The shot noise in tunneling experiments reflects the Poissonian nature of the tunneling process. The shot-noise power is proportional to both the magnitude of the current and the effective charge of the carrier. Shot-noise spectroscopy thus enables us, in principle, to determine the effective charge q of the charge carriers of that tunnel. This can be used to detect electron pairing in superconductors: In the normal state, the noise corresponds to single electron tunneling (q=1e), while in the paired state, the noise corresponds to q=2e. Here, we use a newly developed amplifier to reveal that in typical mesoscopic superconducting junctions, the shot noise does not reflect the signatures of pairing and instead stays at a level corresponding to q=1e. We show that transparency can control the shot noise, and this q=1e is due to the large number of tunneling channels with each having very low transparency. Our results indicate that in typical mesoscopic superconducting junctions, one should expect q=1e noise and lead to design guidelines for junctions that allow the detection of electron pairing.

The recent discovery of cable bacteria has greatly expanded the known length scale of biological electron transport, as these multi-cellular bacteria are capable of mediating electrical currents across centimeter-scale distances. To enable such long-range conduction, cable bacteria embed a network of regularly spaced, parallel protein fibers in their cell envelope. These fibers exhibit extraordinary electrical properties for a biological material, including an electrical conductivity that can exceed 100 S cm ⁻¹. Traditionally, long-range electron transport through proteins is described as a multi-step hopping process, in which the individual hopping steps are described by Marcus electron transport theory. Here, we investigate to what extent such a classical hopping model can explain the conductance data recorded for individual cable bacterium filaments. To this end, the conductive fiber network in cable bacteria is modelled as a set of parallel one-dimensional hopping chains. Comparison of model simulated and experimental current(I)/voltage(V) curves, reveals that the charge transport is field-driven rather than concentration-driven, and there is no significant injection barrier between electrodes and filaments. However, the observed high conductivity levels (>100 S cm ⁻¹) can only be reproduced, if we include much longer hopping distances (a > 10 nm) and lower reorganisation energies (λ < 0.2 eV) than conventionally used in electron relay models of protein structures. Overall, our model analysis suggests that the conduction mechanism in cable bacteria is markedly distinct from other known forms of long-range biological electron transport, such as in multi-heme cytochromes.

Superconductors are materials with zero electrical resistivity and the ability to expel magnetic fields, which is known as the Meissner effect. Their dissipationless diamagnetic response is central to magnetic levitation and circuits such as quantum interference devices. In this work, we used superconducting diamagnetism to shape the magnetic environment governing the transport of spin waves-collective spin excitations in magnets that are promising on-chip signal carriers-in a thin-film magnet. Using diamond-based magnetic imaging, we observed hybridized spin-wave-Meissner-current transport modes with strongly altered, temperature-tunable wavelengths and then demonstrated local control of spin-wave refraction using a focused laser. Our results demonstrate the versatility of superconductor-manipulated spin-wave transport and have potential applications in spin-wave gratings, filters, crystals, and cavities.

We theoretically predict and experimentally observe the onset of weak-link physics in the dynamical response of transition-edge sensors (TESs). We develop a theoretical framework based on a Fokker-Planck description that incorporates both the TESs electrical response, stemming from Josephson phenomena, and the electrothermal effects due to coupling to a thermal bath. Our measurements of a varying dynamic resistance are in excellent agreement with our theory, thereby establishing weak-link phenomena as the main mechanism underlying the operation of TESs. Furthermore, our description enables the calculation of power spectral densities, paving the way for a more thorough investigation of the unexplained "excess noise"in long diffusive junctions and TESs reported in recent experiments.

Quantum sensing has developed into a main branch of quantum science and technology. It aims at measuring physical quantities with high resolution, sensitivity, and dynamic range. Electron spins in diamond are powerful magnetic field sensors, but their sensitivity in the microwave regime is limited to a narrow band around their resonance frequency. Here, we realize broadband microwave detection using spins in diamond interfaced with a thin-film magnet. A pump field locally converts target microwave signals to the sensor-spin frequency via the non-linear spin-wave dynamics of the magnet. Two complementary conversion protocols enable sensing and high-fidelity spin control over a gigahertz bandwidth, allowing characterization of the spin-wave band at multiple gigahertz above the sensor-spin frequency. The pump-tunable, hybrid diamond-magnet sensor chip opens the way for spin-based gigahertz material characterizations at small magnetic bias fields.

Optical photons are ideal carriers for long-distance transmission, while state-of-the-art quantum processors, such as supercon-ducting qubits, operate at microwave frequencies. An important requirement for networked quantum computation is therefore the ability to coherently convert the quantum information from microwave to optical frequencies and vice-versa. We theoretically address a scheme to achieve this via an intermediate conversion to magnons that enhances the weak direct magneto-optical coupling. We wish to demonstrate the feasibility of such a scheme by employing the magnetoelastic coupling between the modes of a magnetic vortex (vortex breathing mode, VBM) and that of the lattice (elastic breathing mode, EBM), which requires no additional external bias field. In our setup all but the opto-mechanical coupling can be made resonant. We propose an alternative Mumax3 simulation post-processing procedure for semi-classical normalization, where we use regression analysis of the the internal energy dependency on excitation amplitude in a limit cycle motion. We provide estimates for direct resonant coupling between the VBM and the EBM.

The temperature dependent order parameter provides important information on the nature of magnetism. Using traditional methods to study this parameter in two-dimensional (2D) magnets remains difficult, however, particularly for insulating antiferromagnetic (AF) compounds. Here, we show that its temperature dependence in AF MPS₃ (M(II) = Fe, Co, Ni) can be probed via the anisotropy in the resonance frequency of rectangular membranes, mediated by a combination of anisotropic magnetostriction and spontaneous staggered magnetization. Density functional calculations followed by a derived orbital-resolved magnetic exchange analysis confirm and unravel the microscopic origin of this magnetization-induced anisotropic strain. We further show that the temperature and thickness dependent order parameter allows to deduce the material’s critical exponents characterising magnetic order. Nanomechanical sensing of magnetic order thus provides a future platform to investigate 2D magnetism down to the single-layer limit.

We propose a scheme for generating and controlling entangled coherent states (ECSs) of magnons, i.e., the quanta of the collective spin excitations in magnetic systems, or phonons in mechanical resonators. The proposed hybrid circuit architecture comprises a superconducting transmon qubit coupled to a pair of magnonic yttrium iron garnet spherical resonators or mechanical beam resonators via flux-mediated interactions. Specifically, the coupling results from the magnetic/mechanical quantum fluctuations modulating the qubit inductor, formed by a superconducting quantum interference device. We show that the resulting radiation-pressure interaction of the qubit with each mode can be employed to generate maximally entangled states of magnons or phonons. In addition, we numerically demonstrate a protocol for the preparation of magnonic and mechanical Bell states with high fidelity including realistic dissipation mechanisms. Furthermore, we have devised a scheme for reading out the prepared states using standard qubit control and resonator field displacements. In this paper, we demonstrate an alternative platform for quantum information using ECSs in hybrid magnonic and mechanical quantum networks.

The temperature dependent order parameter provides important information on the nature of magnetism. Using traditional methods to study this parameter in two-dimensional (2D) magnets remains difficult, however, particularly for insulating antiferromagnetic (AF) compounds. We show that its temperature dependence in AF MPS3 (M(II) = Fe, Co, Ni) can be probed via the anisotropy in the resonance frequency of rectangular membranes, mediated by a combination of anisotropic magnetostriction and spontaneous staggered magnetization. Density functional calculations followed by a derived orbital-resolved magnetic exchange analysis confirm and unravel the microscopic origin of this magnetization inducing anistropic strain. We further show that the temperature and thickness dependent order parameter allows to deduce the material's critical exponents characterising magnetic order. Nanomechanical sensing of magnetic order thus provides a future platform to investigate 2D magnetism down to the single-layer limit.

Magnetostrictive coupling has recently attracted interest as a sensitive method for studying magnetism in two-dimensional (2D) materials by mechanical means. However, its application in high-frequency magnetic actuators and transducers requires rapid modulation of the magnetic order, which is difficult to achieve with external magnets, especially when dealing with antiferromagnets. Here, we optothermally modulate the magnetization in antiferromagnetic 2D material membranes of metal phosphor trisulfides (MPS₃), to induce a large high-frequency magnetostrictive driving force. From the analysis of the temperature-dependent resonance amplitude, we provide evidence that the force is due to a thermo-magnetostrictive effect, which significantly increases near the Neél temperature, due to the strong temperature dependence of the magnetization. By studying its angle dependence, we find the effect is observed to follow anisotropic magnetostriction of the crystal lattice. The results show that the thermo-magnetostrictive effect results in a strongly enhanced thermal expansion force near the critical temperature of magnetostrictive 2D materials, which can enable more efficient actuation of nano-magnetomechanical devices and can also provide a route for studying the high-frequency coupling among magnetic, mechanical, and thermodynamic degrees of freedom down to the 2D limit.

We discuss spin-wave transport in anisotropic ferromagnets with an emphasis on the zeros of the band edges as a function of a magnetic field. An associated divergence of the magnon spin should be observable by enhanced magnon conductivities in nonlocal configurations, especially in two-dimensional ferromagnets.

Magnonics addresses the physical properties of spin waves and utilizes them for data processing. Scalability down to atomic dimensions, operation in the GHz-to-THz frequency range, utilization of nonlinear and nonreciprocal phenomena, and compatibility with CMOS are just a few of many advantages offered by magnons. Although magnonics is still primarily positioned in the academic domain, the scientific and technological challenges of the field are being extensively investigated, and many proof-of-concept prototypes have already been realized in laboratories. This roadmap is a product of the collective work of many authors, which covers versatile spin-wave computing approaches, conceptual building blocks, and underlying physical phenomena. In particular, the roadmap discusses the computation operations with the Boolean digital data, unconventional approaches, such as neuromorphic computing, and the progress toward magnon-based quantum computing. This article is organized as a collection of sub-sections grouped into seven large thematic sections. Each sub-section is prepared by one or a group of authors and concludes with a brief description of current challenges and the outlook of further development for each research direction.

We propose to directly and quantum-coherently couple a superconducting transmon qubit to magnons - the quanta of the collective spin excitations, in a nearby magnetic particle. The magnet's stray field couples to the qubit via a superconducting quantum interference device. We predict a resonant magnon-qubit exchange and a nonlinear radiation-pressure interaction that are both stronger than dissipation rates and tunable by an external flux bias. We additionally demonstrate a quantum control scheme that generates magnon-qubit entanglement and magnonic Schrödinger cat states with high fidelity.

Atomically engineered artificial lattices are a useful tool for simulating complex quantum phenomena, but have so far been limited to the study of Hamiltonians where electron-electron interactions do not play a role. However, it is precisely the regime in which these interactions do matter where computational times lend simulations a critical advantage over numerical methods. Here, we propose a platform for constructing artificial matter that relies on the confinement of field-emission resonances, a class of vacuum-localized discretized electronic states. We use atom manipulation of surface vacancies in a chlorine-terminated Cu(100) surface to reveal square patches of the underlying metal, thereby creating atomically precise potential wells that host particle-in-a-box modes. By adjusting the dimensions of the confining potential, we can access states with different quantum numbers, making these patches attractive candidates as quantum dots or artificial atoms. We demonstrate that the lifetime of electrons in these engineered states can be extended and tuned through modification of the confining potential, either via atomic assembly or by changing the tip-sample distance. We also demonstrate control over a finite range of state filling, a parameter which plays a key role in the evolution of quantum many-body states. We model the transport through the localized state to disentangle and quantify the lifetime-limiting processes, illustrating the critical dependence of the electron lifetime on the properties of the underlying bulk band structure. The interplay with the bulk bands gives rise to negative differential resistance, leading to possible applications in engineering custom atomic-scale resonant tunnelling diodes, which exhibit similar current-voltage characteristics.

Cavity magnonics deals with the interaction of magnons — elementary excitations in magnetic materials — and confined electromagnetic fields. We introduce the basic physics and review the experimental and theoretical progress of this young field that is gearing up for integration in future quantum technologies. Much of its appeal is derived from the strong magnon–photon coupling and the easily-reached nonlinear regime in microwave cavities. The interaction of magnons with light as detected by Brillouin light scattering is enhanced in magnetic optical resonators, which can be employed to cool and heat magnons. The microwave cavity photon-mediated coupling of a magnon mode to a superconducting qubit enables measurements in the single magnon limit.

Compared to monolayer graphene, electrons in Bernal-stacked bilayer graphene (BLG) have an additional layer degree of freedom, offering a platform for developing layered spintronics with the help of proximity-induced magnetism. Based on an effective phenomenological model, we systematically study the effect of this magnetism on the spin-dependent band structure near the Fermi energy and identify the magnetic phases induced in BLG by proximity with magnets. We show that spin polarization can develop in BLG due to this proximity effect. This spin polarization depends strongly on the layer distribution of magnetism, and can always be controlled by gate voltage which shifts spin-dependent band edges and modifies the total band gap. We further show that the band spin polarization can be modified by the proximity-induced staggered sublattice potential. By taking full advantage of layer-dependent magnetism in BLG, we propose that spintronic devices such as a spin filter, a giant magnetoresistance device, and a spin diode can operate under fully electric control, which is easier than the common magnetic field control.

We propose a spin valve that is based on van der Waals antiferromagnetism and is fully electrically controlled. The device is composed of two antiferromagnetic terminals that allow for vertical bias control and a linked central scattering potential region. The magnetoresistance varies significantly when the bias orientations in two terminals are switched from parallel to antiparallel, because this switch induces a mismatch of the bands for the same spin projection in different parts of the system. It is shown from density-functional calculations that bilayer graphene encapsulated by two atomic layers of Cr2Ge2Te6 provides a material platform to realize the antiferromagnetism, which is robust against the required vertical electric fields.