The key issue for the implementation of a metamaterial is to demonstrate the existence of collective modes corresponding to coherent oscillations of the meta-atoms. Atoms of natural materials interact with electromagnetic fields as quantum two-level systems. Artificial quantum two-level systems can be made, for example, using superconducting nonlinear resonators cooled down to their ground state. Here we perform an experiment in which 20 of these quantum meta-atoms, so-called flux qubits, are embedded into a microwave resonator. We observe the dispersive shift of the resonator frequency imposed by the qubit metamaterial and the collective resonant coupling of eight qubits. The realized prototype represents a mesoscopic limit of naturally occurring spin ensembles and as such we demonstrate the AC-Zeeman shift of a resonant qubit ensemble. The studied system constitutes the implementation of a basic quantum metamaterial in the sense that many artificial atoms are coupled collectively to the quantized mode of a photon field.

We study the loss rate for a set of lambda/2 coplanar waveguide resonators at millikelvin temperatures (20 mK - 900mK) and different applied powers (3E-19 W - 1E-12 W). The loss rate becomes power independent below a critical power. For a fixed power, the loss rate increases significantly with decreasing temperature. We show that this behavior can be caused by two-level systems in the surrounding dielectric materials. Interestingly, the influence of the two-level systems is of the same order of magnitude for the different material combinations. That leads to the assumption that the nature of these two-level systems is material independent.Comment: 3 pages, 5 figures, Submitted to Applied Physics Letter

We demonstrate amplification of a microwave signal by a strongly driven two-level system in a coplanar waveguide resonator. The effect, similar to the dressed-state lasing known from quantum optics, is observed with a single quantum system formed by a persistent current (flux) qubit. The transmission through the resonator is enhanced when the Rabi frequency of the driven qubit is tuned into resonance with one of the resonator modes. Amplification as well as linewidth narrowing of a weak probe signal has been observed. The stimulated emission in the resonator has been studied by measuring the emission spectrum. We analyzed our system and found an excellent agreement between the experimental results and the theoretical predictions obtained in the dressed-state model.

We demonstrate the narrow switching distribution of an underdamped Josephson junction from the zero to the finite voltage state at millikelvin temperatures. We argue that such junctions can be used as ultrasensitive detectors of the single photons in the GHz range, operating close to the quantum limit: a given initial (zero voltage) state can be driven by an incoming signal to the finite voltage state. The width of the switching distribution at a nominal temperature of about T = 10 mK was 4.5 nA, which corresponds to an effective noise temperature of the device below 60 mK.

We study a flux qubit in a coplanar waveguide resonator by measuring transmission through the system. In our system with the flux qubit decoupled galvanically from the resonator, the intermediate coupling regime is achieved. In this regime, dispersive readout is possible with weak back action on the qubit. The detailed theoretical analysis and simulations give good agreement with the experimental data and allow us to make the qubit characterization.

We have constructed a microwave detector based on the voltage switching of an underdamped Josephson junction, that is positioned at a current antinode of a λ/4 coplanar waveguide resonator. By measuring the switching current and the transmission through a waveguide capacitively coupled to the resonator at different drive frequencies and temperatures we are able to fully characterize the system and assess its detection efficiency and sensitivity. Testing the detector by applying a classical microwave field with the strength of a single photon yielded a sensitivity parameter of 0.5 in qualitative agreement with theoretical calculations.PACS numbers: 07.57. Kp, 74.78.Na, 85.25.Cp The light emission by single, microscopic quantum systems displays a number of non-classical features which have been exploited in fundamental investigations in quantum physics and which may result in applications in metrology, quantum communication and computing. Potential applications, however, would suffer from the rather weak coupling between atoms and single optical photons. This has stimulated efforts to study the same features with macroscopic artificial atoms. A particularly successful system relies on solid state superconducting circuits. Due to the Josephson non-linearity such circuits have an anharmonic excitation spectrum and may be restricted to an effective two-level systems which can interact resonantly with microwave fields. Besides the stronger coupling of superconducting circuits, an additional advantage is that they can be designed and fabricated on chip-scale, thereby allowing the integration in and scaling to larger systems with multiple components.Essential quantum optical effects with superconducting qubits, such as vacuum Rabi splitting [1], resonance fluorescence of a single artificial atom [2], and single atom lasing [3] have already been observed. Microwave fields can be amplified, detected and fully characterized in homodyne set-ups [4]. The effective coupling to transmission wave guides has made it possible to efficiently monitor the emitted radiation and verify the validity of the quantum trajectories of qubits conditioned on the detection record [5,6], as well as to apply feedback and stabilize coherent superposition states of the qubit [7].Quantum optics benefits from high efficiency single photon detectors. It relies on the energy of the individual photons being sufficient to exploit the photoelectric effect and liberate an electron which can be amplified and detected [8]. Transition edge sensors [9] and superconducting nanowire single photon detectors [10,11] also require a sufficiently large energy of the incident photon to heat and thus modify the current through the detector. The energy of microwave photons is too low to allow detection by these methods, and for this energy range both controllable single photon sources and efficient single photon detectors are still under development.When working in the single photon regime, it is an obvious choice to use the resonant coupling to qubit systems. Indeed...

When optically pumped magnetometers are aimed for the use in Earth's magnetic field, the orientation of the sensor to the field direction is of special importance to achieve accurate measurement result. Measurement errors and inaccuracies related to the heading of the sensor can be an even more severe problem in the case of special operational configurations, such as for example the use of strong off-resonant pumping. We systematically study the main contributions to the heading error in systems that promise high magnetic field resolutions at Earth's magnetic field strengths, namely the non-linear Zeeman splitting and the orientation dependent light shift. The good correspondence of our theoretical analysis to experimental data demonstrates that both of these effects are related to a heading dependent modification of the interaction between the laser light and the dipole moment of the atoms. Also, our results promise a compensation of both effects using a combination of clockwise and counter clockwise circular polarization.

We analyze a system composed of a qubit coupled to the electromagnetic fields in two high quality quantum oscillators. A particular realization of such a system is the superconducting qubit coupled to a transmission-line resonator driven by two signals with frequencies close to the resonator's harmonics. This doubly-driven system can be described in terms of the doubly-dressed qubit states. Our calculations demonstrate the possibility to change the number of photons in the resonator and the transmission of the fundamental-mode signal over a wide parameter range exploiting resonances with the dressed qubit. Experiments show that in the case of high quality resonators the dressed energy levels and corresponding resonance conditions can be probed, even for high driving amplitudes. The interaction of the qubit with photons of two harmonics can be used for the creation of quantum amplifiers or attenuators.