Quantum-enhanced sensing of spin-orbit coupling without fine tuning

Abstract

Spin-orbit coupling plays an important role in both fundamental physics and technological applications. Precise estimation of the spin-orbit coupling is necessary for accurate designing across various physical setups such as solid state devices and quantum hardware. Here, we exploit quantum features in a 1D quantum wire for estimating the Rashba spin-orbit coupling with enhanced sensitivity beyond the capability of classical probes. The Heisenberg limited enhanced precision is achieved across a wide range of parameters and does not require fine tuning. Such advantage is directly related to the gap-closing nature of the probe across the entire relevant range of parameters. This provides clear advantage over conventional criticality-based quantum sensors in which quantum enhanced sensitivity can only be achieved through fine-tuning around the phase transition point. We have demonstrated quantum enhanced sensitivity for both single particle and interacting many-body probes. In addition to extending our results to thermal states and the multi-parameter scenario, we have provided an measurement basis to perform close to the ultimate precision.

Figures (9)

• Figure 1: Scaling analysis of energy gap and QFI. Probe state is the ground state of the Hamiltonian in Eqs. \ref{['eq:ham_main']}-\ref{['eq:hamZ']} for sensing $\alpha_z$ with hopping parameter $t {=} 1$, and $\alpha_y {=} \alpha_z$. (a) Energy gap between first excited state and ground state $\Delta$ with $\alpha_z$ and $B$ for system size $L {=} 100$. The four points in the parameter space are chosen as $(B, \alpha_z) = (0.05, 0.1), (0.9, 0.1), (0.9, 0.9), (0.05, 0.9)$, denoted by the cross, diamond, plus, and circle, respectively. (b) Scaling relation of the energy gap with system size at these four parameter points, labeled by corresponding legends. In all cases numerical fit $\Delta {=} a L^{-\mu} {+} b$ shows almost quadratic scaling of the gap closing. (c) QFI of the probe with respect to $\alpha_z$ in the parameter space spanned by $\alpha_z$ and $B$ for system size $L {=} 100$. The same four points are chosen to study the scaling behavior. (d) Numerical fit confirms the quadratic scaling of QFI in the whole range as $F^{Q} {\sim} L^{\beta}$ with $\beta {\approx} 2$.
• Figure 2: Many-body probe. Probe state is the half-filled ground state of the Hamiltonian in Eq. \ref{['eq:ham2']} with $t {=} 1$, $B{=}0.01t$, and $\alpha_y {=} \alpha_z$. (a) Scaling of energy gap in the non-interacting case ($U{=} V {=} 0$) with system size $L$ for different values of SOC parameter $\alpha_z$. (b) Scaling of QFI with respect to $\alpha_z$ in the non-interacting case for different $\alpha_z$ values. (c) QFI at $\alpha_z {=} 0.1t$ as a function of $U$ when $V {=} 0$. (d) QFI scaling at $\alpha_z {=} 0.1t$ for different $U$ values. (e) Spectrum $E$ as a function of $U$. (f) QFI at $\alpha_z {=} 0.1t$ as a function of $V$ when $U {=} 0$.
• Figure 3: Thermal probe. Probe state is the thermal state of the Hamiltonian in Eq. \ref{['eq:ham2']} with $t {=} 1$, $B{=}0.01t$, $\alpha_y {=} \alpha_z$. (a) QFI vs. temperature in the non-interacting case for different system sizes. As thermal energy surpasses the gap, QFI falls of universally as ${\sim} 1/T$. (b) Variation of QFI with both $U$ and $T$ for $L {=}6$.
• Figure 4: Disorder for single-particle probes. $(B, \alpha_z) = (0.05, 0.1), (0.9, 0.1), (0.9, 0.9), (0.05, 0.9)$ in (a), (b), (c), and (d), respectively. The red, blue, and green circles represent disorder in tunneling, magnetic field, and onsite potential, respectively.
• Figure 5: Disorder for many-body probes. $(B, \alpha_z) = (0.05, 0.1), (0.9, 0.1), (0.9, 0.9), (0.05, 0.9)$ in (a), (b), (c), and (d), respectively. The red, blue, and green circles represent disorder in tunneling, magnetic field, and onsite potential, respectively.