Modification of Hanle and polarization recovery curves under interplay of hopping and quantum measurement back action

TL;DR

This work addresses how localized electron spin dynamics, governed by hyperfine interactions and optical pumping, are modified by inter-site hopping and the quantum measurement back action. A semiclassical kinetic model is developed, incorporating Larmor precession, a Gaussian distribution of Overhauser fields with dispersion $\delta_e$, hopping at rate $W$, pumping rate $\bm g$, and back action strength $\lambda$, with a self-consistent solution for the ensemble spin $\langle \mathbf S \rangle$ and observable $\langle S_z \rangle$. The authors derive analytic expressions for polarization-recovery and Hanle curves in both Faraday and Voigt geometries, revealing that hopping and back action reinforce each other in longitudinal fields but compete in transverse fields; they show nonmonotonic behavior of $\langle S_z(0)\rangle$ with $\lambda$ (anti-Zeno vs Zeno effects) and provide limiting forms such as $\Omega_{PR}=W+2\lambda$ and $\Omega_{Hanle}=\sqrt{1/(T_1 T_2)}$ in appropriate regimes. The results broaden the range of experimental data that can be described with a unified framework and offer a basis for studying nonstationary spin dynamics and spin-noise in localized electron systems, with potential applications to quantum dots, donors, and interface-localized states.

Abstract

The measurements of Hanle and polarization recovery effects for localized charge carriers are the basic tools for determining parameters of the spin dynamics, such as strength of the hyperfine interaction, for example, in quantum dots. We describe the dependence of the spin polarization of localized electrons on transverse and longitudinal magnetic fields taking into account the interplay between electron hopping and measurement back action. We show that these two have a qualitatively similar effect in the Faraday geometry, but compete in the Voigt geometry. This allows one to describe a broad range of the experimental results and study the fundamental effects of quantum measurements.

Figures (3)

• Figure 1: (a) Sketch of the model: quantum dots (purple circles) under continuous optical spin pumping (green wavy arrow) and measurement (red arrow). Small blue circle with a black arrow represents an electron and its spin. Large contoured arrows denote the effective nuclear magnetic field. Blue dotted and orange arrows stand for electron hopping and external magnetic field, respectively. Three lower panels show polarization recovery (red) and Hanle (blue) curves calculated after Eqs. \ref{['eq:SIZF']} and \ref{['eq:Voigt']} for $\delta_e\tau_s=100$ and different hopping and measurement rates: $W=2\lambda=0$ (b); $W=0.01\delta_e$, $2\lambda = 0.05\delta_e$ (c); $W=1000\delta_e$, $2\lambda=10\delta_e$ (d).
• Figure 2: Dependence of the parameters of Hanle and polarization recovery curves on the hopping rate $W$ and measurement back action strength $\lambda$ (calculated for $\delta_e\tau_s=100$). (a---c) Show the depth of the polarization recovery curve, which is also the amplitude of the Hanle curve. (d---f) and (g---i) show HWHM of polarization recovery and Hanle curves, respectively. The left column, (a), (d), (g), shows dependences on both $W$ and $\lambda$ as the color maps. The middle column, (b), (e), (h) and the right column, (c), (f), (i), show the dependences on $W$ and $\lambda$ for a few values $\lambda$ and $W$, respectively, as indicated in the legend.
• Figure 3: Regions of the parameters of Hanle and polarization recovery curves, which are possible in the model: $\left\langle S_z(0) \right\rangle$ and $\Omega_{\text{PR}}$ (a), $\left\langle S_z(0) \right\rangle$ and $\Omega_{\text{Hanle}}$ (b), $\left\langle S_z(0) \right\rangle$ and $\Omega_{\text{Hanle}}/\Omega_{\text{PR}}$ (c). The blue and red lines show the parameters for $\lambda=0$ and $W=0$, respectively. A small green dot in (c) shows the parameters of Hanle and polarization recovery curves from Ref. kirsteinExtendedSpinCoherence2021.