"To our surprise, the use and knowledge of this potential in theoretical studies concerning quantum dynamics in two and three dimensions is minute if not inexistent," team leader Rossen Dandoloff from the University of Cergy-Pontoise in France told nanotechweb.org. "This has to change because present-day technology now puts us in a position to use the binding interaction due to this curvature in applications."

A tight knot is in fact a mathematical idealization. Here, the word tight means something that is structurally stable – that is, its curvature cannot change during an experiment. Team member Victor Atanasov of the Bulgarian Academy of Sciences explained that a qubit can be made by simply tying a knot on a quantum wire – a conducting string in which the quantum dynamics is effectively one-dimensional (see figure). The wire is coated with an insulator to restrict dynamics in its interior and prevent electron tunnelling from the sides.

Binding potential
The device works as follows: a quantum particle (an electron, hole or excitation) constrained inside the quantum wire is subject to a binding potential, Vcurv, and can bind in an eigenstate, which splits into two thanks to tunnelling through the curvature-induced barrier in the knot. A transition between these two levels, which represents the "1" and "0" states of the qubit, can be driven at a resonance frequency by microwaves if the particle trapped inside is charged and can couple with the applied electromagnetic field.

Interqubit interactions
Applications for such qubits would be no different from applications for qubits from other sources, such as spins, said Atanasov. Moreover, if the particle trapped inside the wire is charged, it induces an electrical symmetry in the knot. This means that qubits from knots can couple with each other, so interqubit interactions are possible.

"We are not yet sure of the capabilities of present nanotechnology, but presume that knot qubits from nanoscale quantum wires driven by finely tuned microwaves would not be all that difficult or expensive to make," he added.

The team now plans to study other types of knots. "We also presume that tying many knots on a quantum wire should produce a periodic medium, that is, a quantum simulation of a 1D crystalline solid if the spacing between the knots is kept constant," explained Atanasov. "For example, using a ferrite interior in the quantum wire could make for a new breed of device that is a hybrid between curvature-induced constrained dynamics and spintronics."

The work was reported in arXiv.