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Magnonics is a field of science that addresses the physical properties of spin waves and utilizes them for data processing. Scalability down to atomic dimensions, operations 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 that covers versatile spin-wave computing approaches, conceptual building blocks, and underlying physical phenomena. In particular, the roadmap discusses the computation operations with Boolean digital data, unconventional approaches like neuromorphic computing, and the progress towards magnon-based quantum computing. The 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 the current challenges and the outlook of the further development of the research directions., Comment: 74 pages, 57 figures, 500 references

Brillouin light scattering in ferromagnetic materials usually involves one magnon and two photons and their total angular momentum is conserved. Here, we experimentally demonstrate the presence of a helicity-changing two-magnon Brillouin light scattering in a ferromagetic crystal, which can be viewed as a four-wave mixing process involving two magnons and two photons. Moreover, we observe an unconventional helicity-changing one-magnon Brillouin light scattering, which apparently infringes the conservation law of the angular momentum. We show that the crystal angular momentum intervenes to compensate the missing angular momentum in the latter scattering process., Comment: 14 pages, 6 figures

Magnetostatic modes supported by a ferromagnetic sphere have been known as the Walker modes, each of which possesses an orbital angular momentum as well as a spin angular momentum along a static magnetic field. The Walker modes with non-zero orbital angular momenta exhibit topologically non-trivial spin textures, which we call \textit{magnetic quasi-vortices}. Photons in optical whispering gallery modes supported by a dielectric sphere possess orbital and spin angular momenta forming \textit{optical vortices}. Within a ferromagnetic, as well as dielectric, sphere, two forms of vortices interact in the process of Brillouin light scattering. We argue that in the scattering there is a selection rule that dictates the exchange of orbital angular momenta between the vortices. The selection rule is shown to be responsible for the experimentally observed nonreciprocal Brillouin light scattering., Comment: 7 pages, 4 figures

A ferromagnetic sphere can support \textit{optical vortices} in forms of whispering gallery modes and \textit{magnetic quasi-vortices} in forms of magnetostatic modes with non-trivial spin textures. These vortices can be characterized by their orbital angular momenta. We experimentally investigate Brillouin scattering of photons in the whispering gallery modes by magnons in the magnetostatic modes, zeroing in on the exchange of the orbital angular momenta between the optical vortices and the magnetic quasi-vortices. We find that the conservation of the orbital angular momentum results in different nonreciprocal behaviors in the Brillouin light scattering. New avenues for chiral optics and opto-spintronics can be opened up by taking the orbital angular momenta as a new degree of freedom for cavity optomagnonics., Comment: 5 pages, 4 figures (1 supplemental figure)

A superconducting qubit in the strong dispersive regime of a circuit quantum electrodynamics system is a powerful probe for microwave photons in a cavity mode. In this regime, a qubit spectrum is split into multiple peaks, with each peak corresponding to an individual photon number in the cavity (discrete ac Stark shift). Here, we measure the qubit spectrum in the cavity that is driven continuously with a squeezed vacuum field generated by a Josephson parametric amplifier. By fitting the qubit spectrum with a model which takes into account the finite qubit excitation power, the photon number distribution, which is dissimilar from the apparent peak area ratio in the spectrum, is determined. The photon number distribution shows the even-odd photon number oscillation and quantitatively fulfills Klyshko's criterion for the nonclassicality., Comment: 10 pages, 11 figures, 1 table

We experimentally implement a system of cavity optomagnonics, where a sphere of ferromagnetic material supports whispering gallery modes (WGMs) for photons and the magnetostatic mode for magnons. We observe pronounced nonreciprocity and asymmetry in the sideband signals generated by the magnon-induced Brillouin scattering of light. The spin-orbit coupled nature of the WGM photons, their geometric birefringence and the time-reversal symmetry breaking in the magnon dynamics impose the angular-momentum selection rules in the scattering process and account for the observed phenomena. The unique features of the system may find interesting applications at the crossroad between quantum optics and spintronics., Comment: 5 pages (4 figures) + supplemental material, accepted by PRL

Low-loss transmission and sensitive recovery of weak radio-frequency (rf) and microwave signals is an ubiquitous technological challenge, crucial in fields as diverse as radio astronomy, medical imaging, navigation and communication, including those of quantum states. Efficient upconversion of rf-signals to an optical carrier would allow transmitting them via optical fibers dramatically reducing losses, and give access to the mature toolbox of quantum optical techniques, routinely enabling quantum-limited signal detection. Research in the field of cavity optomechanics has shown that nanomechanical oscillators can couple very strongly to either microwave or optical fields. An oscillator accommodating both functionalities would bear great promise as the intermediate platform in a radio-to-optical transduction cascade. Here, we demonstrate such an opto-electro-mechanical transducer utilizing a high-Q nanomembrane. A moderate voltage bias (<10V) is sufficient to induce strong coupling between the voltage fluctuations in a rf resonance circuit and the membrane's displacement, which is simultaneously coupled to light reflected off its metallized surface. The circuit acts as an antenna; the voltage signals it induces are detected as an optical phase shift with quantum-limited sensitivity. The half-wave voltage is in the microvolt range, orders of magnitude below that of standard optical modulators. The noise added by the membrane is suppressed by the electro-mechanical cooperativity C~6800 and has a temperature of 40mK, far below 300K where the entire device is operated. This corresponds to a sensitivity limit as low as 5 pV/Hz^1/2, or -210dBm/Hz in a narrow band around 1 MHz. Our work introduces an entirely new approach to all-optical, ultralow-noise detection of classical electronic signals, and sets the stage for coherent upconversion of low-frequency quantum signals to the optical domain., Comment: 19 pages, 10 figures, TeX issue fixed

Optical cavity cooling of mechanical resonators has recently become a research frontier. The cooling has been realized with a metal-coated silicon microlever via photo-thermal force and subsequently with dielectric objects via radiation pressure. Here we report cavity cooling with a crystalline semiconductor membrane via a new mechanism, in which the cooling force arises from the interaction between the photo-induced electron-hole pairs and the mechanical modes through the deformation potential coupling. The optoelectronic mechanism is so efficient as to cool a mode down to 4 K from room temperature with just 50 uW of light and a cavity with a finesse of 10 consisting of a standard mirror and the sub-wavelength-thick semiconductor membrane itself. The laser-cooled narrow-band phonon bath realized with semiconductor mechanical resonators may open up a new avenue for photonics and spintronics devices., Comment: 5 pages, 4 figures

We report the generation of polarization-entangled photons by femtosecond-pulse-pumped spontaneous parametric down-conversion in a cascade of two type-I crystals. Highly entangled pulsed states were obtained by introducing a temporal delay between the two orthogonal polarization components of the pump field. They exhibited high-visibility quantum interference and a large concurrence value, without the need of post-selection using narrow-bandwidth-spectral filters. The results are well explained by the theory which incorporates the space-time dependence of interfering two-photon amplitudes if dispersion and birefringence in the crystals are appropriately taken into account. Such a pulsed entangled photon well localized in time domain is useful for various quantum communication experiments, such as quantum cryptography and quantum teleportation., Comment: 12 pages, 11 figures, REVTEX

We experimentally demonstrate that entanglement of bi-photon polarization state can be restored by spectral filters. This restoration procedure can be viewed as a new class of quantum eraser, which retrieves entanglement rather than just interference by manipulating an ancillary degree of freedom., Comment: 4 pages, 4 figures