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Physical review. B./Physical review. B

Quantum tomography of magnons using Brillouin light scattering

Sanchar Sharma, Silvia Viola Kusminskiy, Victor A. S. V. Bittencourt

Published Jul 11, 2024• 10 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.110.014416

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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.
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.
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.
Optomagnonic modulation techniques are an emerging platform for information transfer from the microwave to the optical domain. However, these techniques focus largely on the spectral domain of the transduced signal. Given the potential of the field to bridge the gap between microwave and optical signals, analyzing and studying the interactions real-time in temporal domain becomes equally essential. In this work, we exploit the optomagnonic modulation in a YIG microsphere to demonstrate and study microwave to optical real-time dynamic transfer on a time scale comparable to the decay of magnons. We inductively excite magnons in the microwave domain and use magnon-based Brillouin light scattering to transduce the signature of excited magnonic waveforms to the optical domain. The square type modulation of the magnons is retrieved in the corresponding optical sidebands. Our work enables real-time measurement of the magnonic dynamics and therefore direct access to lifetime measurements of the magnonic mode. Providing insight into the temporal dynamics of magnons, this work can open up new promising research directions such as in magnon coupled superconducting qubits or magnon-based Brillouin memory.
Brillouin microscopy is an emerging label-free imaging technique used to assess local viscoelastic properties. Quantum-enhanced stimulated Brillouin scattering is demonstrated using low power continuous-wave lasers at 795 nm. A signal-to-noise ratio enhancement of 3.4 dB is reported by using two-mode intensity-difference squeezed light generated with the four-wave mixing process in atomic rubidium vapor. The low optical power and the excitation wavelengths in the water transparency window have the potential to provide a powerful bio-imaging technique for probing mechanical properties of biological samples prone to phototoxicity and thermal effects. The performance enhancement affordable through the use of quantum light may pave the way for significantly improved sensitivity that cannot be achieved classically. The proposed method for utilizing squeezed light for enhanced stimulated Brillouin scattering can be easily adapted for both spectroscopic and imaging applications in biology.
Cavity optomagnonics has received considerable research interest in recent years, due to the coherent magnetic Brillioun light scattering in the ferromagnetic material. Here, we theoretically propose and numerically verify a feasible scheme for the full polarization tomography on photon statistics in an optomagnonic whispering-gallery-mode microresonator system in the weak-coupling regime. By performing the polarization pre- and post-selections to manipulate the polarization states of the input and output photons, we find that the rich sub- and super-Poissonian photon statistics can be selectively generated, thanks to quantum interferences. In the parameter space of phase delay, the evolution from photon bunching to antibunching indicates the change from phase to amplitude squeezing. Our obtained result has potential applications in tunable quantum polarized light sources based on the cavity optomagnonic platform in micro-nano scale. It also offers a deeper understanding for full quantum cavity optomagnonics.
We propose a feasible experimental model to investigate the generation and characterization of nonclassical states in a cavity optomagnonic system consisting of a ferromagnetic YIG sphere that simultaneously supports both the magnon mode and two whispering gallery modes of optical photons. The photons undergo the magnon-induced Brillouin light scattering, which is a well-established tool for the cavity-assisted manipulations of magnons as well as magnon spintronics. At first, we derive the desired interaction Hamiltonian under the influence of the anti-Stokes scattering process and then proceed to analyze the dynamical evolution of quantum statistics of photons and magnons as well as their intermodal entanglement. The results show that both photons and magnons generally acquire some nonclassical features, e.g., the strong antibunching and anti-correlation. Interestingly, the system may experience the perfect photon and magnon blockade phenomena, simultaneously. Besides, the nonclassical features may be protected against the unwanted environmental effects for a relatively long time, especially, in the weak driving field regime and when the system is initiated with a small number of particles. However, it should be noted that some fast quantum-classical transitions may occur in-between. Although the unwanted dissipative effects plague the nonclassical features, we show that this system can be adopted to prepare optomagnonic entangled states. The generation of entangled states depends on the initial state of the system and the interaction regime. The intermodal photon-magnon entanglement may be generated and pronounced, especially, if the system is initialized with low intensity even Schrödinger cat state in the strong coupling regime. The cavity-assisted manipulation of magnons is a unique and flexible mechanism that allows an interesting test bed for investigating the interdisciplinary contexts involving quantum optics and spintronics. Moreover, such a hybrid optomagnonic system may be used to design both on-demand single-photon and single-magnon sources and may find potential applications in quantum information processing.