Non-Abelian fermion parity interferometry of Majorana bound states in a Fermi sea

Abstract

We study the quantum dynamics of Majorana and regular fermion bound states coupled to a quasi-one-dimensional metallic lead. The dynamics following the quench in the coupling to the lead exhibits a series of dynamical revivals as the bound state propagates in the lead and reflects from the boundaries. We show that the nature of revivals for a single Majorana bound state depends uniquely on the presence of a resonant level in the lead. When two spatially separated Majorana modes are coupled to the lead, the revivals depend only on the phase difference between their host superconductors. Remarkably, the quench in this case effectively performs a fermion-parity interferometry between Majorana bound states, revealing their unique non-Abelian braiding. Using both analytical and numerical techniques, we find the pattern of fermion parity transfers following the quench, study its evolution in the presence of disorder and interactions, and thus, ascertain the fate of Majorana in a rough Fermi sea.

Topological phases of a dimerized Fermi–Hubbard model for semiconductor nano-lattices

“…However, in many of the possible experimental platforms for quantum simulation of TI using electrons in solids, such as dopant atoms and gate-defined quantum dots in semiconductors [19,20], the electron-electron interaction is much stronger than the hopping amplitude of the electrons [21,22] and therefore the independent-electron approximation is poor. Topological phases of strongly correlated models form a topic of ongoing active research with intense theoretical [23][24][25][26] and experimental effort, including recent implementations in cold atoms [27] and in a real two-dimensional material [28]. There have been various proposals for the equivalent of the single-particle Berry phase (or Zak phase in one dimension) for the characterization of interacting topological phases, from Green's functions [29] to entanglement entropy [30] and entanglement spectrum [31].…”

Multi-impurity chiral Kondo model: correlation functions and anyon fusion rules

“…To illustrate this, consider for example Majorana fermions in quantum wires [34][35][36][37] coupled to gapless modes of a nearby metal. This has been essential for observation of Majorana modes via tunneling, 38,39 as well as in numerous suggestions to probe their properties including braiding [40][41][42][43] and fractional entropy. 44,45 At the same time, the hybridization of Majorana fermions to the surrounding metallic gapless environment leads to decoherence and quasiparticle poissoning.…”

Dynamically Induced Topology and Quantum Monodromies in a Proximity Quenched Gapless Wire

“…Remarkably, we discover signatures of the exchange statistics in our one-dimensional, non-equilibrium setup. For the case of two Majorana fermions with no phase difference, the non-Abelian statistics satisfied by the Majorana modes is manifested as a doubling of the expected period for revivals of the fidelity [9]. The case of the fractional solitons of the SSH chain is more subtle, as the information about the exchange statistics is contained only in the accumulated phase.…”

“…We can think of the process of interfacing the topological phase with a gapless system as a rapid quench of the boundary conditions of the system, in time. Once the interface is in place, the TBSs become free to move through the gapless medium [7][8][9]. Could there be a temporal topological proximity effect, whereby proximity to the topological phase induces the normal system with some topological features dynamically over some coherence time?…”