Maximizing the purity of a qubit evolving in an anisotropic environment

TL;DR

This paper introduces a method to calculate and optimize the purity of a qubit in an anisotropic non-Markovian environment, revealing counterintuitive strategies for initial state preparation to maximize coherence.

Contribution

It provides a general analytical framework for maximizing qubit purity in complex environments, including specific models relevant to quantum dots and advanced dynamical decoupling techniques.

Findings

Preparing the qubit in non-interacting eigenstates often maximizes purity.

Ground state preparation can be the worst choice for purity in certain models.

Analytical results for spin-echo modulations and optimal initial conditions are provided.

Abstract

We provide a general method to calculate and maximize the purity of a qubit interacting with an anisotropic non-Markovian environment. Counter to intuition, we find that the purity is often maximized by preparing and storing the qubit in a superposition of non-interacting eigenstates. For a model relevant to decoherence of a heavy-hole spin qubit in a quantum dot or for a singlet-triplet qubit for two electrons in a double quantum dot, we show that preparation of the qubit in its non-interacting ground state can actually be the worst choice to maximize purity. We further give analytical results for spin-echo envelope modulations of arbitrary spin components of a hole spin in a quantum dot, going beyond a standard secular approximation. We account for general dynamics in the presence of a pure-dephasing process and identify a crossover timescale at which it is again advantageous to initialize the qubit in the non-interacting ground state. Finally, we consider a general two-axis dynamical decoupling sequence and determine initial conditions that maximize purity, minimizing leakage to the environment.