Heisenberg-limited metrology from the quantum-quench dynamics of an anisotropic ferromagnet

Abstract

The emerging field of quantum magnonics seeks to understand and harness the quantum properties of magnons -- quantized collective spin excitations in magnets. Squeezed magnon states arise naturally as the equilibrium ground states of anisotropic ferromagnets and antiferromagnets, representing an important class of nonclassical magnon states. In this work, we show how a qubit-conditioned quantum quench of an anisotropic ferromagnet can be used for Heisenberg-limited parameter estimation based on measurements of the qubit only. In the presence of ground-state squeezing, the protocol yields information about the eigenmode frequency of the coupled magnon-qubit system, whereas no information is gained in the absence of such squeezing. The protocol therefore leverages genuine quantum correlations in the form of magnonic squeezing while simultaneously relying on the equilibrium character of this squeezing -- a feature distinctive to magnetic systems.

Figures (3)

• Figure 1: Schematic of a spin qubit coupled to the Kittel mode of an anisotropic ferromagnet. The ground state of the Kittel mode is a squeezed state whose reduced quantum fluctuations along one quadrature can be harnessed through the qubit for Heisenberg-limited parameter estimation.
• Figure 2: Protocol expressed as a circuit. The magnon mode is allowed to equilibrate while in contact with the qubit held in $\ket{\downarrow}$. The squeezed magnons used for parameter estimation are produced by subjecting the magnon system to a quantum quench conditioned on the state of the qubit being $\ket{\uparrow}$. The quench is triggered by applying a Hadamard gate (denoted H) to the qubit, which, after undergoing free evolution while in contact with the magnon mode, is then measured in the X basis.
• Figure 3: (a) Fisher information $F_{\mathrm{C}}(\phi)$ evaluated using Eqs. \ref{['probability-qubit-measurement']} and \ref{['fisher-information-definition']} for $r=0.75$ (dark blue) and $r=1$ (light blue). As described in the text, the duration $T$ of the free-evolution window should be chosen so that $\phi=\omega_\uparrow T$ is approximately equal to $m\pi$. The free-evolution time $T$ could be tweaked adaptively using the tunability of the squeezing parameter as a function of the applied magnetic field. (b) Probability $p(+\vert\phi=\omega_\uparrow t)=(1/2)(1+\langle \sigma_x\rangle_t)$ of measuring the qubit in the state $\ket{+}$ given a value of $\phi$. In the absence of ground-state squeezing ($\Omega=0$, corresponding to $r_\uparrow=r_\downarrow=r=0$), the probability is $p(+\vert \phi)=1$ independent of $\phi$, and the Fisher information associated with the measurement is zero. Left inset: Squeezing parameter $r$ as a function of the applied magnetic field $h$ for $(2SK_z-SK_y)/2\pi=7$ GHz and $\Omega/2\pi=\chi/2\pi=0.5$ GHz. A field of 180 mT corresponds to a Zeeman splitting of 5.04 GHz (assuming a g-factor of 2). Right inset: The same range of squeezing parameters could be achieved with the same value of $\Omega/2\pi = 0.5$ GHz, $(2SK_z-SK_y)/2\pi=2$ GHz, and a considerably smaller dispersive coupling of $\chi/2\pi = 5$ MHz you2025quantum.