Algorithmic approach to scientific writing style: the structure of a paragraph

With three of my students writing their theses this year, I decided to formalize some advice on a clear writing style. Yes, writing is an art form, yet I find that following these simple rules would produce understandable technical writing - a vast improvement over not following rules at all.

Here are my notes on how to make a paragraph flow.

  1. Pick a keyword/phrase/concept/idea that you would want to focus in the paragraph. This keyword should remain the focus of individual sentences throughout the paragraph.  This simple trick helps the paragraph “flow”.
  2. The first sentence of a paragraph should announce what you intend to communicate in the paragraph. For example, “Below we show that …”. Remember you are writing to be easily understood.
  3.  The last sentence should summarize the paragraph and possibly pre-announce what would happen in the following paragraph tying the paragraphs together.
  4. "Square" rule - typically a paragraph should not occupy more than a "square" on a printed page, i.e., the height of the paragraph should not exceed the column width. Shorter paragraphs are fine. If longer, strongly consider breaking the paragraph in two.
  5. Read  the paragraph ALOUD - even a non-native speaker would be able to tell if the writing "feels" right.

Additional notes: Do not mix passive and active voice in a paragraph.

When would an unanticipated “new physics” event be apparent to an unsuspecting experimentalist?

Suppose an experimentalist has a sensitive device, the conventional physics of which is well under control.  Now let’s assume that once in while the device is perturbed by some unanticipated  “new physics” events, such as an interaction with a lump of dark matter. Suppose the device has enough sensitivity to “new physics”.  When would an unanticipated “new physics” event become apparent to an unsuspecting experimentalist?

This is quite different from particle colliders, when experimentalists do hunt for unusual events. Sometimes specific signal or signature is anticipated (e.g., the Higgs), so let me emphasize that our unsuspecting fellow experimentalist does not specifically look for new physics.

The discovery of the cosmic microwave background could serve as a motivating example of paying attention to “misbehaving” data.

So when would  “new physics” be noticed?  An obvious answer would be: when the new physics perturbs the expected signal in a significant way.

Even this simple statement requires qualifiers. Suppose new physics provides a uniform background to the signal and the signal itself cannot be computed exactly from the first principles. For example, transition frequencies of many-electron atoms can be computed only to 3-4 significant figures while experimentalists can determine some of these frequencies to 18 significant figures. Then (unless there are symmetry arguments, e.g., parity or time-reversal violation and associated external field reversals implemented in an experiment) there is no way to dissect the new physics background from the conventional one.

This leaves us with time/space-dependent new physics signals. I.e., new physics could be noticed if it leads to some noise or drift in time/space-dependent signals. For example, a uniform-in-time drift in atomic frequencies could reveal variation in fundamental constants.

What about “new-physics” noise/spike-like events, such as the perturbation by "lumps" of dark-matter? Suppose the conventional signal is interrupted by new physics events. We could characterize such events by how long an event lasts (short/long interaction times), how frequent the events are (rare/frequent) and if the device is sensitive to the event.  For simplicity we assume that the events do not overlap, i.e., the average time between the individual events is much longer than the event duration.

The event would be missed if the average time between consecutive events is larger than a typical time of continuous operation of the device (i.e., the events are rare). Unfortunately, a single bona fide event could be discarded by an experimentalist as being an outlier. Indeed, one can never guarantee that everything is fully under control, as there still may be occasional perturbations present, such as a student bumping into an optical table or misbehaving power supplies.

Essentially, rare events would be registered as such only if they are anticipated.

This argument brings us to the following conclusion: unanticipated “new physics” events would be noticed only if the sizable events are frequent on time-scale of the experiment.

There is another caveat: suppose the events are so frequent that they look like a white or a flicker noise in the signal. After all it is natural to assume Poissonian distribution of time intervals between consecutive events. Then there is a danger of “integrating out” the events.

Thereby we have to revise our statement: unanticipated “new physics” events would be noticed only if the sizable events are frequent (but not too frequent) on the time-scale of the experiment.

In practical terms, for a typical atomic physics experiment, the events should last longer than a second and there should be hundreds of them per day of operation. Even then, the experimentalist should be gutsy enough to put his/her credibility and comfort at risk and publicly report the data as being unusual.  “New physics” looks for the right fellow to notice and appreciate it.

P.S. I would like to thank Dima Budker and Jeff Sherman for discussions on this topic

Workshop on New Ideas In Low-Energy Tests Of Fundamental Physics

I would like to announce a  workshop  at the intersection of atomic physics with particles and fields (Ok, it has some elements of cosmology too). The workshop is to be held at the Perimeter Institute in mid-June of 2014. Having visited Perimeter for a couple of weeks, I highly recommend its stimulating environment. Here is the announcement:

NEW IDEAS IN LOW-ENERGY TESTS OF FUNDAMENTAL PHYSICS

Conference Date:  Monday, June 16, 2014 (All day) to Thursday, June 19, 2014 (All day)

The purpose of the workshop is to bring together members of theoretical and experimental communities interested in finding new fundamental applications to continuing advancement of new high-precision tools in AMO physics. The foci of the workshop will include novel approaches to searches for axions, axion-like particles and other light exotic fields, which can serve as dark matter candidates; new ideas in application of the networks of time-correlated devices (atomic magnetometers, atomic clocks etc.); new ways of testing properties of gravitational interactions and fundamental constants as well as developing new gravitational wave detectors.

Scientific Organizers:

Asimina Arvanitaki, Stanford University
Dmitry Budker, University of California, Berkeley & Helmholtz Institute, Mainz
Andrei Derevianko, University of Nevada
Peter Graham, Stanford University
Derek Jackson Kimball, California State University
Maxim Pospelov, Perimeter Institute & University of Victoria

More details can be found at the Perimeter workshop webpage.

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.

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.

Tug-of-war model and tuned-out Rydberg

Tug-of-war zero sum of optical forces

Tug-of-war model for a Rydberg atom in optical lattice.  I(z) is the lattice intensity dependence and the atom is made out of a nucleus and two lumps of electronic wave function. For a certain distance between the lumps (\lambda/4),  optical forces on the two lumps cancel each other no matter what the atomic position is.

Finally a chance for a Rydberg atom to tune out, chill out and be all it ever wanna be. Would not it be great to just sail through life hurdles without ever noticing them? Now Rydberg atoms can just do that easily and naturally, thanks to the latest theoretical understanding coming from our group.

We find special "tune-out conditions" that guarantee that Rydberg atom motion remains uninhibited by optical lattice. This is illustrated by  the tug-of-war Figure to the left. Here a 1D Rydberg atom is made out of a nucleus and two rigidly placed lumps of electronic density.  The total dipole optical force vanishes  when the diameter of the orbit is equal to half the lattice constant.

For the 3D case, realistic atoms, and all the technical details, see our publication:
Tune-out wavelengths and landscape-modulated polarizabilities of alkali-metal Rydberg atoms in infrared optical lattices, T. Topcu, A. Derevianko, Phys. Rev. A 88, 053406 (2013) arXiv:1308.6258

Here is the abstract:
Intensity modulated optical lattice potentials can change sign for an alkali metal Rydberg atom, and the atoms are not always attracted to intensity minima in optical lattices with wavelengths near the CO2 laser band. Here we demonstrate that such IR lattices can be tuned so that the trapping potential seen by the Rydberg atom can be made to vanish for atoms in "targeted" Rydberg states. Such state selective trapping of Rydberg atoms can be useful in controlled cold Rydberg collisions, cooling Rydberg states, and species-selective trapping and transport of Rydberg atoms in optical lattices. We tabulate wavelengths at which the trapping potential vanishes for the ns, np, and nd Rydberg states of Na and Rb atoms, and discuss advantages of using such optical lattices for state selective trapping of Rydberg atoms. We also develop exact analytic expressions for the lattice induced polarizability for the m_z=0 Rydberg states, and derive an accurate formula predicting tune-out wavelengths at which the optical trapping potential becomes invisible to Rydberg atoms in targeted l=0 states.