Microwave signatures of the Z2 and Z4 fractional Josephson effects

Abstract

We present a many-body exact diagonalization study of the Z2 and Z4 Josephson effects in circuit quantum electrodynamics architectures. Numerical simulations are conducted on Kitaev chain Josephson junctions hosting nearest-neighbor Coulomb interactions. The low-energy effective theory of highly transparent Kitaev chain junctions is shown to be identical to that of junctions created at the edge of a quantum spin-Hall insulator. By capacitively coupling the interacting junction to a microwave resonator, we predict signatures of the fractional Josephson effects on the cavity frequency and on time-resolved reflectivity measurements. arXiv:1809.11133v1 [cond-mat.mes-hall]

Topological Josephson Bifurcation Amplifier: Semiclassical theory

“…The underlying idea is to induce transitions between the absolute and local minima of the energy spectrum, and to measure the frequency of small oscillations of δ around those minima quickly enough (before energy relaxation to the absolute minimum takes place). We begin by noting that the vertical-in-δ transition between the p = 0 and p = 1 minima cannot be induced by microwave pulses, because electron-photon interactions preserve the MBS parity 17 . This is unlike the case of the two quantum states in a superconducting qubit, the transition between which is routinely induced by microwave pulses.…”

“…In anticipation of the realization of MBS-based qubits, there has been a strong interest on the theoretical front to integrate MBS in circuit quantum electrodynamics (cQED) architectures [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] , the latter of which are widely employed in the readout and control of solid-state qubits 20 . This theoretical effort has been accompanied by experimental progress towards the realization of superconducting circuits that are compatible with sizeable magnetic fields [21][22][23][24][25][26] .…”

Theory of topological spin Josephson junctions

“…Although there are small gaps at φ = π caused by finitesize effects (e.g. slowly oscillatory umklapp or Friedel terms), they can be fairly suppressed under the continuum limit as γ → 0 [55].…”