# Postdoctoral position GPS.DM collaboration

GPS.DM collaboration analyzes navigational satellite and terrestrial atomic clock data for  exotic physics signatures. In particular, the collaboration searches for transient variations of fundamental constants correlated with the Earth’s galactic motion through the dark matter halo. A postdoctoral associate will be primarily responsible for  mining  massive amounts of historic GPS data and developing statistical analysis.

The postdoc will be located at the University of Nevada, Reno and will be directly collaborating with Dr. Andrei Derevianko (Physics) and Dr. Geoffrey Blewitt (Nevada Geodetic Laboratory). Strong computational skills and familiarity with statistical analysis are preferred.

# Dark matter search with GPS: Q&A

In the aftermath of our paper (with Maxim Pospelov) "Hunting for topological dark matter with atomic clocks" having been published, there were quite a number of e-mails with questions about our proposal. There was even an offer for a free-of-charge use of a powerful computational cluster (thank you!). I apologize for not answering all e-mails individually - just not enough time.  One of my friends has also sent me a link to this reddit thread - there is a genuine interest to the details of the proposal. This post is intended to answer some of these questions.

First of all see the previous post that outlines the basic idea of the search.

Topological dark matter:
There are two components that go into dark-matter model building: (i) what the dark matter objects are and (ii) how these objects interact non-gravitationally with us (baryonic or ordinary matter). I emphasize the word non-gravitationally, as the gravitational interaction is a must due to multiple observations of gravitational interactions between dark and ordinary matter (and consistency with general relativity).

Additional model constraints come from various observations and cosmological simulations. Still the allowed parameter space is enormous: even if one were to assume that the dark matter objects are made out of elementary particles, the allowed masses span 50 orders (!) of magnitude. This is just a testament to the current state of confusion in modern physics and cosmology.  The field is ripe for discoveries.

First of all I admit that our model (due to Maxim Pospelov) is speculative, but it is as good as any model out there. WIMPs and axions have additional attractive features as they also might solve other outstanding problems in physics (for example, strong-CP problem in physics can be solved with axions).

So what is the model? (here you might get lost, just read on). For experts, technical discussion can be found in the extensive supplementary material to our paper.

Well, you start with a quantum field and this field has some self-interaction built in. The interaction is such that it allows for several identical minima. For example, the same value of potential minima could be reached at two distinct values of the field +A and -A. Now when the Universe expands it cools down and the field has to settle at the minima of the potential. The field is torn apart by which value to chose - the choice of +A or -A are equivalent. So in some regions of space it picks +A and in the other regions it picks -A. This is called "spontaneous symmetry breaking".

Nature does not like discontinuities and you have to smoothly connect  +A and  -A domains. This transition region is the topological defect or cosmic wall. The thickness of the wall is given by the particle Compton wavelength = h/(m c), where m is the particle mass, is the Plank constant and c is the speed of light.

This example is overly-simplistic but it demonstrates the idea of how topological defects are formed as the Universe cools down: in fact, for a dark-matter model you would like to have the field to be zero everywhere except inside the defects (see the supplement). All the energy (or mass) is stored in topological defects.

Depending on the field's degrees of freedom (scalar vs vector fields) and the self-interaction potential  one may form defects of various geometry: monopoles, strings or domain walls. Especially interesting is the case of monopoles (spherically-symmetric objects) as the gravitationally-interacting gas of monopoles mimics dark matter. The size of the defect is a free parameter - we do not have constraints on how large it could be. GPS would be sensitive to Earth-sized monopoles (huge Compton wavelength translating into particle mass ~10^-14 eV).

Here is a real-life example of spontaneous symmetry breaking and topological defects (due to Rafael Lang, the interview to appear in Sensing Our Planet magazine)

“There’s a wedding and a hundred people are sitting at this big round table. Somebody starts eating the salad. They pick up the fork on their left, so the person next to them has to pick up the fork on the left. Now the bride also starts eating, picking up the fork on the right, so everybody around the bride picks up the right fork. At some point in between this poor guy will be sitting with no fork; on his other side will be someone with two forks. Those two guys are called a topological defect. There’s nothing special going on around the left, the right, but where those two guys are sitting, there’s a disruption of the forks.”

Ok so we are done with choosing dark-matter objects. Now the second ingredient is the non-gravitational interaction between dark matter objects and us. Here you do need to pick one that is "reasonable" (e.g., Lorentz-invariant)  and is sufficiently weak that it went unnoticeable in dedicated experiments and observations. The interaction that we picked is of this kind. Effectively when the defect overlaps with us, it pulls on the particle (electron, proton, neutron, etc) masses and forces acting between the particles. Mind you this pull is really weak, otherwise we would have noticed it. However, there are ultra-sensitive devices, like atomic clocks (see this post) that may be sensitive to such pulls. You might ask - why it might have gone unnoticed before in atomic clocks -  some of the reasons are purely psychological and are related to how an experimentalist discerns signal from noisy background (see this post.)

# Search for topological dark matter with atomic clocks

By monitoring correlated time discrepancy between two spatially-separated clocks one could search for passage of topological defects (TD), such as domain wall pictured here. Domain wall moves at galactic speeds ~ 300 km/s. Here the clocks are assumed to be identical. Before the TD arrival at the first clock, the apparent time difference is zero, as the clocks are synchronized. As the TD passes the first clock, it runs faster (or slower, depending on the TD-SM coupling), with the clock time difference reaching the maximum value. Time difference stays at that level while the defect travels between the two clocks. Finally, as the defect sweeps through the second clock, the phase difference vanishes. For intercontinental scale network, l~ 10,000 km, the characteristic time 30 seconds.

Despite solid observational evidence for the existence of dark matter, its nature remains a mystery. A large and ambitious research program in particle physics assumes that dark matter is composed of heavy-particle-like matter. That community hopes to see events of dark matter particles scattering off individual nuclei. Considering nil results of the latest particle detector experiments (see excellent discussion here), this assumption may not hold true, and significant interest exists to alternatives.

Now what about atomic clocks? Atomic clocks are arguably the most accurate scientific instruments ever build. Modern clocks approach the $10^{-18}$ fractional inaccuracy, which translates into astonishing timepieces guaranteed to keep time within a second over the age of the Universe. Attaining this accuracy requires that the quantum oscillator be well protected from environmental noise and perturbations well controlled and characterized. This opens intriguing prospects of using clocks to study subtle effects, and it is natural to ask if such accuracy can be harnessed for dark matter searches.

Posing and answering this question is the subject of our recent paper:
Hunting for topological dark matter with atomic clocks, A. Derevianko and M. Pospelov, arXiv:1311.1244.

We consider one of alternatives to heavy-particle dark matter and focus on so-called topological dark matter. The argument is that depending on the initial quantum field configuration at early cosmological times, light fields could lead to dark matter via coherent oscillations around the minimum of their potential, and/or form non-trivial stable field configurations in space (topological defects). The stability of this type of dark matter can be dictated by topological reasons.

I know, this sounds a little bit too far fetched to an atomic physicist. Well, ferro-magnets could serve as a familiar analogy. Here topological defects are domain walls separating domains of well-defined magnetization. Above the Curie point, the sample is uniform, but as the temperature is lowered, the domains start to form. So one could argue that as the Universe was cooling down after the Big Bang, quantum fields underwent a similar phase transition.

Generically, one could talk about 0D topological defects (=monopoles), 1D=strings, and 2D=walls. Dark matter would form out of such defects. The light masses of fields forming the defects could lead to a large, macroscopic, size for a defect. Based on observations and simulations, astronomers have a good idea of how dark matter moves around the Solar system. The defects would fly through the Earth at galactic velocities ~ 300 km/s. Now if the defects couple (non-gravitationally) to ordinary matter, one could think of a detection scheme using sensitive listening devices, e.g., atomic clocks. In fact one would benefit from a network of clocks, as one would cross-correlate events occurring at different locations.

Phenomenologically, the dark matter interaction with ordinary matter could be described as a transient variation of fundamental constants. The coupling would shift atomic frequencies and thus affect time readings. During the encounter with a topological defect, as it sweeps through the network, initially synchronized clocks will become desynchronized. This is illustrated in the figure.

The real advantage of clocks is that these are ubiquitous. Several networks of atomic clocks are already operational. Perhaps the most well known are Rb and Cs atomic clocks on-board satellites of the Global Positioning System (GPS) and other satellite navigation systems. Currently there are about 30 satellites in the GPS constellation orbiting the Earth with an orbital radius of 26,600 km with a half of a sidereal day period. As defects sweep through the GPS constellation, satellite clock readings are affected. For two diametrically-opposed satellites the maximum time delay between clock perturbations would be ~ 200 s, assuming the sweep with a typical speed of 300 km/s. Different types of topological defects (e.g., domain walls versus monopoles) would yield distinct cross-correlation signatures. While the GPS is affected by a multitude of systematic effects, e.g., solar flares, temperature and clock frequency modulations as the satellites come in out of the Earth shadow, none of conventional effects would propagate with 300 km/s through the network. Additional constraints can come from analyzing extensive terrestrial network of atomic clocks on GPS tracking stations.

The performance of GPS on-board clocks is certainly lagging behind state-of-the art laboratory clocks. Focusing on laboratory clocks, one could carry out a dark matter search employing the vast network of atomic clocks at national standards laboratories used for evaluating the TAI timescale. Moreover, several elements of high-quality optical links for clock comparisons have been already demonstrated in Europe, with 920 km link connecting two laboratories in Germany.

Naturally I hope that this proposal motivates dark matter searches with atomic physics tools pushing our “listening capabilities” to the next level. This proposal could provide fundamental physics motivation to building high-quality terrestrial and space-based networks of clocks. As the detection schemes would benefit from improved accuracy of short-term time and frequency determination, following this path could stimulate advances in ultra-stable atomic clocks and Heisenberg-limited time-keeping.