Tunnel effect and interaction matrix

Massimo Rontani

A theory for the tunneling of one atom out of a trap containing two interacting cold atoms is developed. The quasiparticle wave function, dressed by the interaction with the companion atom in the trap, replaces the noninteracting orbital at resonance in the tunneling matrix element. The computed decay time for two ^{6}Li atoms agrees with recent experimental results [G. Zürn, F. Serwane, T. Lompe, A. N. Wenz, M. G. Ries, J. E. Bohn, and S. Jochim, Phys. Rev. Lett. 108, 075303 (2012)], unveiling the "fermionization" of the wave function and a novel two-body effect.

Pedro Pereyra Padilla

Ronny Thomale, Stephan Rachel, Peter Schmitteckert

Recent tunneling experiments on InSb hybrid superconductor-semiconductor devices have provided hope for a stabilization of Majorana edge modes in a spin-orbit quantum wire subject to a magnetic field and superconducting proximity effect. Connecting the experimental scenario with a microscopic description poses challenges of a different kind, such as accounting for the effect of interactions on the tunneling properties of the wire. We develop a density matrix renormalization group (DMRG) analysis of the tunneling spectra of interacting Majorana chains, which we explicate for the Kitaev chain model. Our DMRG approach allows us to calculate the spectral function down to zero frequency, where we analyze how the Majorana zero-bias peak is affected by interactions. For topological phase transitions between the topological and trivial superconducting phase in the Majorana wire, the bulk gap closure generically affects the proximity peaks and the Majorana peak.

Yoshie, Kiritani

Alan T. Dorsey, Matthew P. A. Fisher, Marek S. Wartak

In this paper we describe how a quantum system consisting of a single extended coordinate q in a double-well potential V(q), which interacts with a dissipative environment, may be systematically reduced (``truncated'') to an equivalent two-state system interacting with a modified environment. Although we concentrate on Ohmic dissipation, the method which we present is also applicable to other types of environmental spectral densities. The truncation scheme is applicable if there exists a wide separation of energy scales in the problem; we discuss the specific conditions which the system and environment must satisfy before such a scheme can be implemented. Our method proceeds by calculating the effects of the high-frequency environmental modes on the bare tunneling matrix element for transitions between the two wells. We are left with an equivalent two-state system with a renormalized tunneling matrix element, interacting with the remaining low-frequency environmental modes. The renormalized tunneling matrix element is calculated using path-integral techniques in a semiclassical approximation. Explicit results are given for a quartic double-well potential in the underdamped and overdamped regimes.