Tunneling two-level systems in solids: Direct measurements

Back in the ancient mists of time, I did my doctoral work studying tunneling two-level systems (TLS) in disordered solids.  What do these words mean?  First, read this post from 2009.   TLS are little, localized excitations that were conjectured to exist in disordered materials.  Imagine a little double-welled potential, like this image from W. A. Phillips, Rep. Prog. Phys. 50 (1987) 1657-1708.

The low temperature thermal, acoustic, and dielectric properties of glasses, for example, appear to be dominated by these little suckers, and because of the disordered nature of those materials, they come in all sorts of flavors - some with high barriers in the middle, some with low barriers; some with nearly symmetric wells, some with very asymmetric wells.   These TLS also "couple to strain" (that's how they talk to lattice vibrations and influence thermal and acoustic properties), meaning that if you stretch or squish the material, you raise one well and lower the other by an amount proportional to the stretching or squishing.

When I was a grad student, there were a tiny number of experiments that attempted to examine individual TLS, but in most disordered materials they could only be probed indirectly.   Fast forward 20 years.  It turns out that superconducting structures developed for quantum computing can be extremely sensitive to the presence of TLS, which typically exist in the glassy metal oxide layers used as tunnel barriers or at the surfaces of the superconductors.  A very cool new paper on the arxiv shows this extremely clearly.  If you look at Figure 2d, they are able to track the energy splittings of the TLS while straining the material (!), and they can actually see direct evidence of TLS talking coherently to each other.  There are "avoided crossings" between TLS levels, meaning that occasionally you end up with TLS pairs that are close enough to each other that energy can slosh coherently back and forth between them.   I find this level of information very impressive, and the TLS case continues to be an impressive example of theorists concocting a model based on comparatively scant information, and then experimentalists validating it well beyond the original expectations.   From the quantum computing perspective, though, these little entities are not a good thing, and demonstrate a maxim I formulated as a grad student:  "TLSs are everywhere, and they're evil."

(On the quantitative side:  If the energy difference between the bottoms of the two wells is \(\Delta\), and the tunneling matrix element that would allow transitions between the two wells is \(\Delta_{0}\), then a very simple calculation says that the energy difference between the ground state of this system and the first excited state is given by \(\sqrt{\Delta^{2} + \Delta_{0}^{2}}\).  If coupling to strain linearly tunes \(\Delta\), then that energy splitting should trace out a shape just like the curves seen in Fig. 2d of the paper.)