Really doing mechanics at the quantum level

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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.