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Parafermionic zero modes in ultracold bosonic systems

A Bose-Einstein condensate (BEC) forms inside a quasi-one-dimensional trench amid a two-dimensional gas of ultracold atoms.  These atoms had already been put into a fractional quantum Hall (FQH) state.  The trench acts as a defect where two quasi-particles (area indicated here with two large glass spheres) can be snagged. This pair of quasi-particles together constitute a "para-fermion" and might serve as a handy qubit.

In the fractional quantum Hall (FQH) effect, the collective action of electrons in a material form particle-like “quasiparticles” that can appear to possess fractional charge, such as 1/3. In quantum Hall systems, these quasiparticles can become trapped around specially tailored defects, forming so-called "zero-mode" states. One example of a composite particle associated with zero-mode defects is the Majorana fermion.

Many physicists believe that the quantum Hall physics enabling these zero-mode states is not unique to electrons, and thus it should be possible to observe this behavior in other systems. A recent PFC-supported report proposes producing one such state, called a parafermionic zero-mode, in a gas of cold bosonic atoms.

In this case, the defect that captures the quasiparticles is a one-dimensional trench of Bose-Einstein Condensate (BEC) atoms sitting amid a larger two-dimensional formation of cold atoms displaying FQH properties. The parafermion would appear at both ends of the trench, just as Majorana fermions can appear at either end of a superconducting nanowire.

Aside from interest in them for studying fundamental physics, these zero modes might play an important role in quantum computing. This is related to what’s known as topology, which is a sort of global property that can allow for collective phenomena, such as the current of charge around the edge of the sample, to be impervious to the tiny microscopic details of a system. Here the topology endows the FQH system with multiple quantum states with exactly the same energy. The exactness and imperturbability of the energy amid imperfections in the environment makes the FQH system potentially useful for hosting quantum bits. The present report proposes a practical way to harness this predicted topological feature of the FQH system through the appearance of what are known as parafermionic zero-modes.

M.F. Maghrebi, S. Ganeshan, D.J. Clarke, A.V. Gorshkov, J.D. Sau
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