Harnessing Floquet dynamics for selective metrology in few-qubit systems

TL;DR

The paper addresses how to harness non-equilibrium Floquet dynamics to perform selective quantum metrology in a minimal, finite-size system. By studying a three-qubit transverse-field Ising model under a two-step Floquet protocol, it identifies a period-doubling ($\pi$-pairing) dynamical phase that acts as a functional metrological switch: PD enhances sensitivity to the Ising coupling $J$ while suppressing sensitivity to the transverse field $h_x$, as quantified by quantum Fisher information, and this selectivity is observable via accessible measurements such as total magnetization $M_z$ and two-qubit correlations $C_{zz}$ through classical Fisher information. The results persist for larger system sizes, suggesting robustness and practical relevance for near-term quantum sensors on platforms like trapped ions or superconducting qubits. Overall, the work demonstrates that distinct finite Floquet regimes can be exploited to tailor metrological responses, enabling targeted sensing in noisy or multi-parameter environments.

Abstract

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.

Figures (11)

• Figure 1: (a) Sketch of the three-qubit model system. Qubits interact via nearest-neighbor Ising coupling strengths ($J_1$, $J_2$, $J_3$) and are driven by a transverse magnetic field $h_x$. (b) The dynamics are generated by a two-step Floquet protocol: each period $T=T_1+T_2$ consists of a pulse of amplitude $h_x$ during $T_1$, which is followed by Ising evolution for duration $T_2$.
• Figure 2: (a) Average magnetization $\langle \hat{M}_z \rangle_t$ at stroboscopic times $t = nT$, where $n \in \mathbb{Z}$, for PD (blue) and non-PD (red) regimes. The PD regime shows robust PD oscillations, while the non-PD case shows trivial dynamics. (b) Power spectrum of the magnetization dynamics, which shows a strong subharmonic response in the PD regime. For the PD regime, we use $h_xT=2.6$ and $JT=1.57$, while for the non-PD regime, we use $h_xT=2.6$ and $JT=0.1$.
• Figure 3: (a) Phase diagram of the relative subharmonic spectral weight, quantifying the fraction of oscillatory power contained in the subharmonic mode $f=1/2T$. Regions of high spectral weight indicate strong PD dynamics. (b) Corresponding fraction of $\pi$-paired Floquet eigenstates, obtained from the quasienergy spectrum of the Floquet operator $\mathrm{\hat{U}_F}$. The presence of pairs of Floquet states with quasienergy separation close to $\pi/T$ underlies the emergence of PD behavior in finite systems.
• Figure 4: (a) QFI dynamics for the estimation of the transverse field $h_x$, calculated from the Floquet-evolved states, as a function of stroboscopic time $t/T$. The QFI is plotted for the selected PD (blue) and non-PD (red) parameter sets. For the PD regime, we use $h_xT=2.6$ and $JT=1.57$, while for the non-PD regime, we use $h_xT=2.6$ and $JT=0.1$. (b) QFI dynamics for estimating the interaction strength $J$, calculated from the Floquet-evolved states, as a function of stroboscopic time $t/T$. For the PD regime, we use $h_xT=2.6$ and $JT=1.57$, while for the non-PD regime, we use $h_xT=0.1$ and $JT=1.57$. Insets in both panels show $F_Q/t^2$ at short times to highlight the absence of quadratic scaling at early times.
• Figure 5: Phase diagrams of QFI curvature $d^2F_Q/dt^2$ (Eq. \ref{['QFI_curve']}) as a function of interaction strength $J$ and transverse field $h_x$ for estimation of $h_x$ (a) and $J$ (b). The rest of the parameters are the same as in Fig. \ref{['fig:Mz+Power+QE']}.