelength is directly linked to the distance between the mirrors. I find it plausible that such axions may exist but the "unnaturally" tiny interaction constants that are required by the experiments make them less likely. The chameleon scenario would produce some additional potential as well and it is excluded for certain ranges of parameters, too.
This GRS (gravity resonance spectroscopy) approach is a powerful way to test models of very light and weakly interacting fields and particles and extra contributions to Newton's gravitational force. There is some overlap with the experiments that have tested old large dimensions (via modifications of Newton's inverse-square law: I think that if BICEP2 is right, old large dimensions are wrong and no corrections to Newton's law will ever be found in this way) but they are not really the same. GRS discussed here uses the quantum wave functions so it may feel certain things more finely than the very fine, but still classical mechanical experiments that have measured gravity beneath one millimeter.
GRS much like other precision experiments rely on resonances and exact frequencies – experimenters get very far with frequency measurements, indeed.
Neutron spectroscopy constrains axions, chameleons
Reviewed by MCH
on
April 23, 2014
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Reviewed by MCH
on
April 23, 2014
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