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## A dark matter model for decoherence detection

[Added 2015-1-30: The paper is now in print and has appeared in the popular press.]One criticism I’ve had to address when proselytizing the indisputable charms of using decoherence detection methods to look at low-mass dark matter (DM) is this: I’ve never produced a concrete model that would be tested. My analysis (arXiv:1212.3061) addressed the possibility of using matter interferometry to rule out a large class of dark matter models characterized by a certain range for the DM mass and the nucleon-scattering cross section. However, I never constructed an explicit model as a representative of this class to demonstrate in detail that it was compatible with all existing observational evidence. This is a large and complicated task, and not something I could accomplish on my own.

I tried hard to find an existing model in the literature that met my requirements, but without luck. So I had to argue (with referees and with others) that this was properly beyond the scope of my work, and that the idea was interesting enough to warrant publication without a model. This ultimately was successful, but it was an uphill battle. Among other things, I pointed out that new experimental concepts can inspire theoretical work, so it is important that they be disseminated.

I’m thrilled to say this paid off in spades. Bateman, McHardy, Merle, Morris, and Ulbricht have posted their new pre-print “On the Existence of Low-Mass Dark Matter and its Direct Detection” (arXiv:1405.5536). Here is the abstract:

I am sadly not fit to evaluate the astrophysical aspects of their paper, but I look forward to it withstanding criticism.

It’s important to note that, in addition to decoherence detection with matter interferometers, they also discuss the possibility of detecting this dark matter candidate using classical methods, to wit a satellite-based target-mass experiment:

This conflicts with the notion that this dark matter is “classically undetectable” (which is embarrassing to my title). The reason is that, for test masses that are quantum systems localized in phase space, the property of a force being classically undetectable is always defined with respect to a given time scale. Given infinite time, it’s known that arbitrarily small forces can in principle be detected so long as the force doesn’t average to zero. Caves PRL 1985, Giovannetti et al. Science 2004.

^{a }If you have unlimited time, you can just prepare hugely wide wavepackets and let them drift apart extremely slowly. The standard quantum limit was originally discussed in the context of gravitational waves, for which the time-averaged displacement and momentum transfer is zero; therefore there is a naturally time scale to use. Dark matter has no such time scale because there is a non-zero wind, with collisions leading to a Brownian walk with a finite drift speed. Now, the long drift times discussed by Bateman et al. (several minutes) necessitate a space mission, but of course so does the matter interferometry proposal (MAQRO) that would be sensitive to this DM model.There is in principle always a regime for which quantum techniques outperform any classical testFix a maximum time and then take the negligible-momentum-transfer limit, increasing the size of the superpositions to always be larger than the de Broglie wavelength of the particle causing the decoherence.

^{b }. But there will also be cases (like this model) where both techniques may be viable and we need to look at the details to determine which is a more promising experiment.[Edited 2014-6-24]## Footnotes

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