Down-conversion of a single photon as a probe of many-body localization.

Decay of a particle into more particles is a ubiquitous phenomenon to interacting quantum systems, taking place in colliders, nuclear reactors or solids. In a nonlinear medium, even a single photon would decay by down-converting (splitting) into lower-frequency photons with the same total energy1, at a rate given by Fermi's golden rule. However, the energy-conservation condition cannot be matched precisely if the medium is finite and only supports quantized modes. In this case, the fate of the photon becomes the long-standing question of many-body localization, originally formulated as a gedanken experiment for the lifetime of a single Fermi-liquid quasiparticle confined to a quantum dot2. Here we implement such an experiment using a superconducting multimode cavity, the nonlinearity of which was tailored to strongly violate the photon-number conservation. The resulting interaction attempts to convert a single photon excitation into a shower of low-energy photons but fails owing to the many-body localization mechanism, which manifests as a striking spectral fine structure of multiparticle resonances at the standing-wave-mode frequencies of the cavity. Each resonance was identified as a many-body state of radiation composed of photons from a broad frequency range and not obeying Fermi's golden rule theory. Our result introduces a new platform to explore the fundamentals of many-body localization without having to control many atoms or qubits3-9.

The superconducting quasicharge qubit.

The non-dissipative nonlinearity of Josephson junctions1 converts macroscopic superconducting circuits into artificial atoms2, enabling some of the best-controlled qubits today3,4. Three fundamental types of superconducting qubit are known5, each reflecting a distinct behaviour of quantum fluctuations in a Cooper pair condensate: single-charge tunnelling (charge qubit6,7), single-flux tunnelling (flux qubit8) and phase oscillations (phase qubit9 or transmon10). Yet, the dual nature of charge and flux suggests that circuit atoms must come in pairs. Here we introduce the missing superconducting qubit, 'blochnium', which exploits a coherent insulating response of a single Josephson junction that emerges from the extension of phase fluctuations beyond 2π (refs. 11-14). Evidence for such an effect has been found in out-of-equilibrium direct-current transport through junctions connected to high-impedance leads15-19, although a full consensus on the existence of extended phase fluctuations is so far absent20-22. We shunt a weak junction with an extremely high inductance-the key technological innovation in our experiment-and measure the radiofrequency excitation spectrum as a function of external magnetic flux through the resulting loop. The insulating character of the junction is manifested by the vanishing flux sensitivity of the qubit transition between the ground state and the first excited state, which recovers rapidly for transitions to higher-energy states. The spectrum agrees with a duality mapping of blochnium onto a transmon, which replaces the external flux by the offset charge and introduces a new collective quasicharge variable instead of the superconducting phase23,24. Our findings may motivate the exploration of macroscopic quantum dynamics in ultrahigh-impedance circuits, with potential applications in quantum computing and metrology.

Millisecond Coherence in a Superconducting Qubit.

Improving control over physical qubits is a crucial component of quantum computing research. Here we report a superconducting fluxonium qubit with uncorrected coherence time T_{2}^{*}=1.48±0.13 ms, exceeding the state of the art for transmons by an order of magnitude. The average gate fidelity was benchmarked at 0.99991(1). Notably, even in the millisecond range, the coherence time is limited by material absorption and could be further improved with a more rigorous fabrication. Our demonstration may be useful for suppressing errors in the next generation quantum processors.

Local Control of Supercurrent Density in Epitaxial Planar Josephson Junctions.

The critical current response to an applied out-of-plane magnetic field in a Josephson junction provides insight into the uniformity of its current distribution. In Josephson junctions with semiconducting weak links, the carrier density, and therefore the overall current distribution, can be modified electrostatically via metallic gates. Here, we show local control of the current distribution in an epitaxial Al-InAs Josephson junction equipped with five minigates. We demonstrate that not only can the junction width be electrostatically defined but also the current profile can be locally adjusted to form superconducting quantum interference devices. Our studies show enhanced edge conduction in such long junctions, which can be eliminated by minigates to create a uniform current distribution.

Photon-Instanton Collider Implemented by a Superconducting Circuit.

Instantons, spacetime-localized quantum field tunneling events, are ubiquitous in correlated condensed matter and high-energy systems. However, their direct observation through collisions with conventional particles has not been considered possible. We show how recent advances in circuit quantum electrodynamics, specifically, the realization of galvanic coupling of a transmon qubit to a high-impedance transmission line, allows the observation of inelastic collisions of single microwave photons with instantons (phase slips). We develop a formalism for calculating the photon-instanton cross section, which should be useful in other quantum field theoretical contexts. In particular, we show that the inelastic scattering probability can significantly exceed the effect of conventional Josephson quartic anharmonicity and reach order-unity values.

Demonstration of Protection of a Superconducting Qubit from Energy Decay.

Long-lived transitions occur naturally in atomic systems due to the abundance of selection rules inhibiting spontaneous emission. By contrast, transitions of superconducting artificial atoms typically have large dipoles, and hence their lifetimes are determined by the dissipative environment of a macroscopic electrical circuit. We designed a multilevel fluxonium artificial atom such that the qubit's transition dipole can be exponentially suppressed by flux tuning, while it continues to dispersively interact with a cavity mode by virtual transitions to the noncomputational states. Remarkably, energy decay time T_{1} grew by 2 orders of magnitude, proportionally to the inverse square of the transition dipole, and exceeded the benchmark value of T_{1}>2 ms (quality factor Q_{1}>4×10^{7}) without showing signs of saturation. The dephasing time was limited by the first-order coupling to flux noise to about 4 µs. Our circuit validated the general principle of hardware-level protection against bit-flip errors and can be upgraded to the 0-π circuit [P. Brooks, A. Kitaev, and J. Preskill, Phys. Rev. A 87, 052306 (2013)PLRAAN1050-294710.1103/PhysRevA.87.052306], adding protection against dephasing and certain gate errors.

Ancillary qubit spectroscopy of vacua in cavity and circuit quantum electrodynamics.

We investigate theoretically how the spectroscopy of an ancillary qubit can probe cavity (circuit) QED ground states containing photons. We consider three classes of systems (Dicke, Tavis-Cummings, and Hopfield-like models), where nontrivial vacua are the result of ultrastrong coupling between N two-level systems and a single-mode bosonic field. An ancillary qubit detuned with respect to the boson frequency is shown to reveal distinct spectral signatures depending on the type of vacua. In particular, the Lamb shift of the ancilla is sensitive to both ground state photon population and correlations. Backaction of the ancilla on the cavity ground state is investigated, taking into account the dissipation via a consistent master equation for the ultrastrong coupling regime. The conditions for high-fidelity measurements are determined.

Proposal for coherent coupling of Majorana zero modes and superconducting qubits using the 4π Josephson effect.

We propose to use an ancilla fluxonium qubit to interact with a Majorana qubit hosted by a topological one-dimensional wire. The coupling is obtained using the Majorana qubit-controlled 4π Josephson effect to flux bias the fluxonium qubit. We demonstrate how this coupling can be used to sensitively identify topological superconductivity, to measure the state of the Majorana qubit, to construct 2-qubit operations, and to implement quantum memories with topological protection.

Electron shelving of a superconducting artificial atom.

Interfacing long-lived qubits with propagating photons is a fundamental challenge in quantum technology. Cavity and circuit quantum electrodynamics (cQED) architectures rely on an off-resonant cavity, which blocks the qubit emission and enables a quantum non-demolition (QND) dispersive readout. However, no such buffer mode is necessary for controlling a large class of three-level systems that combine a metastable qubit transition with a bright cycling transition, using the electron shelving effect. Here we demonstrate shelving of a circuit atom, fluxonium, placed inside a microwave waveguide. With no cavity modes in the setup, the qubit coherence time exceeds 50 µs, and the cycling transition's radiative lifetime is under 100 ns. By detecting a homodyne fluorescence signal from the cycling transition, we implement a QND readout of the qubit and account for readout errors using a minimal optical pumping model. Our result establishes a resource-efficient (cavityless) alternative to cQED for controlling superconducting qubits.

Fluxonium: single cooper-pair circuit free of charge offsets.

The promise of single Cooper-pair quantum circuits based on tunnel junctions for metrology and quantum information applications is severely limited by the influence of offset charges: random, slowly drifting microscopic charges inherent in many solid-state systems. By shunting a small junction with the Josephson kinetic inductance of a series array of large-capacitance tunnel junctions, thereby ensuring that all superconducting islands are connected to the circuit by at least one large junction, we have realized a new superconducting artificial atom that is totally insensitive to offset charges. Yet its energy levels manifest the anharmonic structure associated with single Cooper-pair effects, a useful component for solid-state quantum computation.