The Hermiticity axiom of quantum mechanics guarantees that the energy spectrum is real and the time evolution is unitary (probability-preserving). Nevertheless, non-Hermitian but -symmetricHamiltonians may also have real eigenvalues. Systems described by such effective -symmetric Hamiltonians have been realized in experiments using coupled systems with balanced loss (dissipation) and gain (amplification), and their corresponding classical dynamics has been studied. A -symmetric system emerging from a quantum dynamics is highly desirable, in order to understand what -symmetry and the powerful mathematical and physical concepts around it will bring to the next generation of quantum technologies. Here, we address this need by proposing and studying a circuit-QED architecture that consists of two coupled resonators and two qubits (each coupled to one resonator). By means of external driving fields on the qubits, we are able to tune gain and losses in the resonators. Starting with the quantum dynamics of this system, we show the emergence of the -symmetry via the selection of both driving amplitudes and frequencies. We engineer the system such that a non-number conserving dipole-dipole interaction emerges, introducing an instability at large coupling strengths. The -symmetry and its breaking, as well as the predicted instability in this circuit-QED system can be observed in a transmission experiment.
We demonstrate that stationary localized solutions (discrete solitons) exist in a one dimensional Bose-Hubbard lattices with gain and loss in the semiclassical regime. Stationary solutions,by defi- nition, are robust and do not demand for state preparation. Losses, unavoidable in experiments, are not a drawback, but a necessary ingredient for these modes to exist. The semiclassical calculations are complemented with their classical limit and dynamics based on a Gutzwiller Ansatz. We argue that circuit QED architectures are ideal platforms for realizing the physics developed here. Finally, within the input-output formalism, we explain how to experimentally access the different phases, including the solitons, of the chain.
We report on the design, fabrication and characterization of superconducting coplanar waveguide resonators with nanometric constrictions. By reducing the size of the center line downto 50 nm, the RF currents are concentrated into a small cross section and the magnetic field in its vicinity is increased. The device characteristics are only slightly modified by the constrictions, with changes in resonance frequency lower than 1% and changes in transmission and Q-factor lower than 20%. These devices could enable the achievement of higher couplings to small magnetic samples or even to single molecular spins and have applications in circuit quantum electrodynamics, quantum computing and electron paramagnetic resonance.
The classical and quantum dynamics of two ultra-strongly coupled and weakly nonlinear resonators cannot be explained using the Discrete Nonlinear Schr“odinger Equation or theBose-Hubbard model, respectively. Instead, a model beyond the Rotating Wave Approximation must be studied. In the classical limit this model is not integrable and becomes chaotic for a finite window of parameters. For the quantum dimer we find corresponding regions of stability and chaos. The more striking consequence for both classical and quantum chaos is that the tunneling time between the sites becomes unpredictable. These results, including the transition to chaos, can be tested in experiments with superconducting microwave resonators.