Harnessing Floquet dynamics for selective metrology in few-qubit systems

Periodically driven quantum systems can function as highly selective parameter filters. We demonstrate this capability in a finite-size, three-qubit system described by the transverse-field Floquet Ising model. In this system, we identify a period-doubling (PD) dynamical phase that exhibits a stark asymmetry in metrological sensitivity to the magnetic field applied on the qubits and to the coupling strength between the qubits. The PD phase originates from $π$-pairing, where the initial state exhibits strong overlap with $π$-paired Floquet eigenstates, leading to robust period-doubled dynamics and enhanced metrological sensitivity. The analysis of quantum Fisher information reveals that the PD regime significantly enhances precision for estimating the Ising interaction strength while simultaneously suppressing sensitivity to the transverse magnetic field. Conversely, non-PD regimes are optimal for sensing the transverse field. This filtering effect is robust for larger system sizes and is quantifiable using experimentally accessible observables, such as magnetization and two-qubit correlations, via the classical Fisher information. Our work shows that distinct dynamical regimes in finite-size Floquet systems can be harnessed for targeted quantum sensing.

💡 Research Summary

The authors investigate how periodic driving (Floquet engineering) can be used as a functional filter for quantum metrology in a minimal three‑qubit transverse‑field Ising model. The system evolves under a two‑step Floquet protocol: a global transverse magnetic field pulse of strength hₓ for half a period (T₁ = 0.5 T) followed by an Ising interaction of uniform strength J for the remaining half (T₂ = T − T₁). The Floquet unitary U_F = e^{-iH_zT₂}e^{-iH_xT₁} governs the stroboscopic dynamics.

A key dynamical feature is the emergence of a period‑doubling (PD) regime, identified by a robust subharmonic response at frequency f = 1/(2T) in the Fourier spectrum of the total magnetization ⟨M_z⟩. The authors quantify PD strength using (i) the relative subharmonic spectral weight and (ii) the fraction of Floquet eigenstates whose quasienergies differ by π/T (π‑pairing). When the initial state |000⟩ has substantial overlap with these π‑paired eigenstates, the system exhibits long‑lived oscillations with period 2T, i.e., a finite‑size analogue of a discrete time crystal.

Metrological performance is assessed via the quantum Fisher information (QFI). For pure states the QFI reduces to F_Q(θ)=4