Abstract
We study the decoherence of Majorana modes of a fermion chain, where the fermions interact with their nearest neighbours. We investigate the effect of dissipation and dephasing on the Majorana modes of a fermionic chain. The dissipative and dephasing noises induce the non-parity- and parity-preserving transitions between the eigenstates of the system, respectively. Therefore, these two types of noises lead to the different decoherence mechanisms. In each type of noise, we discuss the low- and high-frequency regimes to describe the different environments. We numerically calculate the dissipation and dephasing rates in the presence of long-range interactions. We find that the decoherence rate of interacting Majorana modes is different to that of non-interacting modes. We show the examples that the long-range interactions can reduce the decoherence rate. It is advantageous to the potential applications of quantum information processing.
Highlights
We study the decoherence of Majorana modes of a fermion chain, where the fermions interact with their nearest neighbours
We find that the decoherence rate of interacting Majorana modes is different to that of non-interacting modes
The study of Majorana fermions is of fundamental importance and it is useful to the applications of quantum information processing (QIP)
Summary
We study the effect of dissipation on the Majorana modes, where the frequency domain of the noise spectrum is comparable to the transition frequencies between the different eigenstates. We assume that this high-frequency noise does not affect the dynamics between the two degenerate ground states, where their transition frequency is nearly zero. In contrast to the case of dissipation, the dephasing noise gives rise to the transitions between the eigenstates in the same parity In this model, the fermions are coupled to a common bosonic bath. We study the effect of dephasing in the low-frequency regime In this regime, we can express this Hamiltonian in terms of eigenstates of the two lowest degenerate states.
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