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Electron spins hold great promise for quantum computation because of their long coherence times. Long-distance coherent coupling of spins is a crucial step towards quantum information processing with spin qubits. One approach to realizing interactions between distant spin qubits is to use photons as carriers of quantum information. Here we demonstrate strong coupling between single microwave photons in a niobium titanium nitride high-impedance resonator and a three-electron spin qubit (also known as a resonant exchange qubit) in a gallium arsenide device consisting of three quantum dots. We observe the vacuum Rabi mode splitting of the resonance of the resonator, which is a signature of strong coupling; specifically, we observe a coherent coupling strength of about 31 megahertz and a qubit decoherence rate of about 20 megahertz. We can tune the decoherence electrostatically to obtain a minimal decoherence rate of around 10 megahertz for a coupling strength of around 23 megahertz. We directly measure the dependence of the qubit–photon coupling strength on the tunable electric dipole moment of the qubit using the ‘AC Stark’ effect. Our demonstration of strong qubit–photon coupling for a three-electron spin qubit is an important step towards coherent long-distance coupling of spin qubits. Coherent coupling between a three-electron spin qubit and single photons in a microwave resonator is demonstrated, which, unlike previous demonstrations, does not require ferromagnetic components near the qubit.

The strong coupling limit of cavity quantum electrodynamics (QED) implies the capability of a matterlike quantum system to coherently transform an individual excitation into a single photon within a resonant structure. This not only enables essential processes required for quantum information processing but also allows for fundamental studies of matter-light interaction. In this work, we demonstrate strong coupling between the charge degree of freedom in a gate-defined GaAs double quantum dot (DQD) and a frequency-tunable high impedance resonator realized using an array of superconducting quantum interference devices. In the resonant regime, we resolve the vacuum Rabi mode splitting of size 2g/2π=238MHz at a resonator linewidth κ/2π=12MHz and a DQD charge qubit decoherence rate of γ2/2π=40MHz extracted independently from microwave spectroscopy in the dispersive regime. Our measurements indicate a viable path towards using circuit-based cavity QED for quantum information processing in semiconductor nanostructures.

Semiconductor qubits rely on the control of charge and spin degrees of freedom of electrons or holes confined in quantum dots. They constitute a promising approach to quantum information processing, complementary to superconducting qubits. Here, we demonstrate coherent coupling between a superconducting transmon qubit and a semiconductor double quantum dot (DQD) charge qubit mediated by virtual microwave photon excitations in a tunable high-impedance SQUID array resonator acting as a quantum bus. The transmon-charge qubit coherent coupling rate (~21 MHz) exceeds the linewidth of both the transmon (~0.8 MHz) and the DQD charge qubit (~2.7 MHz). By tuning the qubits into resonance for a controlled amount of time, we observe coherent oscillations between the constituents of this hybrid quantum system. These results enable a new class of experiments exploring the use of two-qubit interactions mediated by microwave photons to create entangled states between semiconductor and superconducting qubits. Hybrid quantum devices combine different platforms with the prospect of exploiting the advantages of each. Scarlino et al. demonstrate strong, coherent coupling between a semiconductor qubit and a superconducting qubit by using a high-impedance superconducting resonator as a quantum bus.

Semiconductor quantum dots in which electrons or holes are isolated via electrostatic potentials generated by surface gates are promising building blocks for semiconductor-based quantum technology. Here, we investigate double-quantum-dot (DQD) charge qubits in GaAs capacitively coupled to high-impedance superconducting quantum interference device array and Josephson-junction array resonators. We tune the strength of the electric-dipole interaction between the qubit and the resonator in situ using surface gates. We characterize the qubit-resonator coupling strength, the qubit decoherence, and the detuning noise affecting the charge qubit for different electrostatic DQD configurations. We find all quantities to be systematically tunable over more than one order of magnitude, resulting in reproducible decoherence ratesΓ2/2π<5MHzin the limit of high interdot capacitance. In the opposite limit, by reducing the interdot capacitance, we increase the DQD electric-dipole strength and, therefore, its coupling to the resonator. Employing a Josephson-junction array resonator with an impedance of approximately4kΩand a resonance frequency ofωr/2π∼5.6GHz, we observe a coupling strength ofg/2π∼630MHz, demonstrating the possibility to operate electrons hosted in a semiconductor DQD in the ultrastrong-coupling regime (USC). The presented results are essential for further increasing the coherence of quantum-dot-based qubits and investigating USC physics in semiconducting QDs.

Spin qubits and superconducting qubits are among the promising candidates for realizing a solid state quantum computer. For the implementation of a hybrid architecture which can profit from the advantages of either approach, a coherent link is necessary that integrates and controllably couples both qubit types on the same chip over a distance that is several orders of magnitude longer than the physical size of the spin qubit. We realize such a link with a frequency-tunable high impedance SQUID array resonator. The spin qubit is a resonant exchange qubit hosted in a GaAs triple quantum dot. It can be operated at zero magnetic field, allowing it to coexist with superconducting qubits on the same chip. We spectroscopically observe coherent interaction between the resonant exchange qubit and a transmon qubit in both resonant and dispersive regimes, where the interaction is mediated either by real or virtual resonator photons. Different qubit platforms each have their own advantages and disadvantages. By engineering couplings between them it may be possible to create a more capable hybrid device. Here the authors demonstrate coherent coupling between a semiconductor spin qubit and a superconducting transmon.

The realization of a coherent interface between distant charge or spin qubits in semiconductor quantum dots is an open challenge for quantum information processing. Here, we demonstrate both resonant (real) and nonresonant (virtual) photon-mediated coherent interactions between double quantum-dot charge qubits separated by several tens of micrometers. We present clear spectroscopic evidence of the resonant collective enhancement of the coupling of two qubits and the resonator. With both qubits in resonance with each other but detuned from the resonator, we observe exchange coupling between the qubits mediated by virtual photons. In both instances, pronounced bright and dark states governed by the symmetry of the qubit-field interaction are found. Our observations are in excellent quantitative agreement with master-equation simulations. The extracted two-qubit coupling strengths significantly exceed the linewidths of the combined resonator-qubit system, which indicates that this approach is viable for creating photon-mediated two-qubit gates in quantum-dot-based systems.

Quantum Hall edge channels offer an efficient and controllable platform to study quantum transport in one dimension. Such channels are a prospective tool for the efficient transfer of quantum information at the nanoscale, and play a vital role in exposing intriguing physics. Electric current along the edge carries energy and heat leading to inelastic scattering, which may impede coherent transport. Several experiments attempting to probe the concomitant energy redistribution along the edge reported energy loss via unknown mechanisms of inelastic scattering. Here we employ quantum dots to inject and extract electrons at specific energies, to spectrally analyse inelastic scattering inside quantum Hall edge channels. We show that the missing energy puzzle could be untangled by incorporating non-local Auger-like processes, in which energy is redistributed between spatially separate parts of the sample. Our theoretical analysis, accounting for the experimental results, challenges common-wisdom analyses which ignore such non-local decay channels. Energy relaxation crucially impacts transport properties of mesoscopic devices. Here the authors show that energy can be distributed between distant parts of the sample, which may provide a resolution to an outstanding puzzle concerning energy conservation in transport through quantum Hall edges.

The fundamental concept of light–matter interaction is routinely realized by coupling the quantized electric field in a cavity to the dipole moment of a real or an artificial atom. A recent proposal 1 , 2 , motivated by the prospect of overcoming the decohering effects of distant charge fluctuations, suggests that introduction of and coupling to an electric quadrupole moment of a single electron can be achieved by confining it in a triple quantum dot. Here, we show an experimental realization of this concept by connecting a superconducting microwave resonator to the middle of the three dots, such that the dipole coupling becomes negligible. We demonstrate strong coupling to the electron quadrupole moment and determine that the coherence of our system is limited by short-range charge noise. Our experiment enables the construction and detection of a complex electronic state of a single electron in a solid-state environment that does not exist as such for a free electron. Coupling of the quadrupole moment of an electron in a triple quantum dot to photons has been predicted to be a good platform for reducing the effect of charge noise on the decoherence time of a qubit. Here, the authors create such a coupling.

The pattern of branched electron flow revealed by scanning gate microscopy shows the distribution of ballistic electron trajectories. The details of the pattern are determined by the correlated potential of remote dopants with an amplitude far below the Fermi energy. We find that the pattern persists even if the electron density is significantly reduced such that the change in Fermi energy exceeds the background potential amplitude. The branch pattern is robust against changes in charge carrier density, but not against changes in the background potential caused by additional illumination of the sample.

We present a low-temperature experimental test of the fluctuation theorem for electron transport through a double quantum dot. The rare entropy-consuming system trajectories are detected in the form of single charges flowing against the source-drain bias by using time-resolved charge detection with a quantum point contact. We find that these trajectories appear with a frequency that agrees with the theoretical predictions even under strong nonequilibrium conditions, when the finite bandwidth of the charge detection is taken into account.