Optimal pulse spacing for dynamical decoupling in the presence of a purely-dephasing spin-bath

TL;DR

This study compares the effectiveness of equidistant and non-equidistant dynamical decoupling sequences in preserving quantum coherence within a specific spin-bath environment, finding that equidistant CPMG outperforms UDD in this context.

Contribution

The paper provides experimental evidence that CPMG outperforms UDD for Gaussian-like spectral densities in a solid-state NMR system, clarifying the regimes where each sequence is optimal.

Findings

CPMG sequence outperforms UDD in a Gaussian spectral density environment.

An optical interference analogy explains the superior performance of CPMG.

Experimental validation using solid-state NMR with nuclear spins.

Abstract

Maintaining quantum coherence is a crucial requirement for quantum computation; hence protecting quantum systems against their irreversible corruption due to environmental noise is an important open problem. Dynamical decoupling (DD) is an effective method for reducing decoherence with a low control overhead. It also plays an important role in quantum metrology, where for instance it is employed in multiparameter estimation. While a sequence of equidistant control pulses (CPMG) has been ubiquitously used for decoupling, Uhrig recently proposed that a non-equidistant pulse sequence (UDD) may enhance DD performance, especially for systems where the spectral density of the environment has a sharp frequency cutoff. On the other hand, equidistant sequences outperform UDD for soft cutoffs. The relative advantage provided by UDD for intermediate regimes is not clear. In this paper, we analyze the relative DD performance in this regime experimentally, using solid-state nuclear magnetic resonance. Our system-qubits are 13C nuclear spins and the environment consists of a 1H nuclear spin-bath whose spectral density is close to a normal (Gaussian) distribution. We find that in the presence of such a bath, the CPMG sequence outperforms the UDD sequence. An analogy between dynamical decoupling and interference effects in optics provides an intuitive explanation as to why the CPMG sequence performs superior to any non-equidistant DD sequence in the presence of this kind of environmental noise.