A flux qubit biased at its symmetry point shows a minimum in the energy splitting (the gap), providing protection against flux noise. We have fabricated a qubit of which the gap can be tuned fast and have coupled this qubit strongly to an LC oscillator. We show full spectroscopy of the qubit-oscillator system and generate vacuum Rabi oscillations. When the gap is made equal to the oscillator frequency νosc we find the largest vacuum Rabi splitting of ∼ 0.1νosc. Here being at resonance coincides with the optimal coherence of the symmetry point.Superconducting qubits coupled to quantum oscillators have demonstrated a remarkable richness of physical phenomena in the last few years. After the first reports of coherent state transfer and strong coupling [1, 2], we have witnessed a rapid development of the field called circuit quantum electrodynamics (CQED) using high quality superconducting oscillators in realizing quantum gates [3], algorithms [4] as well as non-classical states of light and matter in artificially fabricated structures [5,6]. Among the different implementations the transmon [1,[3][4][5] and the phase qubit [6] dominated this development. With flux qubits the avoided crossing between qubit and oscillator level was observed [7,8] and the coherent single-photon exchange between qubit and oscillator was demonstrated [8]. However the, coherence of the flux qubit is optimally preserved only in the symmetry point for flux bias, where the energy splitting is minimal. This minimal splitting (h∆) is called the gap and depends (exponentially) on the properties of the Josephson junctions. Therefore, the gap is hard to control in fabrication and it is impossible to make it coincide with a fixed oscillator frequency. We now have developed a flux qubit of which the gap ∆ can be tuned over a broad range on sub-ns time scales [9]. With the use of this control we demonstrate strong coupling of a flux qubit with good coherence to a lumped-element LC oscillator, showing fast and longlived vacuum Rabi oscillations.Parameters of the superconducting qubits can be to a large extent chosen in the design phase. For strong coupling, where the interaction strength g exceeds the cavity and qubit loss rates, the rotating-wave approximation (RWA) can be applied and the system can be described by a Jaynes-Cummings type Hamiltonian. If g approaches the qubit or oscillator frequencies the RWA no longer holds, leading into the ultra-strong coupling regime [10,11]. For a flux qubit the ratio g/ν osc can be an order of magnitude larger than for charge and phase qubits [12], while these latter devices have a coupling that can be several orders of magnitude larger than the atomlight interaction energy [1]. For good coherence, operating the qubit at its spectral symmetry point is required. Therefore, experimentally combining galvanic coupling of oscillator and flux qubit with this symmetry point operation provides a major step forward in the development of CQED systems. For the flux qubit at the symmetry point the anharmonicity (distance ...

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.

An important desired ingredient of superconducting quantum circuits is a readout scheme whose complexity does not increase with the number of qubits involved in the measurement. Here, we present a readout scheme employing a single microwave line, which enables simultaneous readout of multiple qubits. Consequently, scaling up superconducting qubit circuits is no longer limited by the readout apparatus. Parallel readout of 6 flux qubits using a frequency division multiplexing technique is demonstrated, as well as simultaneous manipulation and time resolved measurement of 3 qubits. We discuss how this technique can be scaled up to read out hundreds of qubits on a chip.

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 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.

Frequency-selective readout for superconducting qubits opens the way towards scaling qubit circuits up without increasing the number of measurement lines. Here we demonstrate the readout of an array of 7 flux qubits located on the same chip. Each qubit is placed near an individual λ/4 resonator which, in turn, is coupled to a common microwave transmission line. We performed spectroscopy of all qubits and determined their parameters in a single measurement run.PACS numbers: 03.67.Lx 85.25.Am Superconducting qubits are effective two-level quantum systems with a controllable transition frequency between their eigenstates. They are among the most promising candidates for registers of future quantum computers, because of their potential to be manufactured lithographically in a controlled manner. This gives the designer the freedom to construct custom quantum circuits with well-defined parameters and consisting of a large number of devices. In practice, one of the problems that limits the scalability of qubit circuits is the readout apparatus that measures the qubit states at the end of a computation. Traditionally, the quantum state of superconducting flux 1 or phase 2 qubits is read out by measuring the switching current of a SQUID coupled to the qubit. This readout procedure requires dedicated wiring and additional external circuitry for every qubit. An alternative to this bulky readout is a dispersive readout realized by coupling the qubit to a superconducting resonator 3,4 . A multiplexed readout of two 5 and three 6 qubits through a single resonant cavity has already been demonstrated with Transmon qubits. However, the dispersive scheme cannot be scaled to a large number of devices, because one can not easily distinguish the signals generated by different qubits. In contrast to that, frequency-division multiplexing readout appears to be very promising. This approach has already been demonstrated for kinetic inductance detectors 7 with up to 42 devices 8 , and it is easily extendable to measure hundreds of detectors through a single readout line.In this Letter, we present a scalable implementation of frequency selective readout of an array of flux qubits that uses a dedicated resonator coupled to each qubit.The basic idea of the measurement is as follows. Due to the coupling to its qubit, each resonator acquires a dispersive shift 4 ,depending on the state of the qubit. Hereg is the effective coupling between the resonator and qubit,hω q is a) Electronic mail: ustinov@kit.edu the transition energy between the qubit states, ω r /2π is the resonance frequency of the uncoupled resonator and σ z is ±1 depending on the state of the qubit. Thus the state of the qubit can be determined by measuring ∆ω r . All resonators are coupled to a common transmission line through which their resonance frequencies can be measured.In this experiment, we used coplanar λ/4-resonators with resonance frequencies ranging from 9.3 GHz to 10.3 GHz. These resonators were capacitively coupled to a common transmission line on one end and shor...