Phonon-Induced Population Dynamics and Intersystem Crossing in Nitrogen-Vacancy Centers

M. L. Goldman, A. Sipahigil, M. W. Doherty, N. Y. Yao, S. D. Bennett, M. Markham, D. J. Twitchen, N. B. Manson, A. Kubanek, and M. D. Lukin

Phys. Rev. Lett. 114, 145502 – Published 8 April 2015

Abstract

We report direct measurement of population dynamics in the excited state manifold of a nitrogen-vacancy (NV) center in diamond. We quantify the phonon-induced mixing rate and demonstrate that it can be completely suppressed at low temperatures. Further, we measure the intersystem crossing (ISC) rate for different excited states and develop a theoretical model that unifies the phonon-induced mixing and ISC mechanisms. We find that our model is in excellent agreement with experiment and that it can be used to predict unknown elements of the NV center’s electronic structure. We discuss the model’s implications for enhancing the NV center’s performance as a room-temperature sensor.

Received 13 June 2014

DOI:https://doi.org/10.1103/PhysRevLett.114.145502

Authors & Affiliations

M. L. Goldman^1,*, A. Sipahigil¹, M. W. Doherty², N. Y. Yao¹, S. D. Bennett¹, M. Markham³, D. J. Twitchen³, N. B. Manson², A. Kubanek¹, and M. D. Lukin¹

¹Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
²Laser Physics Centre, Research School of Physics and Engineering, Australian National University, Australian Capital Territory 0200, Australia
³Element Six Ltd, Kings Ride Park, Ascot SL5 8BP, United Kingdom

^*mgoldman@physics.harvard.edu

State-selective intersystem crossing in nitrogen-vacancy centers

M. L. Goldman, M. W. Doherty, A. Sipahigil, N. Y. Yao, S. D. Bennett, N. B. Manson, A. Kubanek, and M. D. Lukin

Phys. Rev. B 91, 165201 (2015)

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Vol. 114, Iss. 14 — 10 April 2015

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Figure 1
The level structure of the NV center. (a) A schematic illustration of the NV center’s level structure. The intersystem crossing (ISC) process is responsible for shelving into $|^{1} E_{1, 2} ⟩$ via the short-lived $|^{1} A_{1} ⟩$ and for pumping into $| 0 ⟩$ . (b) The three-level system of spin-triplet, $m_{s} = 0$ states used to model phonon-induced mixing and dephasing within the ${}^{3}E$ manifold. (c) The states, Hamiltonian matrix elements ( $λ_{E_{1, 2}}$ , $λ_{⊥}$ ), and energy scales ( $Δ$ , $Δ^{'}$ ) involved in the triplet-singlet ISC.
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Figure 2
Phonon-induced mixing between the $| E_{x} ⟩$ and $| E_{y} ⟩$ electronic orbital states. (a) The measured $Γ_{Add} = Γ_{Mix} + Γ_{T_{2}}$ as a function of temperature, with a fit to $Γ_{Add} \propto T^{5}$ [16]. The shaded region is the 95% confidence interval and the inset shows Rabi oscillations on the $| 0 ⟩ \to | E_{x} ⟩$ transition measured at three temperatures, offset for clarity. (b) Background-subtracted fluorescence of $x$ (red) or $y$ (blue) polarization collected after resonant excitation to $| E_{x} ⟩$ . Data were taken at $T = 5.0 K$ (solid lines) and $T = 20 K$ (dashed lines). The fits are simulations to the three-level system depicted in Fig. 1 [16].
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Figure 3
ISC rates from the ${}^{3}E$ triplet excited states. The inset shows the measured PSB fluorescence collected after excitation to $| A_{1} ⟩$ , $| A_{2} ⟩$ , and $| E_{1, 2} ⟩$ measured at $T \sim 5 K$ , normalized to a common peak height and fit to an exponential decay curve. The blue and red bands are fits with 95% confidence intervals to the phonon-induced mixing model described in the text, and the purple and green lines are placed at the mean values of the corresponding data sets.
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Figure 4
The results of the ISC model. (a) The range (blue shading) of predicted values of $Γ_{A_{1}}$ corresponding to the range of possible values of $λ_{⊥}$ . The orange line is the measured value of $Γ_{A_{1}}$ , the black region indicates our extracted value of $Δ$ (the $| A_{1} ⟩ - |^{1} A_{1} ⟩$ energy spacing), and the red region indicates the values of $Δ$ that are excluded by the measured $Γ_{E_{1, 2}} / Γ_{A_{1}}$ ratio. (b) The predicted (blue) and measured (orange) $Γ_{E_{1, 2}} / Γ_{A_{1}}$ ratio. Because we assume no acoustic phonon cutoff, the blue plot represents an upper bound on the ratio for a given $Δ$ . We can therefore exclude the values of $Δ$ indicated by the red region, which is reproduced in (a). (c) The lifetimes of the $m_{s} = 0$ (green) and $| m_{s} | = 1$ (purple) states predicted for a range of temperatures. The data from 295 to 700 K are taken from Refs. [10] (open square and open circle), [9] (open diamond), and [8] (downward triangle).
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