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Europhysics Letters (EPL)

Enhanced phase estimation by implementing dynamical decoupling in a multi-pass quantum metrology protocol

Xing Rong, Pu Huang, Xi Kong, Xiangkun Xu, Fazhan Shi, Ya Wang, Jiangfeng Du

Published Sep 1, 2011• 17 citations
Publisher

Abstract

Based on repetitive generation of the Aharonov-Anandan geometric phase, a multi-pass quantum metrology protocol is realized via the electron spin state of a single nitrogen-vacancy defect center in diamond. It is then demonstrated that high-order dynamical decoupling pulse sequences can be implemented in our metrology protocol and hence improve its performance in phase estimation.

DOI
10.1209/0295-5075/95/60005

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Based on repetitive generation of the Aharonov-Anandan geometric phase, a multi-pass quantum metrology protocol is realized via the electron spin state of a single nitrogen-vacancy defect center in diamond. It is then demonstrated that high-order dynamical decoupling pulse sequences can be implemented in our metrology protocol and hence improve its performance in phase estimation.
We use multipulse dynamical decoupling to increase the coherence lifetime (T2{T}_{2}T2​) of large numbers of nitrogen-vacancy (NV) electronic spins in room temperature diamond, thus enabling scalable applications of multispin quantum information processing and metrology. We realize an order-of-magnitude extension of the NV multispin T2{T}_{2}T2​ in three diamond samples with widely differing spin impurity environments. In particular, for samples with nitrogen impurity concentration $\ensuremath{\lesssim}$1 ppm, we extend T2{T}_{2}T2​ to $>$2 ms, comparable to the longest coherence time reported for single NV centers, and demonstrate a tenfold enhancement in NV multispin sensing of ac magnetic fields.
The Nitrogen-Vacancy (NV) center is becoming a promising qubit for quantum information processing. The defect has a long coherence time at room temperature and it allows spin state initialized and read out by laser and manipulated by microwave pulses. It has been utilized as a ultra sensitive probe for magnetic fields and remote spins as well. Here, we review the recent progresses in experimental demonstrations based on NV centers. We first introduce our work on implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond. Then the quantum nature of the bath around the center spin is revealed and continuous wave dynamical decoupling has been demonstrated. By applying dynamical decoupling, a multi-pass quantum metrology protocol is realized to enhance phase estimation. In the final, we demonstrated NV center can be regarded as a ultra-sensitive sensor spin to implement nuclear magnetic resonance (NMR) imaging at nanoscale.
We demonstrate significant improvements of the spin coherence time of a dense ensemble of nitrogen-vacancy (NV) centers in diamond through optimized dynamical decoupling (DD). Cooling the sample down to 77 K suppresses longitudinal spin relaxation T1{T}_{1}T1​ effects and DD microwave pulses are used to increase the transverse coherence time T2{T}_{2}T2​ from $\ensuremath{\sim}0.7\phantom{\rule{0.28em}{0ex}}\mathrm{ms}$ up to $\ensuremath{\sim}30\phantom{\rule{0.28em}{0ex}}\mathrm{ms}$. We extend previous work of single-axis (Carr-Purcell-Meiboom-Gill) DD towards the preservation of arbitrary spin states. Following a theoretical and experimental characterization of pulse and detuning errors, we compare the performance of various DD protocols. We identify that the optimal control scheme for preserving an arbitrary spin state is a recursive protocol, the concatenated version of the XY8 pulse sequence. The improved spin coherence might have an immediate impact on improvements of the sensitivities of ac magnetometry. Moreover, the protocol can be used on denser diamond samples to increase coherence times up to NV-NV interaction time scales, a major step towards the creation of quantum collective NV spin states.
We perform a detailed theoretical-experimental study of the dynamical decoupling (DD) of the nitrogen-vacancy (NV) center in diamond. We investigate the DD sequences applied to suppress the dephasing of the electron spin of the NV center induced by the coupling to a spin bath composed of the substitutional nitrogen atoms. The decoupling efficiency of various DD schemes is studied, including both periodic and aperiodic pulse sequences. For ideal control pulses, we find that the DD protocols with the Carr-Purcell-Meiboom-Gill (CPMG) timing of the pulses provides best performance. We show that, as the number of control pulses increases, the decoupling fidelity scaling differs qualitatively from the predictions of the Magnus expansion, and explain the origin of this difference. In particular, more advanced symmetrized or concatenated protocols do not improve the DD performance. Next, we investigate the impact of the systematic instrumental pulse errors in different periodic and aperiodic pulse sequences. The DD protocols with the single-axis control do not preserve all spin components in the presence of the pulse errors, and the two-axis control is needed. We demonstrate that the two-axis control sequence with the CPMG timing is very robust with respect to the pulse errors. The impact of the pulse errors can be diminished further by symmetrizing this protocol. For all protocols studied here, we present a detailed account of the pulse error parameters which make the strongest impact on the DD performance. In conclusion, we give specific recommendations about choosing the decoupling protocol for the system under investigation.
Precise parameter estimation plays a central role in science and technology. The statistical error in estimation can be decreased by repeating measurement, leading to that the resultant uncertainty of the estimated parameter is proportional to the square root of the number of repetitions in accordance with the central limit theorem. Quantum parameter estimation, an emerging field of quantum technology, aims to use quantum resources to yield higher statistical precision than classical approaches. Here we report the first room-temperature implementation of entanglement-enhanced phase estimation in a solid-state system: the nitrogen-vacancy centre in pure diamond. We demonstrate a super-resolving phase measurement with two entangled qubits of different physical realizations: an nitrogen-vacancy centre electron spin and a proximal (13)C nuclear spin. The experimental data shows clearly the uncertainty reduction when entanglement resource is used, confirming the theoretical expectation. Our results represent an elemental demonstration of enhancement of quantum metrology against classical procedure.
We propose an efficient quantum measurement protocol for the hyperfine interaction between the electron spin and the 15^{15}15N nuclear spin of a diamond nitrogen-vacancy center. In this protocol, a sequence of quantum operations of successively increasing duration is utilized to estimate the hyperfine interaction with successively higher precision approaching the quantum metrology limit. This protocol does not need the preparation of the nuclear spin state. In the presence of realistic operation errors and electron spin decoherence, the overall precision of our protocol still surpasses the standard quantum limit.