Friday, October 20, 2017

Neutron stars and condensed matter physics

In the wake of the remarkable results reported earlier this week regarding colliding neutron stars, I wanted to write just a little bit about how a condensed matter physics concept is relevant to these seemingly exotic systems.

When you learn high school chemistry, you learn about atomic orbitals, and you learn that electrons "fill up" those orbitals starting with the lowest energy (most deeply bound) states, two electrons of opposite spin per orbital.  (This is a shorthand way of talking about a more detailed picture, involving words like "linear combination of Slater determinants", but that's a detail in this discussion.)  The Pauli principle, the idea that (because electrons are fermions) all the electrons can't just fall down into the lowest energy level, leads to this.  In solid state systems we can apply the same ideas.  In a metal like gold or copper, the density of electrons is high enough that the highest kinetic energy electrons are moving around at ~ 0.5% of the speed of light (!).  

If you heat up the electrons in a metal, they get more spread out in energy, with some occupying higher energy levels and some lower energy levels being empty.   To decide whether the metal is really "hot" or "cold", you need a point of comparison, and the energy scale gives you that.  If most of the low energy levels are still filled, the metal is cold.  If the ratio of the thermal energy scale, \(k_{\mathrm{B}}T\) to the depth of the lowest energy levels (essentially the Fermi energy, \(E_{\mathrm{F}}\) is much less than one, then the electrons are said to be "degenerate".  In common metals, \(E_{\mathrm{F}}\) is several eV, corresponding to a temperature of tens of thousands of Kelvin.  That means that even near the melting point of copper, the electrons are effectively very cold.

Believe it or not, a neutron star is a similar system.  If you squeeze a bit more than one solar mass into a sphere 10 km across, the gravitational attraction is so strong that the electrons and protons in the matter are crushed together to form a degenerate ball of neutrons.  Amazingly, by our reasoning above, the neutrons are actually very very cold.  The Fermi energy for those neutrons corresponds to a temperature of nearly \(10^{12}\) K.  So, right up until they smashed into each other, those two neutron stars spotted by the LIGO observations were actually incredibly cold, condensed objects.   It's also worth noting that the properties of neutron stars are likely affected by another condensed matter phenomenon, superfluidity.   Just as electrons can pair up and condense into a superconducting state under some circumstances, it is thought that cold, degenerate neutrons can do the same thing, even when "cold" here might mean \(5 \times 10^{8}\) K.

Sunday, October 15, 2017

Gravitational waves again - should be exciting

There is going to be a big press conference tomorrow, apparently to announce that LIGO/VIRGO has seen an event (binary neutron star collision) directly associated with a gamma ray burst in NGC 4993.  Fun stuff, and apparently the worst-kept secret in science right now.  This may seem off-topic for a condensed matter blog, but there's physics in there which isn't broadly appreciated, and I'll write a bit about it after the announcement.

Tuesday, October 10, 2017

Piezo controller question - followup.

A couple of weeks ago I posted:

Anyone out there using a Newport NPC3SG controller to drive a piezo positioning stage, with computer communication successfully talking to the NPC3SG?  If so, please leave a comment so that we can get in touch, as I have questions.

No responses so far.  This is actually the same unit as this thing:
https://www.piezosystem.com/products/piezo_controller/piezo_controller_3_channel_version/nv_403_cle/

In our unit from Newport, communications simply don't work properly.  Timeout problems.  The labview code supplied by Newport (the same code paired with the link above) has these problems, as do many other ways of trying to talk with the instrument.  Has anyone out there had success in using a computer to control and read this thing?   At issue is whether this is a hardware problem with our unit, or whether there is a general problem with these.  The vendor has been verrrrrrrrry slow to figure this out.

Sunday, October 08, 2017

The Abnormal Force

How does the chair actually hold you up when you sit down?  What is keeping your car tires from sinking through the road surface?  What is keeping my coffee mug from falling through my desk?  In high school and first-year undergrad physics, we teach people about the normal force - that is a force that acts normal (perpendicular) to a surface, and it takes on whatever value is needed so that solid objects don't pass through each other.

The microscopic explanation of the normal force is that the electrons in the atoms of my coffee mug (etc.) interact with the electrons in the atoms of the desk surface, through a combination of electrostatics (electrons repel each other) and quantum statistics (the Pauli principle means that you can't just shuffle electrons around willy-nilly).  The normal force is "phenomenological" shorthand.  We take the observation that solid objects don't pass through each other, deduce that whatever is happening microscopically, the effect is that there is some force normal to surfaces that touch each other, and go from there, rather than trying to teach high school students how to calculate it from first principles.  The normal force is an emergent effect that makes sense on macroscopic scales without knowing the details.  This is just like how we teach high school students about pressure as a useful macroscopic concept, without actually doing a statistical calculation of the average perpendicular force per area on a surface due to collisions with molecules of a gas or a liquid.  

You can actually estimate the maximum reasonable normal force per unit area.  If you tried to squeeze the electrons of two adjacent atoms into the volume occupied by one atom, even without the repulsion of like charges adding to the cost, the Pauli principle means you'd have to kick some of those electrons into higher energy levels.  If a typical energy scale for doing that for each electron was something like 1 eV, and you had a few electrons per atom, and the areal density of atoms is around 1014 per cm2, then we can find the average force \(F_{\mathrm{av}}\) required to make a 1 cm2 area of two surfaces overlap with each other.   We'd have \(F_{\mathrm{av}} d \sim 10^{15}\)eV, where \(d\) is the thickness of an atom, around 0.3 nm.   That's around 534000 Newtons/cm2, or around 5.3 GPa.   That's above almost all of the yield stresses for materials (usually worrying about tension rather than compression) - that just means that the atoms themselves will move around before you really push electrons around.

Very occasionally, when two surfaces are brought together, there is a force that arises at the interface that is not along the normal direction.  A great example of that is in this video, which shows two graphite surfaces that spontaneously slide in the plane so that they are crystallographically aligned.  That work comes from this paper.

As far as I can tell, there is no official terminology for such a spontaneous in-plane force.  In the spirit of one of my professional heroes David Mermin, who coined the scientific term boojum, I would like to suggest that such a transverse force be known as the abnormal force.  (Since I don't actually work in this area and I'm not trying to name the effect after myself, hopefully the barrier to adoption will be lower than the one faced by Mermin, who actually worked on boojums :-)  ).

Tuesday, October 03, 2017

Gravitational radiation for the win + communicating science

As expected, LIGO was recognized by the Nobel Prize in physics this year.  The LIGO experiment is an enormous undertaking that combines elegant, simple theoretical ideas; incredible engineering and experimental capabilities; and technically virtuosic numerical theoretical calculations and data analysis techniques.  It's truly a triumph.

I did think it was interesting when Natalie Wolchover, one of the top science writers out there today, tweeted:   Thrilled they won, thrilled not to spend this morning speed-reading about some bizarre condensed matter phenomenon.

This sentiment was seconded by Peter Woit, who said he thought she spoke for all science journalists.

Friendly kidding aside, I do want to help.  Somehow it's viewed as comparatively easy and simple to write about this, or this, or this, but condensed matter is considered "bizarre".  

Sunday, October 01, 2017

Gravitational radiation redux + Nobel speculation

This past week, there was exciting news that the two LIGO detectors and the VIRGO interferometer had simultaneously detected the same event, a merger of black holes estimated to have taken place 1.6 billion lightyears away.  From modeling the data, the black hole masses are estimated at around 25 and 30 solar masses, and around 2.7 solar masses worth of energy (!) was converted in the merger into gravitational radiation.  The preprint of the paper is here.  Check out figure 1.  With just the VIRGO data, the event looks really marginal - by eye you would be hard pressed to pick it out of the fluctuating detector output.  However, when that data is thrown into the mix with that from the (completely independent from VIRGO) detectors, the case is quite strong.

This is noteworthy for (at least) two reasons.  First, there has been some discussion about the solidity of the previously reported LIGO results - this paper (see here for a critique of relevant science journalism) argues that there are some surprising correlations in the noise background of the two detectors that could make you wonder about the analysis.  After all, the whole point of having two detectors is that a real event should be seen by both, while one might reasonably expect background jitter to be independent since the detectors are thousands of miles apart.  Having a completely independent additional detector in the mix should be useful in quantifying any issues.  Second, having the additional detector helps nail down the spot in the sky where the gravitational waves appear to originate.  This image shows how previous detections could only be localized by two detectors to a band spanning lots of the sky, while this event can be localized down to a spot spanning a tenth as much solid angle.    This is key to turning gravitational wave detectors into serious astronomy tools, by trying to link gravitational event detection to observations across the electromagnetic spectrum.  There were rumors, for example, that LIGO had detected what was probably a neutron star collision (smaller masses, but far closer to earth), the kind of event thought to produce dramatic electromagnetic signatures like gamma ray bursts.

On that note, I realized Friday that this coming Tuesday is the announcement of the 2017 Nobel in physics.  Snuck up on me this time.  Speculate away in the comments.  Since topology in condensed matter was last year's award, it seems likely that this year will not be condensed matter-related (hurting the chances of people like Steglich and Hosono for heavy fermion and iron superconductors, respectively).  Negative index phenomena might be too condensed matter related.   The passing last year of Vera Rubin and Debra Jin is keenly felt, and makes it seem less likely that galactic rotation curves (as evidence for dark matter) or ultracold fermions would get it this year.  Bell's inequality tests (Aspect, Zeilinger, Clauser) could be there.   The LIGO/VIRGO combined detection happened too late in the year to affect the chances of this being the year for gravitational radiation (which seems a shoe-in soon).

Tuesday, September 26, 2017

The terahertz gap

https://commons.wikimedia.org/wiki/File:Thz_freq_in_EM_spectrum.png?uselang=en-gb
At a thesis proposal talk yesterday, I realized that I hadn't ever written anything specifically about terahertz radiation (THz, or if you're trying to market something, t-rays).   Terahertz (1012 Hz) is the frequency of electromagnetic radiation higher than microwaves, but lower than what is traditionally labeled the far infrared.  Sometimes called "mm wave" radiation (1 THz would be a free-space wavelength of about 0.3 mm or 300 microns), THz is potentially very useful for communications (pdf, from here), imaging (here, here, here), and range detection (see here for an impressive google project; or here for an article about THz for self-driving cars), among other things.  It's also right around the frequency range of a lot of vibrations in molecules and solids, so it can be used for spectroscopy, though it's also around the energy range where water vapor in the atmosphere can be an efficient absorber.

This frequency region is an awkward middle ground, however.  That's sometimes why it's referred to as the "terahertz gap".

We tend to produce electromagnetic radiation by one of two approaches.  Classically, accelerating charges radiate electromagnetic waves.  In the low frequency limit, there are various ways to generate voltages that oscillate - we can in turn use those to drive oscillating currents and thus generate radio waves, for example.  See here for a very old school discussion.  It is not trivial to shake charges back and forth at THz frequencies, however.  It can be done, but it's very challenging.  One approach to generating a pulse of THz radiation is to use a photoconductive antenna.  Take two electrodes close together on a semiconductor substrate, with a voltage applied between them.  Smack the semiconductor with an ultrafast optical pulse that has a frequency high enough to photoexcite a bunch of charge carriers - those then accelerate from the electric field between the electrodes and emit a pulse of radiation, including THz frequencies.

The other limit we often take in generating light is to work with some quantum system that has a difference in energy levels that is the same energy as the photons we want to generate.  This is the limit of atomic emission (say, having an electron drop from the 2p orbital to the 1s orbital of a hydrogen atom, and emitting an ultraviolet photon of energy around 10 eV) and also the way many solid state devices work (say, having an electron drop from the bottom of the conduction band to the top of the valence band in InGaAsP to produce a red photon of energy around 1.6 eV in a red LED).  The problem with this approach for THz is that the energy scale in question is very small - 1 THz is about 4 milli-electron volts (!).  As far as I know, there aren't naturally occurring solids with energy level splittings that small, so the approach from this direction has been to create artificial systems with such electronic energy gaps - see here.   (Ironically, there are some molecular systems with transitions considerably lower in energy than the THz that can be used to generate microwaves, as in this famous example.)

It looks like THz is starting to take off for technologies, particularly as more devices are being developed for its generation and detection.  SiGe-based transistors, for example, can operate at very high intrinsic speeds, and like in the thesis proposal I heard yesterday, these devices are readily made now and can be integrated into custom chips for exactly the generation and detection of radiation approaching a terahertz.  Exciting times.