Floquet-Engineered Superradiant Quantum Sensing via Stroboscopic Liouvillian Control

We propose a stroboscopic Floquet protocol that applies periodic coherent displacement kicks to a cavity–Bose–Einstein condensate system operating in the normal phase near the Dicke superradiant critical point. The kicks leave the Hamiltonian and dissipation rates unchanged, yet generate a period-dependent stroboscopic steady state whose Fisher information exhibits a clear bounded maximum at an optimal strobe period T*. In the linearized Gaussian regime, enhancement arises from stroboscopic resonance at T* ≈ 2π/ω₀. In the full Lindblad treatment, non-commutativity between the free Liouvillian and the kick generator produces Baker–Campbell–Hausdorff corrections that renormalize the effective gap. Numerical fits support the local form μ(T) ≈ μ₀ + a/T² + c T² (a 0) in the intermediate-period regime, leading to an optimal sensing window via competition between gap-closing virtual transitions and restoring interaction effects. Exact diagonalization on truncated Fock–Dicke spaces (N = 3–5) with displacement kicks yields Fisher information gains of ×4.5–5.0 relative to the static case. A higher-truncation benchmark (N = 11) with a squeezing kick shows no enhancement, underscoring strong sensitivity to kick symmetry. Convergence in the thermodynamic limit remains open. The protocol offers a practical route to quantum sensing enhancement near a phase transition without crossing criticality or requiring feedback control. It highlights both the promise and current practical limits of Floquet Liouvillian engineering for metrology