Quantum measurements of magnons are crucial for the development of quantum applications based on magnonics. We theoretically analyze the efficacy of Brillouin light scattering (BLS) for quantum tomography of magnons. We consider a finite-length optomagnonic waveguide made of Yttrium Iron Garnet (YIG), and derive the relation between the transmitted photons and the state of the magnons. While the signal-to-noise ratio (SNR) is low due to a small magneto-optical coupling, we show that significant improvement can be achieved by injecting squeezed vacuum of photons. Then, we discuss a protocol of reconstructing the magnon’s density matrix based on the observed statistics of the transmitted photons, using maximum likelihood principle. We find that the classical component of a magnon state, defined as the regions of positive Wigner function, can be reconstructed with a high accuracy. Reconstructing the nonclassical component requires improved SNR or larger datasets, and we explore potential methods to achieve these goals.
Quantum measurements of magnons are crucial for the development of quantum applications based on magnonics. We theoretically analyze the efficacy of Brillouin light scattering (BLS) for quantum tomography of magnons. We consider a finite-length optomagnonic waveguide made of Yttrium Iron Garnet (YIG), and derive the relation between the transmitted photons and the state of the magnons. While the signal-to-noise ratio (SNR) is low due to a small magneto-optical coupling, we show that significant improvement can be achieved by injecting squeezed vacuum of photons. Then, we discuss a protocol of reconstructing the magnon’s density matrix based on the observed statistics of the transmitted photons, using maximum likelihood principle. We find that the classical component of a magnon state, defined as the regions of positive Wigner function, can be reconstructed with a high accuracy. Reconstructing the nonclassical component requires improved SNR or larger datasets, and we explore potential methods to achieve these goals.
Quantum magnonics, an emerging field focusing on the study of magnons for quantum applications, requires precise measurement methods capable of resolving single magnons. Existing techniques introduce additional dissipation channels and are not apt for magnets in free space. Brillouin light scattering (BLS) is a well-established technique for probing the magnetization known for its high sensitivity and temporal resolution. The coupling between magnons and photons is controlled by a laser input, so it can be switched off when a measurement is not needed. In this article, we theoretically investigate the efficacy of BLS for quantum tomography of magnons. We model a finite optomagnonic waveguide, including the optical noise added by the dielectric, to calculate the signal-to-noise ratio (SNR). We find that the SNR is typically low due to a small magneto-optical coupling; nevertheless, it can be significantly enhanced by injecting squeezed vacuum into the waveguide. We reconstruct the density matrix of the magnons from the statistics of the output photons using a maximum likelihood estimate. The classical component of a magnon state, defined as the regions of positive Wigner function, can be reconstructed with a high accuracy while the non-classical component necessitates either a higher SNR or a larger dataset. The latter requires more compact data structures and advanced algorithms for post-processing. The SNR is limited partially by the input laser power that can be increased by designing the optomagnonic cavity with a heat sink.
Squeezed states, crucial for quantum metrology and emerging quantum technologies, have been demonstrated in various platforms, but quantum squeezing of magnons in macroscopic spin systems remains elusive. Here we report the experimental observation of quantum-level magnon squeezing in a millimeter-scale yttrium iron garnet (YIG) sphere. By engineering a strong dispersive magnon-superconducting qubit coupling via a microwave cavity, we implement a significant self-Kerr nonlinearity to generate squeezed magnon states with their mean magnon number less than one. Harnessing a magnon-assisted Raman process, we perform Wigner tomography, revealing quadrature variances of ∼0.8 (∼1.0~dB squeezing) relative to the vacuum. These results lay the groundwork for quantum nonlinear magnonics and promise potential applications in quantum metrology.
Quantum magnonics, an emerging field focusing on the study of magnons for quantum applications, requires precise measurement methods capable of resolving single magnons. Existing techniques introduce additional dissipation channels and are not apt for magnets in free space. Brillouin light scattering (BLS) is a well-established technique for probing the magnetization known for its high sensitivity and temporal resolution. The coupling between magnons and photons is controlled by a laser input, so it can be switched off when a measurement is not needed. In this article, we theoretically investigate the efficacy of BLS for quantum tomography of magnons. We model a finite optomagnonic waveguide, including the optical noise added by the dielectric, to calculate the signal-to-noise ratio (SNR). We find that the SNR is typically low due to a small magneto-optical coupling; nevertheless, it can be significantly enhanced by injecting a squeezed vacuum into the waveguide. We reconstruct the density matrix of the magnons from the statistics of the output photons using a maximum likelihood estimate. The classical component of a magnon state, defined as the regions of positive Wigner function, can be reconstructed with a high accuracy while the nonclassical component necessitates either a higher SNR or a larger data set. The latter requires more compact data structures and advanced algorithms for postprocessing. The SNR is limited partially by the input laser power that can be increased by designing the optomagnonic cavity with a heat sink.
Hybrid systems based on magnons in ferromagnetic materials, such as yttrium iron garnet, have achieved remarkable development in the last decade. These include the coupling of magnons to microwave and optical photons, superconducting qubits, phonons, spins, the center-of-mass motion of a ferromagnet, etc. Here, we review both the experimental and theoretical progress in this field, focusing on the generation of magnonic quantum states and their applications in a broad range of fields. Since the strong coupling is a prerequisite for achieving coherent quantum control of magnons and preparing magnonic quantum states, we start by introducing representative strong-coupling experiments in cavity magnonics, then review a series of protocols for creating various magnonic quantum states, such as Fock, cat, squeezed, and entangled states, and discuss their potential applications in macroscopic quantum studies, quantum information science, quantum sensing, magnonic quantum devices, dark matter detection, and so on. Finally, we summarize the review and give an outlook for the future study of quantum magnonics.
Quantum magnonics based on yttrium iron garnet (YIG) spheres provides a new arena for observing macroscopic quantum states. Here, we propose to prepare two kinds of non-Gaussian magnonic states by adding a single magnon to two Gaussian states, namely, coherent and thermal states. We adopt an optomagnonic system of a YIG sphere and use fast optical pulses to weakly activate the magnon-induced Stokes scattering. Conditioned on the detection of a polarized single photon, a single magnon can be added to an initial Gaussian state. We use a microwave cavity to prepare an initial magnon coherent state and finally read out the generated single-magnon added coherent or thermal state. Both the non-Gaussian states of a magnon mode in a large YIG sphere are macroscopic quantum states, which exhibit many nonclassical properties, such as sub-Poissonian statistics, quadrature squeezing, and a negative Wigner function. Further, both states show a smooth transition from a quantum state to a classical state with the change of the coherent or thermal magnon excitations and thus can be used for the fundamental study of the quantum-to-classical transition.
Recent studies show that hybrid quantum systems based on magnonics provide a new and promising platform for generating macroscopic quantum states involving a large number of spins. Here, we show how to entangle two magnon modes in two massive yttrium-iron-garnet (YIG) spheres using cavity optomagnonics, where magnons couple to high-quality optical whispering gallery modes supported by the YIG sphere. The spheres can be as large as 1 mm in diameter and each sphere contains more than 1018 spins. The proposal is based on the asymmetry of the Stokes and anti-Stokes sidebands generated by the magnon-induced Brillouin light scattering in cavity optomagnonics. This allows one to utilize the Stokes and anti-Stokes scattering process, respectively, for generating and verifying the entanglement. Our work indicates that cavity optomagnonics could be a promising system for preparing macroscopic quantum states.