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The spin–orbit interaction (SOI) in zincblende semiconductor quantum wells can be set to a symmetry point, in which spin decay is strongly suppressed for a helical spin mode. Signatures of such a persistent spin helix (PSH) have been probed using the transient spin-grating technique, but it has not yet been possible to observe the formation and the helical nature of a PSH. Here we directly map the diffusive evolution of a local spin excitation into a helical spin mode by a time-resolved and spatially resolved magneto-optical Kerr rotation technique. Depending on its in-plane direction, an external magnetic field interacts differently with the spin mode and either highlights its helical nature or destroys the SU(2) symmetry of the SOI and thus decreases the spin lifetime. All relevant SOI parameters are experimentally determined and confirmed with a numerical simulation of spin diffusion in the presence of SOI. Spin–orbit interaction induces spin-polarization decay in semiconductor quantum wells. But this decay can be suppressed in favour of a helical spin mode by tuning the interaction. Optical pump–probe measurements provide direct evidence of the resulting helix—a signature that has so far only been inferred from transport measurements.

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.

Minimal-excitation fermionic quasiparticles are created by applying a potential with Lorentzian time dependence to the contact of a narrow constriction in a two-dimensional electron gas. Levitons produced to order The on-demand generation of pure quantum excitations, important for the operation of quantum systems, is particularly difficult for fermions. This is because perturbations tend to result in a complex superposition of particle and hole excitations. However, it was predicted by Leonid Levitov nearly twenty years ago that it should be possible to generate a minimal excitation, a quasiparticle with only one particle and no hole. The authors report the on-demand generation of such quasiparticles, which they term 'levitons', in an electronic system. They envisage that levitons will find application in quantum information and fundamental studies. The on-demand generation of pure quantum excitations is important for the operation of quantum systems, but it is particularly difficult for a system of fermions. This is because any perturbation affects all states below the Fermi energy, resulting in a complex superposition of particle and hole excitations. However, it was predicted nearly 20 years ago 1 , 2 , 3 that a Lorentzian time-dependent potential with quantized flux generates a minimal excitation with only one particle and no hole. Here we report that such quasiparticles (hereafter termed levitons) can be generated on demand in a conductor by applying voltage pulses to a contact. Partitioning the excitations with an electronic beam splitter generates a current noise that we use to measure their number. Minimal-excitation states are observed for Lorentzian pulses, whereas for other pulse shapes there are significant contributions from holes. Further identification of levitons is provided in the energy domain with shot-noise spectroscopy, and in the time domain with electronic Hong–Ou–Mandel noise correlations 4 , 5 , 6 , 7 , 8 . The latter, obtained by colliding synchronized levitons on a beam splitter, exemplifies the potential use of levitons for quantum information: using linear electron quantum optics 9 in ballistic conductors, it is possible to imagine flying-qubit 10 , 11 operation in which the Fermi statistics are exploited 12 , 13 , 14 to entangle synchronized electrons emitted by distinct sources 15 , 16 , 17 , 18 . Compared with electron sources based on quantum dots 19 , 20 , 21 , the generation of levitons does not require delicate nanolithography, considerably simplifying the circuitry for scalability. Levitons are not limited to carrying a single charge, and so in a broader context n -particle levitons could find application in the study of full electron counting statistics 22 , 23 , 24 , 25 . But they can also carry a fraction of charge if they are implemented in Luttinger liquids 3 or in fractional quantum Hall edge channels 26 ; this allows the study of Abelian and non-Abelian quasiparticles in the time domain. Finally, the generation technique could be applied to cold atomic gases 27 , 28 , leading to the possibility of atomic levitons.

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.

Quantum-mechanical correlations of interacting fermions result in the emergence of exotic phases. Magnetic phases naturally arise in the Mott-insulator regime of the Fermi-Hubbard model, where charges are localized and the spin degree of freedom remains. In this regime, the occurrence of phenomena such as resonating valence bonds, frustrated magnetism, and spin liquids is predicted. Quantum systems with engineered Hamiltonians can be used as simulators of such spin physics to provide insights beyond the capabilities of analytical methods and classical computers. To be useful, methods for the preparation of intricate many-body spin states and access to relevant observables are required. Here, we show the quantum simulation of magnetism in the Mott-insulator regime with a linear quantum-dot array. We characterize the energy spectrum for a Heisenberg spin chain, from which we can identify when the conditions for homogeneous exchange couplings are met. Next, we study the multispin coherence with global exchange oscillations in both the singlet and triplet subspace of the Heisenberg Hamiltonian. Last, we adiabatically prepare the low-energy global singlet of the homogeneous spin chain and probe it with two-spin singlet-triplet measurements on each nearest-neighbor pair and the correlations therein. The methods and control presented here open new opportunities for the simulation of quantum magnetism benefiting from the flexibility in tuning and layout of gate-defined quantum-dot arrays.

A quantum simulation platform based on quantum dots is reported that can operate at relatively low temperatures, and its utility is shown by simulating a Fermi–Hubbard model. Quantum simulations on quantum dots Quantum simulations have been performed on various different platforms, for example using vacancies in diamond or ultracold quantum gases. Quantum dots have been regarded as a promising constituent of quantum simulation platforms for some time, but owing to difficulties in calibrating them it has so far been impossible to run a successful simulation. Here, the authors overcome these difficulties and demonstrate a quantum simulation of a Fermi–Hubbard model, which is a famous model in condensed matter physics. Quantum simulation platforms based on quantum dots are predicted to be able to reach lower temperatures than atomic-physics-based platforms. This could help to clarify puzzles in condensed matter physics, such as high-temperature superconductivity. Interacting fermions on a lattice can develop strong quantum correlations, which are the cause of the classical intractability of many exotic phases of matter 1 , 2 , 3 . Current efforts are directed towards the control of artificial quantum systems that can be made to emulate the underlying Fermi–Hubbard models 4 , 5 , 6 . Electrostatically confined conduction-band electrons define interacting quantum coherent spin and charge degrees of freedom that allow all-electrical initialization of low-entropy states and readily adhere to the Fermi–Hubbard Hamiltonian 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 . Until now, however, the substantial electrostatic disorder of the solid state has meant that only a few attempts at emulating Fermi–Hubbard physics on solid-state platforms have been made 18 , 19 . Here we show that for gate-defined quantum dots this disorder can be suppressed in a controlled manner. Using a semi-automated and scalable set of experimental tools, we homogeneously and independently set up the electron filling and nearest-neighbour tunnel coupling in a semiconductor quantum dot array so as to simulate a Fermi–Hubbard system. With this set-up, we realize a detailed characterization of the collective Coulomb blockade transition 20 , which is the finite-size analogue of the interaction-driven Mott metal-to-insulator transition 1 . As automation and device fabrication of semiconductor quantum dots continue to improve, the ideas presented here will enable the investigation of the physics of ever more complex many-body states using quantum dots.

Artificial cavity photon resonators with ultrastrong light-matter interactions are attracting interest both in semiconductor and superconducting systems because of the possibility of manipulating the cavity quantum electrodynamic ground state with controllable physical properties. We report here experiments showing ultrastrong light-matter coupling in a terahertz (THz) metamaterial where the cyclotron transition of a high-mobility two-dimensional electron gas (2DEG) is coupled to the photonic modes of an array of electronic split-ring resonators. We observe a normalized coupling ratio, g = \\[\\frac{\\Omega } {{{\\omega _c}}}\\]0.58, between the vacuum Rabi frequency, Q, and the cyclotron frequency, ω c . Our system appears to be scalable in frequency and could be brought to the microwave spectral range with the potential of strongly controlling the magnetotransport properties of a high-mobility 2DEG.

Engineered, highly controllable quantum systems are promising simulators of emergent physics beyond the simulation capabilities of classical computers 1 . An important problem in many-body physics is itinerant magnetism, which originates purely from long-range interactions of free electrons and whose existence in real systems has been debated for decades 2 , 3 . Here we use a quantum simulator consisting of a four-electron-site square plaquette of quantum dots 4 to demonstrate Nagaoka ferromagnetism 5 . This form of itinerant magnetism has been rigorously studied theoretically 6 – 9 but has remained unattainable in experiments. We load the plaquette with three electrons and demonstrate the predicted emergence of spontaneous ferromagnetic correlations through pairwise measurements of spin. We find that the ferromagnetic ground state is remarkably robust to engineered disorder in the on-site potentials and we can induce a transition to the low-spin state by changing the plaquette topology to an open chain. This demonstration of Nagaoka ferromagnetism highlights that quantum simulators can be used to study physical phenomena that have not yet been observed in any experimental system. The work also constitutes an important step towards large-scale quantum dot simulators of correlated electron systems. A quantum dot device designed to host four electrons is used to demonstrate Nagaoka ferromagnetism—a model of itinerant magnetism that has so far been limited to theoretical investigation.

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.