Squeezing and quantum control of antiferromagnetic magnon pseudospin

TL;DR

This work develops a quantum theory of the antiferromagnetic magnon pseudospin, showing that spin-non-conserving interactions induce equilibrium magnon squeezing and a controllable pseudospin via a rotating-squeezing framework beyond the rotating wave approximation. By deriving a NiO-based Hamiltonian and performing Bogoliubov and pseudospin rotations, the authors obtain squeezed eigenmodes and quantify ground-state fluctuations through a pseudospin squeezing parameter, with explicit results for how $D_r$ and $D_s$ drive squeezing and mode hybridization. They demonstrate enhanced and tunable coupling to itinerant electrons through pseudospin squeezing, and reveal ground-state quantum superpositions that can be probed by qubit spectroscopy through dispersive AFM–qubit coupling, including concrete small-$
chi$ and small-$D_r$ limits. The formalism also extends to hematite and other bosonic pseudospin systems, where adjusted couplings $ ilde{D}_r$ and $ ilde{D}_s$ preserve the squeezing mechanism, highlighting quantum fluctuations engineering of a general bosonic pseudospin with potential applications in quantum information and spintronics.

Abstract

Antiferromagnets have been shown to harbor strong magnon squeezing in equilibrium, making them a potential resource for quantum correlations and entanglement. Recent experiments have also found them to host coherently coupled magnonic excitations forming a magnon pseudospin, in analogy to electronic spin. Here, we delineate the quantum properties of antiferromagnetic magnon pseudospin by accounting for spin non-conserving interactions and going beyond the rotating wave approximation. Employing concrete examples of nickel oxide and hematite, we find strong squeezing of the magnon pseudospin highlighting its important role in determining the eigenmode quantum properties. Via ground state quantum fluctuations engineering, this pseudospin squeezing enables an enhancement and control of coupling between the magnonic modes and other excitations. Finally, we evaluate the quantum superpositions that comprise a squeezed pseudospin ground state and delineate a qubit spectroscopy protocol to detect them. Our results are applicable to any system of coupled bosons and thus introduce quantum fluctuations engineering of a general bosonic pseudospin.

Figures (7)

• Figure 1: Representation of the eigenmodes $\hat{\psi}_\pm^\dagger$ on a unit sphere with uncertainty area of the non-commuting pseudospin components $\hat{L}_y$ and $\hat{L}_z$. The sphere poles are the pure spin-up and spin-down magnons, represented by creation operators $\hat{\alpha}^\dagger$ and $\hat{\beta}^\dagger$. The considered pseudofield $\boldsymbol{\omega}$ is along the $\hat{L}_x$-axis and characterizes spin-0 modes.
• Figure 2: (a) Expectation value and variances of pseudospin (PS) components $\langle\hat{L}_x\rangle$, $\langle \Delta\hat{L}_y^2\rangle$ and $\langle \Delta\hat{L}_z^2\rangle$ as a function of $D_s$ with $D_r/\omega = 0.3$, $m=1$ and $n=0$. (b) Pseudospin squeezing $\xi_{10}$ as a function of $D_s$ for different values of $D_r$. The curves are limited by the ground state stability condition $2|D_s| < (\omega - |D_r|)$.
• Figure 3: (a) Uncertainty region of the quadratures $\hat{X}_{1/2}$ and $\hat{Y}_{1/2}$ of sublattice spin operators $\hat{\boldsymbol{S}}_{A/B}$ for an AFM with $D_s\approx 0$ (grey) and AFM with SNC interactions (green). (b) Coupling enhancement $\cosh(r + r_+)/\cosh r$ of $\psi_+$ in the ground state $\ket{0_+, 0_-}$ for an uncompensated interface as a function of $D_s$, with intrinsic squeezing $r=1$.
• Figure 4: (a) Control of pseudofield via qubit in the ground state $\ket{g}$ (green) and excited state $\ket{e}$ (pink). (b) Contrast of the nontrivial peak in the small $\chi/D_r \ll1$ approximation as a function of $\chi$ with $D_r/\omega = 0.3$ for three values of $D_s$.
• Figure S1: Plot of (a) pseudospin components and variances $|\langle\hat{L}_x\rangle_{12}|$, $\langle\Delta\hat{L}_y^2\rangle_{12}$ and $\langle\Delta\hat{L}_z^2\rangle_{12}$ in the eigenstate $\ket{1,2}$ for fixed $D_r/\omega = 0.3$ (b) pseudsospin squeezing $\xi_{12}$ as a function of $D_s$ .