Photon-assisted tunnelling of zero modes in a Majorana wire

Abstract

Hybrid nanowires with proximity-induced superconductivity in the topological regime host Majorana zero modes (MZMs) at their ends, and networks of such structures can produce topologically protected qubits. In a double-island geometry where each segment hosts a pair of MZMs, inter-pair coupling mixes the charge parity of the islands and opens an energy gap between the even and odd charge states at the inter-island charge degeneracy. Here, we report on the spectroscopic measurement of such an energy gap in an InAs/Al double-island device by tracking the position of the microwave-induced quasiparticle (qp) transitions using a radio-frequency (rf ) charge sensor. In zero magnetic field, photon assisted tunneling (PAT) of Cooper pairs gives rise to resonant lines in the 2e-2e periodic charge stability diagram.In the presence of a magnetic field aligned along the nanowire, resonance lines are observed parallel to the inter-island charge degeneracy of the 1e-1e periodic charge stability diagram, where the 1e periodicity results from a zero-energy subgap state that emerges in magnetic field. Resonant lines in the charge stability diagram indicate coherent photon assisted tunneling of singleelectron states, changing the parity of the two islands. The dependence of resonant frequency on detuning indicates a sizable (GHz-scale) hybridization of zero modes across the junction separating islands.In a mesoscopic superconducting island, the presence of a single unpaired electron comes at an energy cost δ determined by the lowest quasiparticle state. As a consequence, the odd-parity charge states are elevated in energy. The total energy of a charge state with N electrons is E N = E C (N − n g ) 2 + δ mod(N, 2), where E C is the single-electron charging energy and n g is the gateinduced charge. For δ > E C (Fig. 1a), the island ground states are of even charge parity only, and the island occupation changes in steps of 2e as n g is changed [1]. When * These authors contributed equally to this work † email: marcus@nbi.ku.dk the island is weakly coupled to a superconducting reservoir the coherent exchange of Cooper pairs, characterized by Josephson energy E J , mixes ground states of equal parity, resulting in an anti-crossing (blue lines in Fig. 1a). This superposition of even-parity charge states is the basis of conventional superconducting qubits [2]. In a topological superconducting island, nonoverlapping Majorana zero modes comprise a zero-energy qp state denoted a Majorana bound state (MBS). Since δ = 0 in this case, the island charge occupation changes with regular steps of width 1e. Overlap between MZMs within the island leads to δ = 0. Consequently, the width of Coulomb valleys with even parity will either increase or decrease depending on the sign of δ [3], as recently demonstrated experimentally [4][5][6]. In contrast to the intra-island coupling of MZMs, the wave function overlap with an exterior MZM, characterized by E M , leaves δ unchanged but mixes states of different parity (see Fig. 1c). The ground states of the i...

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

“…In an ideal topological transmon, a pair of Majorana zero modes (MZMs) straddle the Josephson junction, and are coupled via coherent single-electron tunneling with a characteristic energy scale E M , which accompanies the usual Josephson coupling, E J , across the junction [23,28,29]. From the perspective of circuit quantum electrodynamics spectroscopy, E M splits the parity-preserving level crossings thereby doubling the number of spectral lines [23].…”

Photon-assisted resonant Andreev reflections: Yu-Shiba-Rusinov and Majorana states

“…This has been at the focus of a large number of experiments [25] and a recent measurement shows evidence for this quantized conductance [26]. Our theory for photon-assisted resonant Andreev reflections is readily adapted to include tunneling into Majorana bound states [17,28], and we find that photon-assisted tunneling can be an important tool to differentiate Majorana bound states from other subgap states. This is particularly true for tunneling from superconducting tips which were repeatedly used for improved resolution in Majorana experiments on chains of magnetic adatoms [29][30][31][32].…”

“…Photon-assisted tunneling constitutes a powerful method to probe the nature of charge transfer. The absorption and emission of photons leads to the appearance of sidebands in the conductance both in the absence [10,11] and in the presence [12][13][14][15][16][17] of Coulomb blockade. Frequently, the spacing of the sidebands in bias voltage as well as their modulation as a function of the amplitude of the HF radiation directly reveal the amount of charge that is transferred in an elementary tunneling event [18].…”

Visibility of noisy quantum dot-based measurements of Majorana qubits

“…While the dependence on ω min is weak it should be noted that Eqs. (18), (19) emphasize that similar to conventional qubits, the measurement apparatus of topological qubits needs to be regularly recalibrated. For numerical estimates we use ω −1 min = 10τ m with τ m = 1 µs.…”

“…As a direct consequence of their nonlocal nature, Majorana-based qubits are, in principle, less susceptible to decoherence and can provide better protected gates when compared to conventional qubits. Throughout the past decade a lot of experimental progress has been made on detecting signatures of the MZMs via observing zero-bias conductance peaks [6][7][8][9][10][11][12], a 4π-periodic Josephson effect [13][14][15], signatures of exponential length-dependence of energy splittings [16,17], and coherent single electron charge transfer between superconductors [18]. Though promising, these signatures have been proved inconclusive to make a definitive judgment on the presence of the MZMs in the system [19][20][21][22][23][24][25][26].…”