Floquet-Engineered Superradiant Quantum Sensing via Stroboscopic Liouvillian Control

Numerical fits support the local behavior[\mu(T) \approx \mu_0 + \frac{a}{T^2} + cT^2,\qquad a<0,;c>0.]This produces an optimal sensing period determined by competition between the two terms.Numerical simulations at moderate truncation levels ((N=3\text{–}5)) with a displacement kick yield a Fisher information gain of (\times4.5\text{–}5.0) relative to the static case. However, a higher-truncation benchmark at (N=11) using a squeezing kick shows no detectable enhancement.

That benchmark simultaneously changes the kick type, the coupling (g/\kappa), and the kick strength (\epsilon) relative to the (N\leq5) runs, and therefore does not isolate a truncation effect.As shown in Sec. 4.3, the squeezing null is instead a first-moment sector effect that does not depend on truncation: the enhancement resides entirely in the stroboscopic mean[R^*(T)=\left(I-e^{AT}\right)^{-1}d](Appendix A). A squeezing kick contributes no affine displacement ((d=0)), so the corresponding homodyne Fisher information vanishes identically.The displacement-kick gains are shown to be exactly truncation-converged (Sec. 4.4) and therefore represent robust finite-(N) enhancements.

In the thermodynamic limit (N\rightarrow\infty) at fixed (g/\sqrt{N}), the enhancement decays as a power law. The protocol is therefore best understood as a finite-size resonance rather than a thermodynamic-limit divergence.The protocol offers a route to sensing enhancement without operating at the critical point or requiring feedback. Its performance is highly sensitive to the choice of kick operator, highlighting both the promise and the practical limits of Floquet control for quantum metrology.</p>