Quantum State Preparation of Ferromagnetic Magnons by Parametric Driving

Abstract

We propose a method to prepare and certify Gaussian quantum states of the ferromagnetic resonance spin-wave modes in ferromagnets using a longitudinal drive. Contrary to quantum optics-based strategies, our approach harnesses a purely magnonic feature - the spin-wave nonlinearity - to generate magnon squeezing. This resource is used to prepare vacuum-squeezed states, as well as entangled states between modes of different magnets coupled via a microwave cavity. We propose methods to detect such states with classical methods, such as ferromagnetic resonance or local pickup coils, and quantify the required detection efficiency. We analytically solve the case of ellipsoidal yttrium iron garnet ferrimagnets, but our method applies to a vast range of shapes and sizes. Our work enables quantum magnonics experiments without single-magnon sources or detectors (qubits), thus bringing the quantum regime within reach of the wider magnonics community.

Figures (3)

• Figure 1: (a) The ferromagnetic resonance (FMR) mode of a ferromagnetic ellipsoid saturated by an homogeneous magnetic field $B_0$ along a short axis can be prepared in a vacuum-squeezed state by a parametric drive applied along the same axis. (b-d) FMR mode Wigner function at $T<400~\text{mK}$. In the absence of parametric drive the magnetization vacuum fluctuations are anisotropic (b) but the state is isotropic in quadrature representation (c), thus showing no quantum squeezing. Under parametric drive with frequency $\omega_\text{d} \approx 2\omega_\text{m}$ the state becomes squeezed, as fluctuations of certain quadratures decrease below the ground-state value (d). Black lines in (b-d) show the Wigner function at half maximum.
• Figure 2: (a) Squeezing measure, Eq. \ref{['eq:R']}, versus parametric drive strength for various detunings $\Delta_\text{m}$ and $\phi=0$. Hatched area marks parametric instability. Inset: parametric instability threshold amplitude $B_\text{d}$ versus ellipsoid aspect ratio. (b) Vacuum squeezing can be detected by microwave reflection. (c) Reflectivity spectrum for $\Delta_\text{m}/2\pi = 2~\text{MHz}$ and different degrees of squeezing (dashed line corresponds to no squeezing). In this and other figures we take the following parameters for YIG: $\gamma = -1.76 \times 10^{11}~\text{T}^{-1}\text{s}^{-1}$, $M_\text{S} = 5870~\text{kA}/\text{m}$, $\gamma_\text{m}/2\pi = 0.4~\text{MHz}$, $B_0 = 0.4~\text{T}$, and $\lambda=2$.
• Figure 3: (a) Scheme for preparing entangled magnon states and detecting them using pickup coils. (b) Steady-state entanglement versus magnon-cavity coupling rate $g_{\rm mc}$ and drive detuning from the instability threshold $\delta$, for $\Delta_\text{m}/2\pi = 2~\text{MHz}$, $\Delta_\text{c} = \Delta_\text{m} + 10 g_\text{mc}$ and $\kappa = 10^{-4}\omega_\text{c}$. Hatched areas indicate collective instability regions. (c) Measured entanglement for $\delta/2\pi = 1.5~\text{MHz}$ and for different coil detection efficiencies. Dashed curves show the analytic approximation Eq. \ref{['eq:nu_eta']}.