Condensed matter physics is so cool! Bounce 4 laser beams off mirrors to make an interference pattern with 8-fold symmetry. Put a Bose–Einstein condensate of potassium atoms into this “optical lattice” and you get a superfluid quasicrystal!
You see, no periodic pattern in the plane can have 8-fold symmetry, so the interference pattern of the light is ‘quasiperiodic’: it never repeats itself, thought it comes arbitrarily close, sort of like this pattern drawn by Greg Egan:
In the Bose–Einstein condensate all the particles have the same wavefunction, and the wavefunction itself, influenced by the light, also becomes quasiperiodic.
But that’s not all! As you increase the intensity of the lasers, the Bose-Einstein condensate suddenly collapses from a quasicrystal to a ‘localized’ state where all the atoms sit in the same place!
Below the gray curve is the potential V formed by the lasers, while the blue curve is the absolute value squared of the wavefunction of the Bose–Einstein condensate, |ψ0|2.
At top the lasers are off so V is zero and |ψ0|2 is constant. In the middle the lasers are on, but not too bright, so V and |ψ0| is quasiperiodic. At the bottom the lasers are brighter, so V is quasiperiodic and larger, and |ψ0|2 is localized.
It’s well known that when a crystal is sufficiently disordered, its electrons may localize: instead of having spread-out wavefunctions, they get trapped in specific regions as shown here:
This phenomenon is called ‘Anderson localization’, and it was discovered around 1958.
But when a Bose-Einstein condensate localizes, all the atoms get trapped in the same place—because they’re all in exactly the same state! This phenomenon was discovered experimentally at the University of Cambridge very recently:
• Matteo Sbroscia, Konrad Viebahn, Edward Carter, Jr-Chiun Yu, Alexander Gaunt and Ulrich Schneider, Observing localisation in a 2D quasicrystalline optical lattice.
The evidence for it is somewhat indirect, so I’m sure people will continue to study it. Localization of a Bose–Einstein condensate in a one-dimensional quasiperiodic potential was seen much earlier, in 2008:
• Giacomo Roati, Chiara D’Errico, Leonardo Fallani, Marco Fattori, Chiara Fort, Matteo Zaccanti, Giovanni Modugno, Michele Modugno and Massimo Inguscio, Anderson localization of a non-interacting Bose–Einstein condensate, Nature 453 (2008), 895–898.
The holy grail, a ‘Bose glass’, remains to be seen. It’s a Bose-Einstein condensate that’s also a glass: its wavefunctions is disordered rather than periodic or quasiperiodic.
New forms of matter with strange properties—I love ’em!
For more popularizations of these ideas, see:
• Julia C. Keller, Researchers create new form of matter—supersolid is crystalline and superfluid at the same time, Phys.org, 3 March 2018.
• University of Texas at Dallas, Solid research leads physicists to propose new state of matter, Phys.org, 9 April 2018.
The latter says “The term ‘superfluid quasicrystal’ sounds like something a comic-book villain might use to carry out his dastardly plans.”