The Jordan-Wigner transformation maps a one-dimensional spin-1/2 system onto a Fermionic model without spin degree of freedom. Here we show that a double chain of qubits with XX andZZ couplings of neighboring qubits along and between the chains, respectively, can be mapped on a spin-full 1D Fermi-Hubbard model. The qubit system can thus be used to emulate the quantum properties of this model. We analyze physical implementations of such analog quantum simulators, including one based on transmon qubits, where the ZZ interaction arises due to an inductive coupling and the XX interaction due to a capacitive interaction. We propose protocols to gain confidence in the results of the simulation through measurements of local operators.
A metamaterial formed by superconducting circuits or quantum dots can serve as active lasing medium when coupled to a microwave resonator. For these artificial atoms, in contrast toreal atoms, variations in their parameters cannot be avoided. In this paper, we examine the influence of disorder on such a multi-atom lasing setup. We find that the lasing process evolves into a self-organized stationary state that is quite robust against disorder. The reason is that photons created by those atoms which are in or close to resonance with the resonator stimulate the emission also of more detuned atoms. Not only the number of photons grows with the number of atoms, but also the width of the resonance as function of the detuning. Similar properties are found for other types of disorder such as variations in the individual coupling. We present relations how the allowed disorder scales with the number of atoms and confirm it by a numerical analysis. We also provide estimates for the sample-to-sample variations to be expected for setups with moderate numbers of atoms.
Manipulating the propagation of electromagnetic waves through sub-wavelength sized artificial structures is the core function of metamaterials. Resonant structures, such as split ringresonators, play the role of artificial „atoms“ and shape the magnetic response. Superconducting metamaterials moved into the spotlight for their very low ohmic losses and the possibility to tune their resonance frequency by exploiting the Josephson inductance. Moreover, the nonlinear nature of the Josephson inductance enables the fabrication of truly artificial atoms. Arrays of such superconducting quantum two-level systems (qubits) can be used for the implementation of a quantum metamaterial. Here, we perform an experiment in which 20 superconducting flux qubits are embedded into a single microwave resonator. The phase of the signal transmitted through the resonator reveals the collective resonant coupling of up to 8 qubits. Quantum circuits of many artificial atoms based on this proof-of-principle experiment offer a wide range of prospects, from detecting single microwave photons to phase switching, quantum birefringence and superradiant phase transitions.
Motivated by recent „circuit QED“ experiments we investigate the noise
properties of coherently driven nonlinear resonators. By using Josephson
junctions in superconductingcircuits, strong nonlinearities can be engineered,
which lead to the appearance of pronounced effects already for a low number of
photons in the resonator. Based on a master equation approach we determine the
emission spectrum and observe for typical circuit QED parameters, in addition
to the primary Raman-type peaks, second-order peaks. These peaks describe
higher harmonics in the slow noise-induced fluctuations of the oscillation
amplitude of the resonator and provide a clear signature of the nonlinear
nature of the system.