Coupling Majorana fermion excitations to coherent external fields is an important stage towards their manipulation and detection. We analyse the charge and transmon regimes of a topological nano-wire embedded within a Cooper-Pair-Box, where the super
conducting phase difference is coupled to the zero energy parity states that arise from Majorana quasi-particles. We show that at special gate bias points, the photon-qubit coupling can be switched off via quantum interference, and in other points it is exponentially dependent on the control parameter $E_J/E_C$. As well as a probe for topological-superconductor excitations, we propose that this type of device could be used to realise a tunable high coherence four-level system in the superconducting circuits architecture.
In this book chapter we analyze the high excitation nonlinear response of the Jaynes-Cummings model in quantum optics when the qubit and cavity are strongly coupled. We focus on the parameter ranges appropriate for transmon qubits in the circuit quan
tum electrodynamics architecture, where the system behaves essentially as a nonlinear quantum oscillator and we analyze the quantum and semi-classical dynamics. One of the central motivations is that under strong excitation tones, the nonlinear response can lead to qubit quantum state discrimination and we present initial results for the cases when the qubit and cavity are on resonance or far off-resonance (dispersive).
The driven-damped Jaynes-Cummings model in the regime of strong coupling is found to exhibit a coexistence between the quantum photon blockaded state and a quasi-coherent bright state. We characterize the slow time scales and the basin of attraction
of these metastable states using full quantum simulations. This form of bistability can be useful for implementing a qubit readout scheme that does not require additional circuit elements. We propose a coherent control sequence that makes use of a simple linear chirp of drive amplitude and frequency as well as qubit frequency. By optimizing the parameters of the system and the control pulse we demonstrate theoretically very high readout fidelities (>98%) and high contrast, with experimentally realistic parameters for qubits implemented in the circuit QED architecture.
We calculate the dynamical fluctuation spectrum of electronic spins in a semiconductor under a steady-state illumination by light containing polarization squeezing correlations. Taking into account quasi-particle lifetime and spin relaxation for this
non-equilibrium situation we consider up to fourth order optical effects which are sensitive to the squeezing phases. We demonstrate the possibility to control the spin fluctuations by optically modulating these phases as a function of frequency, leading to a non-Lorentzian spectrum which is very different from the thermal equilibrium fluctuations in n-doped semiconductors. Specifically, in the time-domain spin-spin correlation can exhibit time delays and sign flips originating from the phase modulations and correlations of polarizations, respectively. For higher light intensity we expect a regime where the squeezing correlations will dominate the spectrum.
