Multiple-Quantum Transitions and Charge-Induced Decoherence of Donor Nuclear Spins in Silicon

We study single- and multiquantum transitions of the nuclear spins of an ensemble of ionized arsenic donors in silicon and find quadrupolar effects on the coherence times, which we link to fluctuating electrical field gradients present after the application of light and bias voltage pulses. To determine the coherence times of superpositions of all orders in the 4-dimensional Hilbert space, we use a phase-cycling technique and find that, when electrical effects were allowed to decay, these times scale as expected for a fieldlike decoherence mechanism such as the interaction with surrounding ${}^{29}\mathrm{Si}$ nuclear spins.

Figure 1

(a) Energy levels of the nuclear spin of ionized donors ${\mathrm{As}}^{+}$ in Si with and without an electric field gradient caused by a strain $\epsilon$. (b) Schematic representation of the sample and the interdigit contact structure. (c) Schematic representation of the ENDOR pulse sequence used in this work. Examples for manipulation pulse sequence are given on top of (d) and (e). Echo decays of a satellite SQT (d) for a $500\text{−}\mu \mathrm{s}$-long light pulse and $t_{\text{space}}=0.5$, 2.5, 20, 80, and 950 ms and (e) for a $500\text{−}\mu \mathrm{s}$-long combined light and bias voltage pulse and $t_{\text{space}}=0.5$, 2.5, 10, 80, 300, and 950 ms. Solid lines represent fits with superexponential decays ($\alpha =2$).

Figure 2

(a) Coherence times $T_2^{\text{sSQT}}$ resulting from the measurements shown in Figs. 1 and 1. (b) Scaling of $T_2$ with the number of refocusing pulses $n$ in a Carr-Purcell sequence (dc voltage data reproduced from Ref. [13]). The straight lines are guides to the eye.

Figure 3

Timeline (a) and schematic illustration (b) of our model of the charge-induced decoherence process. After the application of light or light-voltage pulses (i), charge recombination leads to fluctuating field gradients [high $d{V}_{33}/dt$, (ii)]. Quadrupolar decoherence effects are hence strong, leading to a short $T_2^{\text{sSQT}}$. Once a stable charge environment is reached, this effect vanishes and $T_2^{\text{sSQT}}$ is increased (iii). For details, see text.

Figure 4

(a) Summary of the time evolution frequencies $\mathrm{\Delta }{\nu }_{ij}$ of the density matrix elements. (b) Echo amplitude as a function of the phase of the second pulse of the nuclear spin echo sequence. (c) Fourier transform, showing the contributions of different coherence transfer paths to the echo signal. For details see text. (d) Echo decays for the SQT ($\mathrm{\Delta }p=\pm 2$), DQT ($\mathrm{\Delta }p=\pm 4$), and TQT ($\mathrm{\Delta }p=\pm 6$) signals for a waiting time $t_{\text{space}}=1\mathrm{s}$. The solid lines are fits with exponential functions.