Sideband-mediated nuclear-spin-wave memory for an Andreev spin qubit: required coherence and Floquet feasibility

A Floquet-driven red-sideband architecture is proposed and quantitatively analyzed that couples an Andreev spin qubit (ASQ) in a semiconductor Josephson junction to a collective nuclear spin-wave bright mode of the host, establishing a parameterized feasibility map and actionable design criteria for an ASQ–nuclear-spin quantum memory. The frequency-modulated exchange bridges the GHz ASQ transition and the MHz nuclear Larmor frequency with effective coupling g eff = g mg J 1 (β), where β = Ω d /ω d is the modulation index. An analytical model of a single-isotope 75 As (I = 3/2) bright-mode envelope with N eff = 10 5 –10 6 nuclei gives g eff /2π in the 9–367 kHz range for two explicit parameter sets, with SWAP times of 0.7–28 μs. A next-order Floquet expansion identifies, within the single-circular-component limit g− ≪ g+, the n = 0 Jaynes–Cummings dispersive dressing as the dominant off-resonant contribution, decomposing into a static (β = 0) component δ static ≃ 2g 2 mg /ω d and a drive-induced increment δ AC ≃ −g 2 mg β 2 /ω d that are distinguishable by modulation-on/off spectroscopy combined with an independent bare-reference calibration. A diagnostic M≡ 2π(g eff /2π)T 2,ASQ = 1 requires T 2,ASQ ∼ 0.4–17 μs, while a high-fidelity write–read cycle (FWR ≳ 0.9, M≳ 30) requires T 2,ASQ ∼ 13–520 μs. A two-mode stroboscopic Lindblad simulation independently reproduces the M≳ 30 crossover at fixed g eff /(2π) = 100 kHz and shows the direct counter-rotating g− contribution is sub-percent at the baseline resolved-sideband point (ε − = g −,eff /(2ω n ) = 0.025), while worst-case g − /g + = 1 at the optimistic coupling produces a 2.3-percentage-point penalty. Currently demonstrated T 2,ASQ ∼ 10–100 ns lie two to five orders of magnitude below the M≳ 30 regime; the analysis identifies sweet-spot operation, phase-bias engineering, and Floquet-dressed subspace protection as concrete engineering directions to close the gap.