Phonon- and magnon-mediated decoherence of a magnonic qubit

TL;DR

This work analyzes the decoherence of a magnonic qubit in a ferromagnetic insulator by merging Bloch--Redfield theory with the Keldysh formalism to compute relaxation and dephasing from magnon--phonon and magnon--magnon interactions. For a quadratic long-wavelength dispersion and a uniform qubit mode ${\boldsymbol{k}}_0=0$, the zero-temperature relaxation proceeds only via two-phonon emission, which is strongly suppressed in YIG due to a small qubit frequency $\omega_0$ and a heavy unit cell, while pure dephasing scales as $\propto 1/N$ and $\alpha^{-1}$, potentially becoming large in small, clean magnets. The results suggest that intrinsic decoherence channels are weak in typical YIG nanomagnets—consistent with experiments where surface defects dominate—yet they provide quantitative benchmarks and identify parameter regimes where momentum-nonconserving dephasing or non-Markovian effects could become relevant for magnon-based quantum devices. Overall, the framework offers a tractable route to assess magnonic qubit viability and guides design choices in nanoscale magnetic systems for quantum information processing.

Abstract

We investigate the decoherence of magnonic qubits in small ferromagnetic insulators and compute the relaxation and dephasing rates due to magnon-phonon and magnon-magnon interactions. We combine a Bloch--Redfield description with Keldysh non-equilibrium field theory to find explicit expressions for the rates. For a quadratic dispersion and assuming a uniform mode defines the qubit, we find that decay into two phonons is the only allowed relaxation process at zero temperature. The low resonance frequency and heavy unit cell strongly suppress this process in yttrium-iron-garnet. We also find that the dephasing rate scales with the inverse of size and damping of the magnet, and could become large for small and clean magnets. Our calculation thus provides additional insight into the viability of magnon-based quantum devices.

Figures (5)

• Figure 1: The system under consideration. A specific magnon mode with wave vector ${\boldsymbol{k}}_0$ is coupled to an environment of other magnons with wave vectors ${\boldsymbol{k}}\neq{\boldsymbol{k}}_0$ and phonon modes with wave vectors ${\boldsymbol{q}}$ and polarization $\lambda$. The coupling of the environment to itself is encoded in a phenomenological damping rate $\eta_{\boldsymbol{k}}$ ($\tilde{\eta}_{{\boldsymbol{q}},\lambda}$) for the environmental magnons (phonons).
• Figure 2: The Keldysh contour. Two operators, $\hat{v}_1$ and $\hat{v}_2$, will be ordered differently on the forward and backward branches.
• Figure 3: The vertices for the processes contributing to the relaxation rate, where a magnon with specific momentum ${\boldsymbol{k}}_0$ (solid lines) is created due to interactions with phonons (wavy lines) and magnons with wave vectors ${\boldsymbol{k}}\neq{\boldsymbol{k}}_0$ (dashed lines). Only the out-scattering vertices are shown; the full interaction also contains the in-scattering vertices, which can be found by time inversion.
• Figure 4: The different contributions to the relaxation rate of a magnon qubit at ${\boldsymbol{k}}_0=0$, from (a) one-magnon--two-phonon processes, (b) two-magnon--one-phonon processes, and (c) four-magnon processes where the dotted lines show the approximate analytical low-temperature result from Eq. \ref{['eq:MagnonDecay']}. We have set $v_l=2v_t$ and in (b) we have set $B_\perp=2B_\parallel$, as appropriate for YIG Streib.
• Figure 5: The contribution to the dephasing rate from anisotropy- (red line) and exchange-mediated (blue line) interaction. The dashed lines show the corresponding low-temperature analytical solutions from Eqs. \ref{['eq:dephK']} and \ref{['eq:gammaexLT']}, respectively.