Quantum degeneracy in an attractive bosonic system

Jay Deep Sau, Bertrand I. Halperin, Karsten Flensberg +1 more

Semiconducting nanowires in proximity to superconductors are among promising candidates to search for Majorana fermions and topologically protected degeneracies, which may ultimately be used as building blocks for topological quantum computers. The prediction of neutral Majorana fermions in the proximity-induced superconducting systems ignores number conservation and thus leaves open the conceptual question of how a topological degeneracy that is robust to all local perturbations arises in a number-conserving system. In this work, we study how local attractive interactions generate a topological ground-state near-degeneracy in a quasi-one-dimensional superfluid using bosonization of the fermions. The local attractive interactions opens a topological quasiparticle gap in the odd channel wires (with more than one channel) with end Majorana modes associated with a topological near-degeneracy. We explicitly study the robustness of the topological degeneracy to local perturbations and find that such local perturbations result in quantum phase slips, which split of the topological degeneracy by an amount that does not decrease exponentially with the length of the wire, but still decreases rapidly if the number of channels is large. Therefore a bulk superconductor with a large number of channels is crucial for true topological degeneracy.

J. S. Dowker

Florian Schreck

This thesis presents studies of quantum degenerate atomic gases of fermionic 6Li and bosonic 7Li. Degeneracy is reached by evaporative cooling of 7Li in a strongly confining magnetic trap. Since at low temperatures direct evaporative cooling is not possible for a polarized fermionic gas, 6Li is sympathetically cooled by thermal contact with 7Li. In a first series of experiments both isotopes are trapped in their low-field seeking higher hyperfine states. A Fermi degeneracy of is achieved for 105 fermions. For more than ~300 atoms, the 7Li condensate collapses, due to the attractive interatomic interaction in this state. This limits the degeneracy reached for both species. To overcome this limit, in a second series of experiments 7Li and 6Li atoms are transferred to their low field seeking lower hyperfine states, where the boson-boson interaction is repulsive but weak. The inter-isotope collisions are used to thermalize the mixture. A 7Li Bose-Einstein condensate (BEC) of 104 atoms immersed in a Fermi sea is produced. The BEC is quasi-one-dimensional and the thermal fraction can be negligible. The measured degeneracies are . The temperature is measured using the bosonic thermal fraction, which vanishes at the lowest temperatures, limiting our measurement sensitivity. In a third series of experiments, the bosons are transferred into an optical trap and their internal state is changed to , the lowest energy state. A Feshbach resonance is detected and used to produce a BEC with tunable atomic interactions. When the effective interaction between atoms is tuned to be small and attractive, we observe the formation of a matter-wave bright soliton. Propagation of the soliton without spreading over a macroscopic distance of 1.1~mm is observed.

Elisa Todarello, P. Sikivie

G. Roati, Francesco Riboli, Giovanni Carlo Modugno +1 more

We report on the achievement of simultaneous quantum degeneracy in a mixed gas of fermionic 40K and bosonic 87Rb. Potassium is cooled to 0.3 times the Fermi temperature by means of an efficient thermalization with evaporatively cooled rubidium. Direct measurement of the collisional cross-section confirms a large interspecies attraction. This interaction is shown to affect the expansion of the Bose-Einstein condensate released from the magnetic trap, where it is immersed in the Fermi sea.