Foams! (or, why my split pea side dish boils over every Thanksgiving)

Foams can be great examples of mechanical metamaterials.  

Adapted from TOC figure of this paper

Consider my shaving cream.  You might imagine that the (mostly water) material would just pool as a homogeneous liquid, since water molecules have a strong attraction for one another.  However, my shaving cream contains surfactant molecules.  These little beasties have a hydrophilic/polar end and a hydrophobic/nonpolar end.  The surfactant molecules can lower the overall energy of the fluid+air system by lowering the energy cost of the liquid/surfactant/air interface compared with the liquid/air interface.  There is a balancing act between air pressure, surface tension/energy, and gravity that has to be played, but under the right circumstances you end up with formation of a dense foam comprising many many tiny bubbles.  On the macroscale (much larger than the size of individual bubbles), the foam can look like a very squishy but somewhat mechanically integral solid - it can resist shear, at least a bit, and maintain its own shape against gravity.  For a recent review about this, try this paper (apologies for the paywall) or a taste of this in a post from last year. 

What brought this to mind was my annual annoyance yesterday in preparing what has become a regular side dish at our family Thanksgiving.  That recipe begins with rinsing, soaking, and then boiling split peas in preparation for making a puree.  Every year, without fail, I try to keep a close eye on the split peas as they cook, because they tend to foam up.  A lot.  Interestingly, this happens regardless of how carefully I rinse them before soaking, and the foaming (a dense white foam of few-micron-scale bubbles) begins well before the liquid starts to boil.  I have now learned two things about this.  First, pea protein, which leaches out of the split peas, is apparently a well-known foam-inducing surfactant, as explained in this paper (which taught me that there is a journal called Food Hydrocolloids).  Second, next time I need to use a bigger pot and try adding a few drops of oil to see if that suppresses the foam formation.

Nanopasta, no, really

Fig. 1 from the linked paper

Here is a light-hearted bit of research that touches on some fun physics.  As you might readily imagine, there is a good deal of interdisciplinary and industrial interest in wanting to create fine fibers out of solution-based materials.  One approach, which has historical roots that go back even two hundred years before this 1887 paper, is electrospinning.  Take a material of interest, dissolve it in a solvent, and feed a drop of that solution onto the tip of an extremely sharp metal needle.  Then apply a big voltage (say a few to tens of kV) between that tip and a nearby grounded substrate.  If the solution has some amount of conductivity, the liquid will form a cone on the tip, and at sufficiently large voltages and small target distances, the droplet will be come unstable and form a jet off into the tip-target space.  With the right range of fluid properties (viscosity, conductivity, density, concentration) and the right evaporation rate for the solvent, the result is a continuously forming, drying fiber that flows off the end of the tip.  A further instability amplifies any curves in the fiber path, so that you get a spiraling fiber spinning off onto the substrate.   There are many uses for such fibers, which can be very thin.

The authors of the paper in question wanted to make fibers from starch, which is nicely biocompatible for medical applications.  So, starting from wheat flour and formic acid, they worked out viable parameters and were able to electrospin fibers of wheat starch (including some gluten - sorry, for those of you with gluten intolerances) into nanofibers 300-400 nm in diameter.  The underlying material is amorphous (so, no appreciable starch crystallization).  The authors had fun with this and called the result "nanopasta", but it may actually be useful for certain applications.

Brief items

 A few tidbits that I encountered recently:

• The saga of Ranga Dias at Rochester draws to a close, as described by the Wall Street Journal.  It took quite some time for this to propagate through their system.  This is after multiple internal investigations that somehow were ineffective, an external investigation, and a lengthy path through university procedures (presumably because universities have to be careful not to shortcut any of their processes, or they open themselves up to lawsuits).
• At around the same time, Mikhail Eremets passed away.  He was a pioneer in high pressure measurements of material properties and in superconductivity in hydrides.
• Also coincident, this preprint appeared on the arXiv, a brief statement summarizing some of the evidence for relatively high temperature superconductivity in hydrides at high pressure.
• Last week Carl Bender gave a very nice colloquium at Rice, where he spoke about a surprising result.  When we teach undergrad quantum mechanics, we tell students that the Hamiltonian (the expression with operators that gives the total energy of a quantum system) has to be Hermitian, because this guarantees that the energy eigenvalues have to be real numbers.  Generically, non-hermitian Hamiltonians would imply complex energies, which would imply non-conservation of total probability. That is one way of treating open quantum systems, when particles can come and go, but for closed quantum systems, we like real energies.  Anyway, it turns out that one can write an explicitly complex Hamiltonian that nonetheless has a completely real energy spectrum, and this has deep connections to PT symmetry conservation.  Here is a nice treatment of this.
• Just tossing this out:  The entire annual budget for the state of Arkansas is $6.5B.  The annual budget for Stanford University is $9.5B.  

More soon.

Really doing mechanics at the quantum level

A helpful ad from Science Made Stupid.

Since before the development of micro- and nanoelectromechanical techniques, there has been an interest in making actual mechanical widgets that show quantum behavior.  There is no reason that we should not be able to make a mechanical resonator, like a guitar string or a cantilevered beam, with a high enough resonance frequency so that when it is placed at low temperatures ( \(\hbar \omega \gg k_{\mathrm{B}}T\)), the resonator can sit in its quantum mechanical ground state.  Indeed, achieving this was Science's breakthrough of the year in 2010.  

This past week, a paper was published from ETH Zurich in which an aluminum nitride mechanical resonator was actually used as a qubit, where the ground and first excited states of this quantum (an)harmonic oscillator represented \(|0 \rangle\) and \(|1 \rangle\).  They demonstrate actual quantum gate operations on this mechanical system (which is coupled to a more traditional transmon qubit - the setup is explained in this earlier paper).  

One key trick to being able to make a qubit out of a mechanical oscillator is to have sufficiently large anharmonicity.  An ideal, perfectly harmonic quantum oscillator has an energy spectrum given by \((n + 1/2)\hbar \omega\), where \(n\) is the number of quanta of excitations in the resonator.  In that situation, the energy difference between adjacent levels is always \(\hbar \omega\).  The problem with this from the qubit perspective is, you want to have a quantum two-level system, and how can you controllably drive transitions just between a particular pair of levels when all of the adjacent level transitions cost the same energy?  The authors of this recent paper have achieved a strong anharmonicity, basically making the "spring" of the mechanical resonator softer in one displacement direction than the other.  The result is that the energy difference between levels \(|0\rangle\) and \(|1\rangle\) is very different than the energy difference between levels \(|1\rangle\) and \(|2\rangle\), etc.  (In typical superconducting qubits, the resonance is not mechanical but an electrical \(LC\)-type, and a Josephson junction acts like a non-linear inductor, giving the desired anharmonic properties.)  This kind of mechanical anharmonicity means that you can effectively have interactions between vibrational excitations ("phonon-phonon"), analogous to what the circuit QED folks can do.  Neat stuff.

Recent papers to distract....

Time for blogging has continued to be scarce, but here are a few papers to distract (and for readers who are US citizens:  vote if you have not already done so!).

• Reaching back, this preprint by Aharonov, Collins, Popescu talks about a thought experiment in which angular momentum can seemingly be transferred from one region to another even though the probability of detecting spin-carrying particles between the two regions can be made arbitrarily low.  I've always found these kinds of discussions to be fun, even when the upshot for me is usually, "I must not really understand the subtleties of weak measurements in quantum mechanics."  This is a specific development based on the quantum Cheshire cat idea.  I know enough to understand that when one is talking about post-selection in quantum experiments, some questions are just not well-posed.  If we send a wavepacked of photons at a barrier, and we detect with a click a photon that (if it was in the middle of the incident wavepacket) seems to have therefore traversed the barrier faster than c, that doesn't mean much, since the italicized parenthetical clause above is uncheckable in principle.  
• Much more recently, this paper out last week in Nature reports the observation of superconductivity below 200 mK in a twisted bilayer of WSe2.  I believe that this is the first observation of superconductivity in a twisted bilayer of an otherwise nonsuperconducting 2D semiconductor other than graphene.  As in the graphene case, the superconductivity shows up at a particular filling of the moiré lattice, and interestingly seems to happen around zero applied vertical electric field (displacement field) in the device.  I don't have much to say here beyond that it's good to see interesting results in a broader class of materials - that suggests that there is a more general principle at work than "graphene is special".
• This preprint from last week from Klein et al. is pretty impressive.  It's been known for over 25 years (see here) that it is possible to use a single-electron transistor (SET) as a scannable charge sensor and potentiometer.  Historically, making these devices and operating them has been a real art.  They are fragile, static-sensitive, and fabricating them from evaporated metal on the tips of drawn optical fibers is touchy.  There have been advances in recent years from multiple quarters, and this paper demonstrates a particularly interesting idea: Use a single charge trap in a layer of WSe2 as the SET, and effectively put the sample of interest on the scannable tip.  This is an outgrowth of the quantum twisting microscope.