Entanglement in topological spin Josephson junctions

We study the spin transport through 1D quantum Ising-XY-Ising junctions that emulates topological Superconducting-Normal-Superconducting junctions via Jordan-Wigner transformation. We calculate, both numerically and analytically, the spectrum of Andreev bound states and the resulting Z₂ fractional spin Josephson effect from Majorana Fermions. Deep in the topological regime, we identify an effective time-reversal symmetry that leads to Z₄ fractional spin Josephson effect in the presence of interactions within junctions. Interestingly, in the lattice model, a hidden lattice time-reversal symmetry is revealed to protect Z₄ fractional spin Josephson effect in odd chain sites that persists in the absence of interactions. We also evaluate the resulting spin texture in the presence of the spin currents and highlight the effects of Majorana bound states on the entanglement of neighboring spin within junctions quantified by the concurrence. We propose to use a microwave cavity setup (cQED) for detecting the aforementioned Josephson effects by dispersive readout methods. Our results are relevant for a plethora of spin systems, such as trapped ions, coupled quantum dots, or magnetic impurities on surfaces.

[1] Pei-Xin Shen, Silas Hoffman, and Mircea Trif (to be submitted).