[Paper Review] Influence of Nuclear Quadrupole Moments on Electron Spin Coherence in Semiconductor Quantum Dots

Erik Welander, E. A. Chekhovich+2 more|arXiv (Cornell University)|May 6, 2014

Quantum and electron transport phenomena3 citations

TL;DR

This paper investigates how nuclear quadrupole moments (QPMs) enhance electron spin coherence in semiconductor quantum dots by suppressing nuclear spin flip-flop processes via energy-level shifts from electric field gradients. Using theoretical modeling of electron spin echo experiments, it shows that inhomogeneous quadrupolar shifts increase coherence time significantly—comparable to 70% nuclear spin polarization—offering a practical alternative to full dynamic nuclear spin polarization for extending qubit coherence.

ABSTRACT

We theoretically investigate the influence of the fluctuating Overhauser field on the spin of an electron confined to a quantum dot (QD). The fluctuations arise from nuclear angular momentum being exchanged between different nuclei via the nuclear magnetic dipole coupling. We focus on the role of the nuclear electric quadrupole moments (QPMs), which generally cause a reduction in internuclear spin transfer efficiency in the presence of electric field gradients. The effects on the electron spin coherence time are studied by modeling an electron spin echo experiment. We find that the QPMs cause an increase in the electron spin coherence time and that an inhomogeneous distribution of the quadrupolar shift, where different nuclei have different shifts in energy, causes an even larger increase in the electron coherence time than a homogeneous distribution. Furthermore, a partial polarization of the nuclear spin ensemble amplifies the effect of the inhomogeneous quadrupolar shifts, causing an additional increase in electron coherence time, and provides an alternative to the experimentally challenging suggestion of full dynamic nuclear spin polarization.

Motivation & Objective

• To understand how nuclear quadrupole moments (QPMs) influence electron spin coherence in semiconductor quantum dots.
• To investigate the role of electric field gradients (EFGs) in modifying nuclear spin dynamics via quadrupolar shifts.
• To evaluate whether inhomogeneous quadrupolar shifts can enhance electron spin coherence time as effectively as dynamic nuclear spin polarization.
• To determine the impact of partial nuclear spin polarization on coherence enhancement via QPMs.
• To provide a theoretical framework for using QPMs as a practical alternative to experimentally challenging full dynamic nuclear spin polarization.

Proposed method

• Modeling the electron spin echo experiment using a Hamiltonian that includes hyperfine coupling, Overhauser field fluctuations, and quadrupolar shifts.
• Incorporating nuclear spin dynamics via the dipolar coupling Hamiltonian, which enables spin exchange between nuclei.
• Introducing quadrupolar shifts proportional to $ I_z^2 $, with both homogeneous and inhomogeneous distributions across nuclei.
• Simulating electron spin coherence using time-dependent density matrix evolution under stochastic Overhauser fields.
• Analyzing coherence times $ T_{2a} $ and $ T_{2b} $, corresponding to fast and slow decoherence components, respectively.
• Calculating asymptotic fidelity $ F_{\infty} $ and coherence weight ratios $ F_b/F_a $ to quantify long-term coherence and relative contributions of inhibited transitions.

Experimental results

Research questions

• RQ1 How do nuclear quadrupole moments affect electron spin coherence in quantum dots with inhomogeneous electric field gradients?
• RQ2 What is the relative impact of homogeneous versus inhomogeneous quadrupolar shifts on electron coherence time?
• RQ3 Can inhomogeneous quadrupolar shifts mimic the effect of dynamic nuclear spin polarization in extending electron coherence?
• RQ4 How does partial nuclear spin polarization interact with quadrupolar shifts to influence electron spin decoherence?
• RQ5 What is the quantitative enhancement in electron coherence time achievable through quadrupole moments alone?

Key findings

• Inhomogeneous quadrupolar shifts increase electron spin coherence time significantly more than homogeneous shifts, with $ T_{2b} $ rising strongly with increasing quadrupolar strength $ \nu_Q $.
• The slow decoherence component $ T_{2b} $, associated with inhibited transitions, increases substantially with $ \nu_Q $, while $ T_{2a} $, linked to $ \Delta I_z = \pm1 $ transitions, remains largely unchanged.
• Asymptotic fidelity $ F_{\infty} $ exceeds 50% for inhomogeneous quadrupolar shifts at $ \nu_Q \approx 600 $ Hz, matching the performance of 90% nuclear polarization in the absence of QPMs.
• The ratio $ F_b/F_a $ increases slightly with $ \nu_Q $, indicating that the slow decoherence component becomes increasingly dominant over time.
• There is little difference in coherence enhancement between linear and random inhomogeneous quadrupolar shift distributions, suggesting robustness to distribution type.
• Partial nuclear polarization (70%) amplifies the coherence enhancement from inhomogeneous quadrupolar shifts, providing a practical route to long electron coherence times without requiring full dynamic nuclear spin polarization.