Robust dynamical decoupling sequences for individual-nuclear-spin addressing

J. Casanova, Z.-Y. Wang, J. F. Haase, and M. B. Plenio

Phys. Rev. A 92, 042304 – Published 5 October 2015

Abstract

We propose the use of non-equally-spaced decoupling pulses for high-resolution selective addressing of nuclear spins by a quantum sensor. The analytical model of the basic operating principle is supplemented by detailed numerical studies that demonstrate the high degree of selectivity and the robustness against static and dynamic control-field errors of this scheme. We exemplify our protocol with a nitrogen-vacancy-center-based sensor to demonstrate that it enables the identification of individual nuclear spins that form part of a large spin ensemble.

Received 17 June 2015

DOI:https://doi.org/10.1103/PhysRevA.92.042304

Authors & Affiliations

J. Casanova^*, Z.-Y. Wang^†, J. F. Haase^‡, and M. B. Plenio^§

Institut für Theoretische Physik and IQST, Albert-Einstein-Allee 11, Universität Ulm, D-89069 Ulm, Germany

^*jcasanovamar@gmail.com
^†zhenyu3cn@gmail.com
^‡jan.haase@uni-ulm.de
^§martin.plenio@uni-ulm.de

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Issue

Vol. 92, Iss. 4 — October 2015

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Images

Figure 1
(a), (b) Robust composite pulses with adaptable time variables $x_{i}$ and $y_{i}$ to increase the spectral resolution. Each bar corresponds to a $π$ rotation around the axis defined by $φ$ [denoted as ${(π)}_{φ}$ ]. The (a) X and (b) Y composite pulses will be connected in the robust AXY- $n$ sequence. (c) First Fourier component, a half-period, of the modulation function $F (t)$ for a composite pulse. A whole period $τ$ corresponds to two successive X and (or) Y composite pulses. (d) Nonrobust pulse unit $\tilde{X}$ where all $π$ rotations are applied in the same direction.
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Figure 2
Sensor response (transition probability of a NV center coupled to a single nuclear spin) for different pulse sequences. The total evolution time is around $1.4$ ms, $B_{z} = 200$ G, and microwave $π$ pulses with a duration of $12.5$ ns are applied. A detuning of $Δ = 1$ MHz and a microwave amplitude mismatch of $5 %$ have been included. (a) response for a CPMG sequence (600 pulses). Panel (b) uses the AXY-8 sequence, while in panel (c) each X or Y is replaced by the $\tilde{X}$ composite pulse. The patterns in panels (b) and (c) are the result of applying 3040 decoupling pulses with an interpulse spacing such that $f_{1_{D D}} = \frac{1}{10} \frac{4}{π}$ and $f_{2} = f_{3} = f_{4} = 0$ . In panel (b) we denote, with arrows, the location of spurious resonances; see main text. The red line crossing the figure denotes the location of the resonance frequency.
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Figure 3
Difference between ideal and error-included patterns. (a) Quantity used for comparing the behavior of distinct sequences in the presence of errors—the difference between transition probabilities (see arrow) averaged over the frequency interval of the figure. In panels (b) and (c), the difference for the sequences used in Figs. 2 and 2 is obtained for different values of the detuning and amplitude error. Panel (d) shows the patterns without (solid line) and with (red crosses) a time-dependent microwave fluctuation in the control field.
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Figure 4
(a) Resonance pattern for a CPMG sequence, 9th harmonic used. The position of the vertical lines denote $ω_{j} / k$ and their height denotes the strength of interaction between the sensor and the nucleus. In panel (b) we can observe the effect of the overlap caused by $k = 35$ (diamonds), 33 (triangles), and 39 (crosses) harmonics on the spectrum of the $k = 37$ (circles) harmonic. Panels (c) and (d) show resonance pattern in the AXY-8 sequence for the 1st and 3rd harmonics, respectively. In each plot, the horizontal axis corresponds to the frequency range of the modulation function one should explore in order to obtain the nuclear response in the appropriate harmonic.
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