Guiding diamond spin qubit growth with computational methods

Editors' Suggestion

Guiding diamond spin qubit growth with computational methods

Jonathan C. Marcks, Mykyta Onizhuk, Nazar Delegan, Yu-Xin Wang (王语馨), Masaya Fukami, Maya Watts, Aashish A. Clerk, F. Joseph Heremans, Giulia Galli, and David D. Awschalom

Phys. Rev. Materials 8, 026204 – Published 28 February 2024

Abstract

The nitrogen-vacancy (NV) center in diamond, a well-studied, optically active spin defect, is the prototypical system in many state-of-the-art quantum sensing and communication applications. In addition to the enticing properties intrinsic to the NV center, its diamond host's nuclear and electronic spin baths can be leveraged as resources for quantum information rather than considered solely as sources of decoherence. However, current synthesis approaches result in stochastic defect spin positions, reducing the technology's potential for deterministic control and yield of NV spin bath systems, as well as scalability and integration with other technologies. Here, we demonstrate the use of theoretical calculations of electronic central spin decoherence as an integral part of an NV spin bath synthesis workflow, providing a path forward for the quantitative design of NV center-based quantum sensing systems. We use computationally generated coherence data to characterize the properties of single NV center qubits across relevant growth parameters to find general trends in coherence time distributions dependent on spin bath dimensionality and density. We then build a maximum likelihood estimator with our theoretical model, enabling the characterization of a test sample through NV $T_{2}^{*}$ measurements. Finally, we explore the impact of dimensionality on the yield of strongly coupled electron spin systems. The methods presented herein are general and applicable to other qubit platforms that can be appropriately simulated.

Received 13 August 2023
Accepted 31 January 2024

DOI:https://doi.org/10.1103/PhysRevMaterials.8.026204

Physics Subject Headings (PhySH)

Open quantum systems & decoherence Quantum engineering Quantum information with solid state qubits

Quantum Information, Science & Technology

Authors & Affiliations

Jonathan C. Marcks ^1,2,*, Mykyta Onizhuk ^3,1,*, Nazar Delegan ^2,1, Yu-Xin Wang (王语馨)¹, Masaya Fukami ¹, Maya Watts^2,1, Aashish A. Clerk ¹, F. Joseph Heremans ^2,1, Giulia Galli ^1,3,2, and David D. Awschalom ^1,4,2,†

¹Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
²Center for Molecular Engineering and Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
³Department of Chemistry, University of Chicago, Chicago, Illinois 60637, USA
⁴Department of Physics, University of Chicago, Chicago, Illinois 60637, USA

^*These authors contributed equally to this work.
^†Corresponding author: awsch@uchicago.edu

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 8, Iss. 2 — February 2024

Reuse & Permissions

Access Options

Article part of CHORUS

Accepted manuscript will be available starting 27 February 2025.

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Growth process workflow. The current process steps (blue) for synthesizing a diamond NV sample. Iterations of growth and SIMS analysis are required to confirm nitrogen doping densities. The theoretical predictions and density maximum likelihood estimation (MLE) model in this work (green) enable a nondestructive feedback process to circumvent SIMS and allow for an efficient experimental design.
Reuse & Permissions
Figure 2
Computational and diamond growth methods. (a) Schematic representation of the cluster correlation expansion (CCE) approach. (b) Example of the Hahn-echo coherence calculated using the PyCCE code [60] for various ${}^{14}N$ P1 spin baths. The values of $T_{2}$ times are extracted from a stretched exponential fit of the form $exp [- {(\frac{t}{T_{2}})}^{n}]$ (dashed line). (c) $T_{2}$ and $T_{2}^{*}$ coherence times overlaid with corresponding experimental data [57], validating our computational methods. (d) Schematic of isotopically pure ( ${}^{12}C$ ) PE-CVD (100) diamond overgrowth with isotopically tagged ${}^{15}N$ nitrogen $δ$ doping. This sample geometry with varying nitrogen incorporation density and thickness is considered throughout this paper. (e), (f) Carbon (top) and nitrogen (bottom) isotope concentrations measured via SIMS on characterization sample, demonstrating isotopic purification of host material and isotopically tagged nitrogen incorporation. Carbon SIMS is used to calibrate the growth rate, shown in (d). The nitrogen concentration is quantified with NV coherence measurements in Sec. 2e.
Reuse & Permissions
Figure 3
Single-spin coherence in low-dimensional spin baths. (a) Ramsey (left) and Hahn-echo (right) microwave measurement pulse sequences. (b), (c) Mean of ${log}_{10} (T_{2}^{*} / [1 m s])$ distributions $μ = 10^{〈 {log}_{10} (T_{2}^{*} / [1 m s]) 〉}$ (b) and variance $σ^{2} = 〈 {log}_{10}^{2} (T_{2}^{*} / [1 m s]) 〉 - {〈 {log}_{10} (T_{2}^{*} / [1 m s]) 〉}^{2}$ (c) as a function of P1 density and layer thickness. Values are linearly interpolated between data points. The black dashed line in (c) indicates the thickness equal to the average nearest-neighbor bath spin distance $〈 r_{NN} 〉 = 0.554 ρ^{- 1 / 3}$ for each density $ρ$ (see text, Sec. 2f), demonstrating a boundary between dimensionalities. At right in (b) and (c) are line cuts of $μ$ and $σ$ at densities of 1, 5, and $9 ppm$ . Inset in (c) is $σ$ at multiple densities with thickness normalized by $〈 r_{NN} 〉$ , demonstrating universal behavior versus dimensionality. (d), (e) The same data as (b) and (c) presented for $T_{2}$ coherence times.
Reuse & Permissions
Figure 4
NV center measurements. (a) DEER spectroscopy with NV center confirming the presence of a P1 center electron spin bath. Marked values of $f_{P 1}$ correspond to P1 ESR transitions corresponding to the static magnetic field of $311 G$ and internal P1 hyperfine parameters. (b) Ramsey interferometry measurement to extract $T_{2}^{*}$ coherence time. (c) Compiled decoherence rates for eight measured NV centers (red squares, the two rightmost points overlap) and the probability function $P$ , drawn directly from the histogram of computed coherence times for parameters determined in Sec. 2e.
Reuse & Permissions
Figure 5
Maximum likelihood estimation. (a) Likelihood of data set in Fig. 4 calculated for each set of bath parameters from theoretical results. (b) Likelihood restricted to a thickness of $t_{SIMS} = 4 n m$ [from Fig. 2], from which we extract a density of $4.1 \pm . 8 ppm$ . (c) Calculated error of density estimation across full density range with fixed thickness, calculated for 200 random data sets at each density. (d) MLEs on a test data set of four NV centers generated from calculations of coherence times for a 3-nm-thick 5-ppm bath. The combined MLE (right), where the likelihood is calculated joint across both data sets, is the most sensitive. Scale bars are the same as in (a).
Reuse & Permissions
Figure 6
Dimensionality dependence of strong coupling. (a) Computed distribution (using PyCCE) of ratio of nearest-neighbor P1 coupling to background decoherence rate for $10^{5} 3 ppm$ density P1 bath configurations with varying thickness. Curves are offset for clarity. Shaded regions right of the dashed line indicate $ν \geq 2 π$ . (b) Percentage of NV-P1 bath systems with at least one strongly coupled bath spin for varying bath density and thickness. The average spin-spin distance is marked atop curves for each density. (c) Calculated visibility distributions for 3D and 2D spin baths (solid lines), with most likely values shown with dashed lines.
Reuse & Permissions

Physical Review Materials