Majorana Fermions in Equilibrium and in Driven Cold-Atom Quantum Wires

Liang Jiang,Peter Zoller,Jason Alicea,David Pekker,A R Akhmerov,Gil Refael,Mikhail D Lukin,J Ignacio Cirac,Eugene Demler,Takuya Kitagawa

doi:10.1103/physrevlett.106.220402

Abstract

We introduce a new approach to create and detect Majorana fermions using optically trapped 1D fermionic atoms. In our proposed setup, two internal states of the atoms couple via an optical Raman transition-simultaneously inducing an effective spin-orbit interaction and magnetic field-while a background molecular BEC cloud generates s-wave pairing for the atoms. The resulting cold-atom quantum wire supports Majorana fermions at phase boundaries between topologically trivial and nontrivial regions, as well as "Floquet Majorana fermions" when the system is periodically driven. We analyze experimental parameters, detection schemes, and various imperfections.

Highlights

We introduce a new approach to create and detect Majorana fermions using optically trapped 1D fermionic atoms
Two internal states of the atoms couple via an optical Raman transition—simultaneously inducing an effective spin-orbit interaction and magnetic field—while a background molecular BEC cloud generates s-wave pairing for the atoms
Majorana fermions (MFs) can even emerge in 1D quantum wires, such as the spinless pwave superconducting chain [9] which is effectively realized in semiconductor wire/bulk superconductor hybrid structures with spin-orbit interaction and strong magnetic field [10, 11]

Summary

Majorana Fermions in Equilibrium and Driven Cold Atom Quantum Wires

Liang Jiang,1,2,∗ Takuya Kitagawa,3,∗ Jason Alicea, A. Two internal states of the atoms couple via an optical Raman transition—simultaneously inducing an effective spin-orbit interaction and magnetic field—while a background molecular BEC cloud generates s-wave pairing for the atoms. Combined with s-wave pairing induced by the surrounding BEC of Feshbach molecules, the cold atom quantum wire supports MFs at the boundaries between topologically trivial and non-trivial superconducting regions [10]. In contrast to the earlier 2D cold-atom MF proposals that require sophisticated optical control like tilted optical lattices [19] or multiple laser beams [16, 18], our scheme uses the Raman transition with photon recoil to obtain spin-orbit interaction.

The kinetic energy is εp

The position of the MFs can be changed by adiabatically

The effective magnetic field