Abstract
We study nanowire-based Josephson junctions shunted by a capacitor and take into account the presence of low-energy quasiparticle excitations. These are treated by extending conventional models used to describe superconducting qubits to include the coherent coupling between fermionic quasiparticles, in particular the Majorana zero modes that emerge in topological superconductors, and the plasma mode of the junction. Using accurate, unbiased matrix-product state techniques, we compute the energy spectrum and response function of the system across the topological phase transition. Furthermore, we develop a perturbative approach, valid in the harmonic limit with small charging energy, illustrating how the presence of low-energy quasiparticles affects the spectrum and response of the junction. Our results are of direct interest to on-going experimental investigations of nanowire-based superconducting qubits.
Highlights
IntroductionDue to the macroscopic coherence of the superconducting state and their non-linearity as circuit elements, Josephson junctions are a workhorse of quantum state engineering [1]
We have carefully studied the response of a capacitively shunted topological Josephson junction, using a combination of accurate numerical techniques and theoretical approaches that allow us to incorporate a microscopic description of the topological phase
Our results indicate that detecting the signatures of the topological phase in the transmon-like setup of Fig. 1, as proposed for instance in Ref. [60] and as described in Sec. 3, can be complicated by two factors
Summary
Due to the macroscopic coherence of the superconducting state and their non-linearity as circuit elements, Josephson junctions are a workhorse of quantum state engineering [1]. In conjunction with the growing interest in MZMs, different research groups have developed and studied superconducting devices with semiconductor-based Josephson junctions either in nanowires [31, 32] or 2DEGs [33], as well as in graphene-based heterostructures [34, 35] These junctions, characterized by few conducting channels and potentially high transparency, can be used for the development of qubits based on conventional Andreev bound states (ABSs) [36,37,38,39,40]. The correlation function determines the observed spectra in a typical circuit QED (cQED) experiment, making our method suitable for direct comparison with experimental measurements This approach allows us to determine the expected frequency spectra even close to the critical point—a regime which cannot be captured by existing toy models—and to include additional Andreev bound states.
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