Topological Quantum Systems – University of Copenhagen

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Topological Quantum Systems

The implications are far-reaching, from the predicted existence of quasiparticles with non-abelian exchange statistics – possibly unique in physics – to novel approaches to quantum computing where the topology of qubit protects it against decoherence. 

In the center, we focus on two systems with topological quasiparticles, namely fractional quantum Hall effect and hybrid superconductor-semiconductor heterostructures, designed to support Majorana Fermions.

GaAs chip with Hall bars, quantum point contacts and anti-dot devices mounted to the end of 10mK copper cold finger that provides cooling power. This sample holder sits inside the bore of a superconducting magnet with perpendicular fields up to 12 Tesla. These devices allow the study of non-abelian quasiparticles in the fractional quantum hall regime.

Fractional quantum Hall (FQH) states are predicted to have non-Abelian quasiparticles. The state appears below 50 mK in GaAs two-dimensional electron systems at filling factor (the ratio of 2D electrons to applied flux quanta) 5/2.  This state and its spin-reversed partner at v = 7/2 are the only fractional quantum Hall  states with even-denominator filling fractions. The prevailing theory of the 5/2 state involves p-wave pairing of composite fermions edges carrying charge e/4 and having non-Abelian particle statistics. It is known that the 5/2 state can exist in even lithographically patterned micron-scale structures, which allows us to pursue verification of predicted signatures of non-Abelian statistics in quantum dots, antidots, and interferometers.

In recent years it has been realized that one can design materials with induced p-wave superconducting order. This exotic superconducting state with broken time-reversal is known to have localized Majorana Fermions as end states, and it is in fact another realization of the same physics as in the 5/2 fractional quantum Hall states. The notion of Majorana Fermions makes an interesting connection to particle physics, where there is a long-standing debate whether such particles, being their own antiparticles, can exist. The quantum states of a Majorana particles, represented by the parity of fermion number, is topologically protected and therefore potentially useful for quantum computation purposes.

In the center we investigate designs of strong spin-orbit materials in the form of semiconducting nanowires or heterostructures connected to conventional superconductors, with the aim of controlling and studying the properties of Majorana fermions. For the manipulation of their quantum state, we investigate the possibility of interfacing with "conventional" mesoscopic quantum systems, such as quantum dots.