Majorana oscillations and parity crossings in semiconductor nanowire-based transmon qubits

Abstract

We show that the microwave (MW) spectra in semiconductor-nanowire-based transmon qubits provide a strong signature of the presence of Majorana bound states in the junction. This occurs as an external magnetic field tunes the wire into the topological regime and the energy splitting of the emergent Majorana modes oscillates around zero energy owing to their wave function spatial overlap in finite-length wires. In particular, we discuss how these Majorana oscillations, and the concomitant fermion parity switches in the ground state of the junction, result in distinct spectroscopic features-in the form of an intermittent visibility of absorption lines-that strongly deviate from standard transmon behavior. In contrast, nonoscillating zero modes, such as topologically trivial Andreev bound states resulting from sufficiently smooth potentials, exhibit an overall standard transmon response. These differences in the MW response could help determine whether the junction contains topological Majoranas or not.

Destructive Little-Parks Effect in a Full-Shell Nanowire-Based Transmon

“…Proposals to realize transmons based on topological superconductors typically require sizeable applied magnetic fields to drive the system into the topological phase [21][22][23][24][25]. In these schemes, a properly oriented magnetic field splits the spin-orbit band, typically requiring ∼1 T to reach the topological regime [26], a challenge to most superconducting technologies [7] with some exceptions [27].…”

“…The prediction of E M from device parameters is difficult as E M depends sensitively on the potential in the junction. While E M is expected to increase as the junction barrier is lowered, its value is likely limited by the presence of additional transport channels within the subgap spectrum of the junction [25,30].…”

Singlet-doublet transitions of a quantum dot Josephson junction detected in a transmon circuit

“…Important extensions of our work could arise if the hybrid nanowire in our microwave circuit was driven into the Majorana topological phase [69][70][71]89], which is currently challenging because of a large parameter space [90] and because of demanding disorder requirements [91]. Including a quantum dot in a Josephson junction between two topological superconductors could be beneficial for the detection of the 4π Josephson effect: as we have seen, it mitigates quasiparticle poisoning, although it would not resolve [92] the problem of distinguishing Majorana zero modes from trivial zero-energy Andreev bound states [93].…”

“…( 2) to calculate the transmon transition frequencies [60]. The projection onto the lowest-energy state of the Josephson junction in each sector is enough to capture the salient features of our experiment, although the inclusion of excited Andreev states of the quantum dot junction in the circuit model is theoretically possible [35,50,[69][70][71].…”

Observation of Phase Controllable Majorana-like Bound States in Metamaterial-based Kitaev Chain Analogues

“…Most importantly, when their hybridization changes its sign, there is a switch between whether the symmetric or the antisymmetric combination corresponds to the lower frequency. In the MZM analogue, this behavior results in so-called parity switching [40][41][42]49]. Here, consequences of the switch are rather profound: the two end MZMs form a Dirac fermionic state that can be occupied or unoccupied, essentially a topological qubit, thus giving the system odd or even parity.…”