Encoding quantum information in quantum states with disjoint wave-function support and noise insensitive energies is the key behind the idea of qubit protection. While fully protectedqubits are expected to offer exponential protection against both energy relaxation and pure dephasing, simpler circuits may grant partial protection with currently achievable parameters. Here, we study a fluxonium circuit in which the wave-functions are engineered to minimize their overlap while benefiting from a first-order-insensitive flux sweet spot. Taking advantage of a large superinductance (L∼1 μH), our circuit incorporates a resonant tunneling mechanism at zero external flux that couples states with the same fluxon parity, thus enabling bifluxon tunneling. The states |0⟩ and |1⟩ are encoded in wave-functions with parities 0 and 1, respectively, ensuring a minimal form of protection against relaxation. Two-tone spectroscopy reveals the energy level structure of the circuit and the presence of 4π quantum-phase slips between different potential wells corresponding to m=±1 fluxons, which can be precisely described by a simple fluxonium Hamiltonian or by an effective bifluxon Hamiltonian. Despite suboptimal fabrication, the measured relaxation (T1=177±3 μs) and dephasing (TE2=75±5 μs) times not only demonstrate the relevance of our approach but also opens an alternative direction towards quantum computing using partially-protected fluxonium qubits.
Electromagnetic fields possess zero point fluctuations (ZPF) which lead to observable effects such as the Lamb shift and the Casimir effect. In the traditional quantum optics domain,these corrections remain perturbative due to the smallness of the fine structure constant. To provide a direct observation of non-perturbative effects driven by ZPF in an open quantum system we wire a highly non-linear Josephson junction to a high impedance transmission line, allowing large phase fluctuations across the junction. Consequently, the resonance of the former acquires a relative frequency shift that is orders of magnitude larger than for natural atoms. Detailed modelling confirms that this renormalization is non-linear and quantum. Remarkably, the junction transfers its non-linearity to about 30 environmental modes, a striking back-action effect that transcends the standard Caldeira-Leggett paradigm. This work opens many exciting prospects for longstanding quests such as the tailoring of many-body Hamiltonians in the strongly non-linear regime, the observation of Bloch oscillations, or the development of high-impedance qubits.
We report on the fabrication and characterization of 50 Ohms, flux-tunable, low-loss, SQUID-based transmission lines. The fabrication process relies on the deposition of a thin dielectriclayer (few tens of nanometers) via Atomic Layer Deposition (ALD) on top of a SQUID array, the whole structure is then covered by a non-superconducting metallic top ground plane. We present experimental results from five different samples. We systematically characterize their microscopic parameters by measuring the propagating phase in these structures. We also investigate losses and discriminate conductor from dielectric losses. This fabrication method offers several advantages. First, the SQUID array fabrication does not rely on a Niobium tri-layer process but on a simpler double angle evaporation technique. Second, ALD provides high quality dielectric leading to low-loss devices. Further, the SQUID array fabrication is based on a standard, all-aluminum process, allowing direct integration with superconducting qubits. Moreover, our devices are in-situ flux tunable, allowing mitigation of incertitude inherent to any fabrication process. Finally, the unit cell being a single SQUID (no extra ground capacitance is needed), it is straightforward to modulate the size of the unit cell periodically, allowing band-engineering. This fabrication process can be directly applied to traveling wave parametric amplifiers.
An amplifier combining noise performances as close as possible to the quantum limit with large bandwidth and high saturation power is highly desirable for many solid state quantum technologiessuch as high fidelity qubit readout or high sensitivity electron spin resonance for example. Here we introduce a new Traveling Wave Parametric Amplifier based on Superconducting QUantum Interference Devices. It displays a 3 GHz bandwidth, a -102 dBm 1-dB compression point and added noise near the quantum limit. Compared to previous state-of-the-art, it is an order of magnitude more compact, its characteristic impedance is in-situ tunable and its fabrication process requires only two lithography steps. The key is the engineering of a gap in the dispersion relation of the transmission line. This is obtained using a periodic modulation of the SQUID size, similarly to what is done with photonic crystals. Moreover, we provide a new theoretical treatment to describe the non-trivial interplay between non-linearity and such periodicity. Our approach provides a path to co-integration with other quantum devices such as qubits given the low footprint and easy fabrication of our amplifier.
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.