Interference-induced state engineering and Hamiltonian control for noisy collective-spin metrology

Abstract

Interference provides a fundamental mechanism for generating and manipulating entanglement in many-body quantum systems. Here, we develop an interference framework in which the nonlinear dynamics of collective spin-$\tfrac{1}{2}$ ensembles are mapped onto phase accumulation and self-interference in phase space, providing a direct and physically transparent description of entanglement formation. Within this framework, one-axis twisting produces Greenberger-Horne-Zeilinger (GHZ) states, while two-axis twisting generates multi-component GHZ superpositions relevant for multiparameter quantum metrology. Building on this interference-based description, we analyze metrological performance under realistic Markovian noise, including local and collective emission, pumping, and dephasing, and examine the role of Hamiltonian control based on linear and nonlinear interactions. We show that while control can enhance single-parameter sensitivity in a noise-dependent regime, the achievable precision in multiparameter estimation is fundamentally constrained. These results establish interference as a unifying principle linking nonlinear dynamics, entanglement generation, and metrological performance, and reveal intrinsic limitations of multiparameter quantum sensing. Our framework provides broadly applicable insight into the design of robust quantum-enhanced measurement protocols in noisy many-body systems.

Figures (11)

• Figure 1: (a) Evolution of a spin ensemble under OAT. Starting from the coherent state $|N/2, -N/2\rangle$, the system undergoes squeezing and self-interference, producing constructive and destructive interference patterns in the $z$-$y$ plane. At $\chi t = \pi/2$, this leads to the formation of a GHZ state, $|\psi_{\mathrm{GHZ}_z}\rangle = \frac{1}{\sqrt{2}} \left( |N/2,N/2\rangle + |N/2, -N/2\rangle \right)$. (b) Evolution under TAT, starting from the GHZ state $|\psi_{\mathrm{GHZ}_z}\rangle$. The state undergoes squeezing along multiple directions, gradually developing into a multi-component GHZ state. Results are shown for $N = 50$.
• Figure 2: (a,b) The QFI $Q(t)$ as a function of time $t$ under different noise channels. (c,d) The metrological gain $G(t)=Q(t)/t^2$ for the same cases. Parameters: $N=10$, with local dissipation rates $\gamma=0.2$ and collective dissipation rates $\Gamma=0.2$ for each channel.
• Figure 3: (a) Maximum QFI $Q_{\text{max}}$ under local noise as a function of the spin number $N$. (b) Optimal sensing time $t_{\text{opt}}$ corresponding to $Q_{\text{max}}$. (c) Maximum metrological gain $G_{\text{max}} = Q_{\text{max}} / t_{\text{opt}}^2$. (d-f) Same quantities as in panels (a-c), but for collective noise.
• Figure 4: Metrological gain under the local noise. Panels (a-c) show the results for the local emission, while panels (d-f) correspond to the local dephasing. In (a,b) and (d,e), the metrological gain $G(t)$ is plotted for different control strengths $\chi$ (color-coded), comparing the linear control Hamiltonian $H_{\rm ctrl}=\chi J_x$ and the nonlinear control $H_{\rm ctrl}=\chi J_x^2$. (c,f) show the integrated gain $\mathcal{I}=\int_0^T G(t)$ as a function of $\chi$, for a truncation of $T = 50$.
• Figure 5: Metrological gain under the collective noise. (a-c) show the results for the collective emission, while (d-f) correspond to the collective dephasing. Panels (a,b) and (d,e) display the metrological gain $G(t)$ for different control strengths $\chi$ (color-coded), comparing the linear control Hamiltonian $H_{\rm ctrl}=\chi J_x$ and the nonlinear control Hamiltonian $H_{\rm ctrl}=\chi J_x^2$. (c,f) show the integrated gain $\mathcal{I}$ as a function of $\chi$.