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Coherence enhancement of solid-state qubits by local manipulation of the electron spin bath

Abstract

The performance of qubit-based technologies can be strongly limited by environmental sources of noise and disorder that cause decoherence. Qubits used in quantum sensing are usually very close to the host surface to enhance their coupling to external targets. This leaves them vulnerable to the effects of the surrounding noisy electron spin bath near the surface, which is very challenging to eliminate. Here we developed an efficient method to engineer the immediate electrostatic environment of nitrogen vacancy centre qubits located several nanometres beneath the diamond surface. We adopt a ‘pull-and-push’ strategy for near-surface charge manipulation using the strong local electric field of an atomic force microscope tip. Our technique is particularly effective for extremely shallow nitrogen vacancy centres, increasing their spin echo time by up to 20 fold. This corresponds to an 80-fold enhancement in the potential sensitivity for detecting individual external proton spins. Our work not only represents a step towards overcoming a fundamental restriction to applications of shallow nitrogen vacancy centres for quantum sensing but may also provide a general route for enhancing the coherence of solid-state qubits.

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Fig. 1: The ‘pull-and-push’ strategy for charge manipulation near the NV by using the local electric field of an AFM tip.
Fig. 2: The coherence enhancement after charge manipulation.
Fig. 3: Noise analyses using DEER and the spectral decomposition technique.
Fig. 4: Demonstration of the improved sensitivity of the manipulated NV for quantum sensing.

Data availability

Source data that support the findings of this study are available with this paper. All other data that support the plots within this paper are available from the corresponding authors upon reasonable request. Source data are provided with this paper.

Code availability

The custom codes for fitting the data are available from the corresponding authors upon reasonable request.

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Acknowledgements

We thank F. Giessibl for his valuable help on qPlus-based AFM under ambient condition. This work was supported by the National Key R&D Program under grant nos. 2021YFA1400500 and 2017YFA0205003, the National Natural Science Foundation of China under grant nos. 11888101 and 21725302 and the Strategic Priority Research Program of the Chinese Academy of Sciences under grant no. XDB28000000. Y.S. and S.Y. were supported by Hong Kong RGC (GRF/14304618). R.S., A.D. and J.W. were supported by the ERC grant SMeL and the VW Foundation.

Author information

Authors and Affiliations

Authors

Contributions

Y.J. and S.Y. designed and supervised the project. K.B. constructed the experimental setup. R.S. and A.D. grew the diamond chips and fabricated the shallow NVs. W.Z. and K.B. performed the experiments and data acquisition. W.Z., K.B., X.C., Y.S., S.C., J.W., S.Y. and Y.J. performed the data analysis and interpretation. K.B., S.Y. and Y.J. wrote the article, with input from all other authors. All the authors commented on the final article.

Corresponding authors

Correspondence to Ke Bian, Sen Yang or Ying Jiang.

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The authors declare no competing interests.

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Nature Physics thanks Helena Knowles and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Suitable tip position for T2 enhancement in ‘pushing’ step.

a, The confocal mapping when a negatively biased tip is scanned over a single shallow NV centre. The dark disk-like feature corresponds to NV+ state, caused by the strong tip-induced upward band bending effect. Scale bar: 500 nm. Laser power: 30 μW. Tip bias: −220 V. b, Schematic diagram showing the tip-induced band bending effect. When the tip is laterally close to NV within 300 nm, the large upward band bending effect induced by the negatively biased tip leads to NV+ state. The charge transition levels of NV+/NV0 and NV0/NVˉ are denoted by the short blue and red lines, respectively. The charge transition level of paramagnetic spins is denoted by the purple line. EF is the Fermi level, EC and EV denote the edges of the conduction and valance bands, respectively. c,d, Spin-echo mapping of one NV centre in the ‘pushing’ step under the tip bias of −100 V and −150 V, respectively, by fixing the delay time of spin-echo measurements. The images were expanded from 20 × 20 pixels to 40 × 40 pixels through the interpolation. The white disc denotes the position of NV. A grey arrow denotes the scanning direction, along which an overall decay of spin-echo signal was observed due to the thermal drift during the 6-hours imaging. The ‘hot’ regions demonstrating the longer T2 time are highlighted by the dashed curves. Scale bar: 400 nm. e, The T2 measurements at different positions in c. At every position denoted by the alphabets in c, we applied spin-echo measurements at full time range and fitted the T2. The dashed horizontal line denotes the original T2. The variation of T2 in e indicates the suitable tip position for enhancing the T2 under the ‘pushing’ step.

Source data

Extended Data Fig. 2 DEER spectra for depth calibration of shallow NVs.

a, Schematics showing the principle of DEER measurement. An extra π-pulse is applied at the middle of the spin-echo sequence, flipping the surrounding electron spins. Thus, the magnetic field from electron spins is sensed by the NV centre. b, Typical results of DEER spectra and spin-echo of a single shallow NV. Additional decoherence caused by the electron spins obviously appears in the DEER. c, Normalized DEER spectra for eliminating unwanted oscillations and peaks caused by the 13C residual spins or misalignment of biased magnetic field. d, Two typical normalized DEER spectra demonstrated in log-log plot of two shallow NV centres. The transition time is clearly observed, which reflects the depth of the NV centres. The dashed and dotted lines represent the powers of 2 and 2/3, respectively. e, The graph summarizing seven measured NV centres, which shows a positive relation between T2 and the depth. The red curve is used for guiding the eyes.

Source data

Extended Data Fig. 3 Transition time in log-log plot of DEER spectra before and after the coherence enhancement.

The DEER spectra of single NV demonstrated in the log-log plot showing the change of the transition time from ~21 μs to 64 μs before and after the charge manipulation. The coherence time was enhanced from 57 ± 3 μs up to 151 ± 5 μs. The dashed and dotted lines represent the powers of 2 and 2/3, respectively. In the model of configurational averaged surface spins, the transition time at which the DEER curve begins to demonstrate stretched exponential decay should be only sensitive to the depth of NV, regardless of the density of surface spins34. However, there should be subsurface electron spins such as P1 centre and charged vacancies induced by the ion implantation, which would also contribute to the decoherence and DEER signals of shallow NVs. Such subsurface spins may be located between the NV and the diamond surface, hence, the change of transition time indicates a changed distribution of the subsurface spins.

Source data

Extended Data Fig. 4 Sensitivity enhancement for proton detection.

a, Schematics showing the principle of detecting external protons by single NV centre. An ensemble of protons within the detecting volume (highlighted) contribute signals. b, The calculated sensitivity of single NV and its dependence on according to the Equation 5. The detected field strength \(B_{{{{\mathrm{rms}}}}}^2\) is chosen to be fitted from the red curve in d. The grey curve shows the corresponding signal contrast calculated by the Equation 4. The blue curve shows the sensitivity calculated based on the approximation of tiny signal contrast (Supplementary Text 5). Only within the region of small signal contrast (highlighted), the red and blue curve show good consistence. For simplicity, both the sensitivity and signal contrast were calculated by setting \(C(n\tau )\)=1. c, Spin-echo measurements of a very shallow NV showing T2 enhancement of ~20 fold with our method. d, XY8-2 (blue curve) and XY8-12 (red curve) measurements of the same NV in c showing that after ‘pull-and-push’ method, such a quantum sensor with poor coherence can be used for detecting external protons, with the capability of detecting a minimum magnetic variance corresponding to ~0.18 protons. The red curve is offset for clarity. The external magnetic field is 303 Gauss.

Source data

Extended Data Fig. 5 Laser power dependence of surface polarization.

The fluorescence of one shallow NV centre under varied laser power with tip bias of +50 V (red points). The NVˉ completely coverts into NV+ at ~100 μW, which can be considered as a criterion for the degree of surface polarization. Assuming that there is no geometric change in the gaussian-like focus spot at different laser power, this transition laser power can be used for the estimation of polarized area. For example, considering the typical size of our laser focus and the power used during the ‘pulling’ step, we can estimate a polarized area of ~ 265 × 265 nm2 under a laser power of ~300 μW and a tip bias of +50 V. Inset: the schematics showing the process of surface polarization described in Methods. When polarizing the surface, we fixed the laser focus on one NV centre and scanned the tip with positive bias around it.

Source data

Supplementary information

Supplementary information

Supplementary Texts 1–7, Table 1, Figs. 1–7 and refs. 1–16.

Source data

Source Data Fig. 1

Raw data for Fig. 1c.

Source Data Fig. 2

Raw data for Fig. 2a–c.

Source Data Fig. 3

Raw data for Fig. 3b,c.

Source Data Fig. 4

Raw data for Fig. 4b–e.

Source Data Extended Data Fig. 1

Raw data for Extended Data Fig. 1a,c,d,e.

Source Data Extended Data Fig. 2

Raw data for Extended Data Fig. 2b–e.

Source Data Extended Data Fig. 3

Raw data for Extended Data Fig. 3.

Source Data Extended Data Fig. 4

Raw data for Extended Data Fig. 4c,d.

Source Data Extended Data Fig. 5

Raw data for Extended Data Fig. 5.

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Zheng, W., Bian, K., Chen, X. et al. Coherence enhancement of solid-state qubits by local manipulation of the electron spin bath. Nat. Phys. 18, 1317–1323 (2022). https://doi.org/10.1038/s41567-022-01719-4

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