Enhancement and state tomography of a squeezed vacuum with circuit quantum electrodynamics

We study the dynamics of a general quartic interaction Hamiltonian under the influence of dissipation and non-classical driving. We show that this scenario could be realised with a cascaded superconducting cavity-qubit system in the strong dispersive regime in a setup similar to recent experiments. In the presence of dissipation, we find that an effective Hartree-type decoupling with a Fokker-Planck equation yields a good approximation. We find that the stationary state is approximately a squeezed vacuum, which is enhanced by the $Q$-factor of the cavity but conserved by the interaction. The qubit non-linearity, therefore, does not significantly influence the highly squeezed intracavity microwave field but, for a range of realistic parameters, enables characterisation of itinerant squeezed fields

Hybrid teleportation via entangled coherent states in circuit quantum electrodynamics

We propose a deterministic scheme for teleporting an unknown qubit through continuous-variable entangled states in superconducting circuits. The qubit is a superconducting two-level system and the bipartite quantum channel is a photonic entangled coherent state between two cavities. A Bell-type measurement performed on the hybrid state of solid and photonic states brings a discrete-variable unknown electronic state to a continuous-variable photonic cat state in a cavity mode. This scheme further enables applications for quantum information processing in the same architecture of circuit-QED such as verification and error-detection schemes for entangled coherent states. Finally, a dynamical method of a self-Kerr tunability in a cavity state has been investigated for minimizing self-Kerr distortion and all essential ingredients are shown to be experimentally feasible with the state of the art superconducting circuits.Comment: 9 pages and 5 figure

Differentiating Majorana from Andreev Bound States in a Superconducting Circuit

We investigate the low-energy theory of a one-dimensional finite capacitance topological Josephson junction. Charge fluctuations across the junction couple to resonant microwave fields and can be used to probe microscopic excitations such as Majorana and Andreev bound states. This marriage between localized microscopic degrees of freedom and macroscopic dynamics of the superconducting phase, leads to unique spectroscopic patterns which allow us to reveal the presence of Majorana fermions among the low-lying excitations.Comment: 9 pages, 3 figure

Protected ground states in short chains of coupled spins in circuit quantum electrodynamics

The two degenerate ground states of the anisotropic Heisenberg (XY) spin model of a chain of qubits (pseudo-spins) can encode quantum information, but their degree of protection against local perturbations is known to be only partial. We examine the properties of the system in the presence of non-local spin-spin interactions, possibly emerging from the quantum electrodynamics of the device. We find a phase distinct from the XY phase admitting two ground states which are highly protected against all local field perturbations, persisting across a range of parameters. In the context of the XY chain we discuss how the coupling between two ground states can be used to observe signatures of topological edge states in a small controlled chain of superconducting transmon qubits.Comment: 10 pages, 11 figure

Fermion parity measurement and control in Majorana circuit quantum electrodynamics

We investigate the quantum electrodynamics of a device based on a topological superconducting circuit embedded in a microwave resonator. The device stores its quantum information in coherent superpositions of fermion parity states originating from Majorana fermion hybridization. This generates a highly isolated qubit whose coherence time could be greatly enhanced. We extend the conventional semiclassical method and obtain analytical derivations for strong transmon-photon coupling. Using this formalism, we develop protocols to initialize, control, and measure the parity states. We show that, remarkably, the parity eigenvalue can be detected via dispersive shifts of the optical cavity in the strong-coupling regime and its state can be coherently manipulated via a second-order sideband transition.Comment: 7 pages, 3 figures (published version

Designing Kerr interactions using multiple superconducting qubit types in a single circuit

The engineering of Kerr interactions has great potential for quantum information processing applications in multipartite quantum systems and for investigation of many-body physics in a complex cavity-qubit network. We study how coupling multiple different types of superconducting qubits to the same cavity modes can be used to modify the self- and cross-Kerr effects acting on the cavities and demonstrate that this type of architecture could be of significant benefit for quantum technologies. Using both analytical perturbation theory results and numerical simulations, we first show that coupling two superconducting qubits with opposite anharmonicities to a single cavity enables the effective self-Kerr interaction to be diminished, while retaining the number splitting effect that enables control and measurement of the cavity field. We demonstrate that this reduction of the self-Kerr effect can maintain the fidelity of coherent states and generalised Schr\"{o}dinger cat states for much longer than typical coherence times in realistic devices. Next, we find that the cross-Kerr interaction between two cavities can be modified by coupling them both to the same pair of qubit devices. When one of the qubits is tunable in frequency, the strength of entangling interactions between the cavities can be varied on demand, forming the basis for logic operations on the two modes. Finally, we discuss the feasibility of producing an array of cavities and qubits where intermediary and on-site qubits can tune the strength of self- and cross-Kerr interactions across the whole system. This architecture could provide a way to engineer interesting many-body Hamiltonians and a useful platform for quantum simulation in circuit quantum electrodynamics

Extended Hubbard model for mesoscopic transport in donor arrays in silicon

Arrays of dopants in silicon are promising platforms for the quantum simulation of the Fermi-Hubbard model. We show that the simplest model with only on-site interaction is insufficient to describe the physics of an array of phosphorous donors in silicon due to the strong intersite interaction in the system. We also study the resonant tunneling transport in the array at low temperature as a mean of probing the features of the Hubbard physics, such as the Hubbard bands and the Mott gap. Two mechanisms of localization which suppresses transport in the array are investigated: The first arises from the electron-ion core attraction and is significant at low filling; the second is due to the sharp oscillation in the tunnel coupling caused by the intervalley interference of the donor electron's wavefunction. This disorder in the tunnel coupling leads to a steep exponential decay of conductance with channel length in one-dimensional arrays, but its effect is less prominent in two-dimensional ones. Hence, it is possible to observe resonant tunneling transport in a relatively large array in two dimensions

Optimal control of two qubits via a single cavity drive in circuit quantum electrodynamics

Optimization of the fidelity of control operations is of critical importance in the pursuit of fault-tolerant quantum computation. We apply optimal control techniques to demonstrate that a single drive via the cavity in circuit quantum electrodynamics can implement a high-fidelity two-qubit all-microwave gate that directly entangles the qubits via the mutual qubit-cavity couplings. This is performed by driving at one of the qubits' frequencies which generates a conditional two-qubit gate, but will also generate other spurious interactions. These optimal control techniques are used to find pulse shapes that can perform this two-qubit gate with high fidelity, robust against errors in the system parameters. The simulations were all performed using experimentally relevant parameters and constraints.Comment: Final published versio

Semiconductor Microstructure in a Squeezed Vacuum: Electron-Hole Plasma Luminescence

We consider a semiconductor quantum-well placed in a wave guide microcavity and interacting with the broadband squeezed vacuum radiation, which fills one mode of the wave guide with a large average occupation. The wave guide modifies the optical density of states so that the quantum well interacts mostly with the squeezed vacuum. The vacuum is squeezed around the externally controlled central frequency \om_0, which is tuned above the electron-hole gap $E_g$, and induces fluctuations in the interband polarization of the quantum-well. The power spectrum of scattered light exhibits a peak around \om_0, which is moreover non-Lorentzian and is a result of both the squeezing and the particle-hole continuum. The squeezing spectrum is qualitatively different from the atomic case. We discuss the possibility to observe the above phenomena in the presence of additional non-radiative (e-e, phonon) dephasing.Comment: 6 pages, 3 figure