We report on the implementation and detailed modelling of a Josephson Parametric Amplifier (JPA) made from an array of eighty Superconducting QUantum Interference Devices (SQUIDs),forming a non-linear quarter-wave resonator. This device was fabricated using a very simple single step fabrication process. It shows a large bandwidth (45 MHz), an operating frequency tunable between 5.9 GHz and 6.8 GHz and a large input saturation power (-117 dBm) when biased to obtain 20 dB of gain. Despite the length of the SQUID array being comparable to the wavelength, we present a model based on an effective non-linear LC series resonator that quantitatively describes these figures of merit without fitting parameters. Our work illustrates the advantage of using array-based JPA since a single-SQUID device showing the same bandwidth and resonant frequency would display a saturation power 15 dB lower.

Exploring the quantum world often starts by drawing a sharp boundary between a microscopic subsystem and the bath to which it is invariably coupled. In most cases, knowledge of thephysical processes occuring in the bath is not required in great detail. However, recent developments in circuit quantum electrodynamics are presenting regimes where the actual dynamics of engineered baths, such as microwave photon resonators, becomes relevant. Here we take a major technological step forward, by tailoring a centimeter-scale on-chip bath from a very long metamaterial made of 4700 tunable Josephson junctions. By monitoring how each measurable bosonic resonance of the circuit acquires a phase-shift due to its interaction with a transmon qubit, one can indirectly measure qubit properties, such as transition frequency, linewidth and non-linearity. This new platform also demonstrates the ultra-strong coupling regime for the first time in the context of Josephson waveguides. Our device combines a large number of modes (up to 10 in the present setup) that are simultaneously hybridised with the two-level system, and a broadening dominated by the artificial environment that is a sizeable fraction of the qubit transition frequency. Finally, we provide a quantitative and parameter-free model of this large quantum system, and show that the finite environment seen by the qubit is equivalent to a truly macroscopic bath.

The quest to understand interaction between light and matter stretches back to the ray optics of Euclid and Ptolemy. In recent decades, studies at the quantum scale were performed bycoupling an isolated emitter to a single mode of the electromagnetic field, standard quantum optics providing a complete toolbox for describing such a setup. Current efforts aim to explore the coherent dynamics of systems containing an emitter coupled to several electromagnetic degrees of freedom. Combining superconducting metamaterials and qubits could allow for the observation of genuinely macroscopic quantum effects such as a giant Lamb shift or non-classical states of multimode optical fields. In this work, we couple a transmon qubit to a high impedance, centimeter-scale, metamaterial waveguide, made of 4700 in-situ tunable Josephson junctions. Our device combines three essential properties required to go beyond the standard quantum optics paradigm and reach the multi-mode, many-body regime, namely: a tunable waveguide with a high density of electromagnetic modes, a qubit non-linearity comparable to the other relevant energy scales, and ultrastrong coupling between the qubit and the waveguide modes. Besides providing experimental evidence for these non-trivial requirements, we also develop a quantitative theoretical description that does not contain any phenomenological parameters and that accurately takes into account vacuum fluctuations of our large scale quantum circuit in the regime of ultrastrong coupling and intermediate non-linearity. Furthermore, we show that the influence on the transmon of our fully controllable on-chip environment well approximates that of the macroscopic bath envisioned in the celebrated work of Caldeira and Leggett. Our work demonstrates that Josephson waveguides offer a promising platform to explore many-body quantum optics.

We experimentally and theoretically investigate the quantum trajectories of jointly monitored transmon qubits embedded in spatially separated microwave cavities. Using nearly quantum-noiselimited superconducting amplifiers and an optimized setup to reduce signal loss between cavities, we can efficiently track measurement-induced entanglement generation as a continuous process for single realizations of the experiment. The quantum trajectories of transmon qubits naturally split into low and high entanglement classes corresponding to half-parity collapse. The distribution of concurrence is found at any given time and we explore the dynamics of entanglement creation in the state space. The distribution exhibits a sharp cut-off in the high concurrence limit, defining a maximal concurrence boundary. The most likely paths of the qubits‘ trajectories are also investigated, resulting in three probable paths, gradually projecting the system to two even subspaces and an odd subspace. We also investigate the most likely time for the individual trajectories to reach their most entangled state, and find that there are two solutions for the local maximum, corresponding to the low and high entanglement routes. The theoretical predictions show excellent agreement with the experimental entangled qubit trajectory data.

We present experimental results in which the unexpected zero-two transition of a circuit composed of two inductively coupled transmons is observed. This transition shows an unusualmagnetic flux dependence with a clear disappearance at zero magnetic flux. In a transmon qubit the symmetry of the wave functions prevents this transition to occur due to selection rule. In our circuit the Josephson effect introduces strong couplings between the two normal modes of the artificial atom. This leads to a coherent superposition of states from the two modes enabling such transitions to occur.

The creation of a quantum network requires the distribution of coherent information across macroscopic distances. We demonstrate the entanglement of two superconducting qubits, separatedby more than a meter of coaxial cable, by designing a joint measurement that probabilistically projects onto an entangled state. By using a continuous measurement scheme, we are further able to observe single quantum trajectories of the joint two-qubit state, confirming the validity of the quantum Bayesian formalism for a cascaded system. Our results allow us to resolve the dynamics of continuous projection onto the entangled manifold, in quantitative agreement with theory.

Superconducting circuits and microwave signals are good candidates to realize quantum networks, which are the backbone of quantum computers. We have realized a universal quantum nodebased on a 3D microwave superconducting cavity parametrically coupled to a transmission line by a Josephson ring modulator. We first demonstrate the time-controlled capture, storage and retrieval of an optimally shaped propagating microwave field, with an efficiency as high as 80 %. We then demonstrate a second essential ability, which is the timed-controlled generation of an entangled state distributed between the node and a microwave channel.

Making a system state follow a prescribed trajectory despite fluctuations and
errors commonly consists in monitoring an observable (temperature,
blood-glucose level…) and reactingon its controllers (heater power, insulin
amount …). In the quantum domain, there is a change of paradigm in feedback
since measurements modify the state of the system, most dramatically when the
trajectory goes through superpositions of measurement eigenstates. Here, we
demonstrate the stabilization of an arbitrary trajectory of a superconducting
qubit by measurement based feedback. The protocol benefits from the long
coherence time ($T_2>10 mu$s) of the 3D transmon qubit, the high efficiency
(82%) of the phase preserving Josephson amplifier, and fast electronics
ensuring less than 500 ns delay. At discrete time intervals, the state of the
qubit is measured and corrected in case an error is detected. For Rabi
oscillations, where the discrete measurements occur when the qubit is supposed
to be in the measurement pointer states, we demonstrate an average fidelity of
85% to the targeted trajectory. For Ramsey oscillations, which does not go
through pointer states, the average fidelity reaches 75%. Incidentally, we
demonstrate a fast reset protocol allowing to cool a 3D transmon qubit down to
0.6% in the excited state.

Using a superconducting circuit, the Josephson mixer, we demonstrate the
first experimental realization of spatially separated two-mode squeezed states
of microwave light. Driven bya pump tone, a first Josephson mixer generates,
out of quantum vacuum, a pair of entangled fields at different frequencies on
separate transmission lines. A second mixer, driven by a $pi$-phase shifted
copy of the first pump tone, recombines and disentangles the two fields. The
resulting output noise level is measured to be lower than for vacuum state at
the input of the second mixer, an unambiguous proof of entanglement. Moreover,
the output noise level provides a direct, quantitative measure of entanglement,
leading here to the demonstration of 6 Mebit.s$^{-1}$ (Mega entangled bits per
second) generated by the first mixer.