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Statistical Transmutation in Floquet Driven Optical Lattices

Graphic depiction of the changing band structure and its effect on the bosons. The upper part of the graphic depicts the lowest energy band in the presence of an optical lattice. The linearly aligned clump of white lines in the middle of this band represent bosons condensing prior to shaking. When the lattice shakes (represented here by a grey oscillatory overlay), a moat appears in the band structure, as shown in the lower part of the graphic. Now the lines--bosons-- are fermionic, and are clearly not aligned, indicating a lack of condensation and long-range order. (Credit: E. Edwards/JQI) 

Particles can be classified as bosons or fermions. A defining characteristic of a boson is its ability to pile into a single quantum state with other bosons. Fermions are not allowed to do this. One broad impact of fermionic anti-social behavior is that it allows for carbon-based life forms, like us, to exist. If the universe were solely made from bosons, life would certainly not look like it does. Recently, PFC-supported researchers have proposed an elegant method for achieving transmutation--that is, making bosons act like fermions.

This transmutation is an example of emergent behavior, specifically what’s known as quasiparticle excitations—one of the concepts that make condensed matter systems so interesting. Particles by themselves have mostly well-defined characteristics, but en masse, can work together such that completely distinctive, even exotic phenomena appear. 

The authors propose a method for realizing and observing such unusual excitations—here fermionicquasiparticles. To do this, they propose a technique to transmute bosons into fermions; one way to accomplish this is to construct an optical lattice whose band structure looks like a moat.

It turns out that getting the requisite moat to appear has not been so easy. Surprisingly, the team found that if, instead of modifying the lattice geometry itself, they take a simple two-dimensional lattice and shake it back and forth, then a moat appears in what was otherwise an unremarkable, almost flat band structure. The rate of shaking is specially chosen such that the bands undergo this transformation. 

The particles themselves do not actually change from bosons to fermions. What’s happening is that the environment of the lattice is modifying the bosonic behavior. When the lattice is quivering periodically at a specially determined frequency, the bosons act as if they are governed by fermionic statistics. In the new band structure, the bosons do not form a condensate.

T.A. Sedrakyan, V.M. Galitski, A. Kamenev
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