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arXiv:1208.1622 · Physical Review B

Spin coherence lifetime extension in Tm 3 + :YAG through dynamical decoupling

M. F. Pascual-Winter, R.-C. Tongning, T. Chanelière, J.-L. Le Gouët

Published Nov 6, 2012• 31 citations
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Abstract

We report on spin coherence lifetime extension in Tm${}^{3+}$:YAG obtained through dynamically decoupling the thulium spins from their magnetic environment. The coherence lifetime reached with a Carr-Purcell-Meiboom-Gill sequence revealed a 450-fold extension [$\ensuremath{\sim}$$(230\ifmmode\pm\else\textpm\fi{}30)$ ms] with respect to previously measured values. Comparison to a simple theoretical model allowed us to estimate the correlation time of the fluctuations of the ground-level transition frequency to $(172\ifmmode\pm\else\textpm\fi{}30)$ $\ensuremath{\mu}$s at 1.7 K. For attaining efficient decoupling sequences, we developed a strategy inspired by the zero-first-order Zeeman effect to minimize the large inhomogeneous broadening of the ground-level spin transition.

DOI
10.1103/physrevb.86.184301

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We report on spin coherence lifetime extension in Tm3+{}^{3+}3+:YAG obtained through dynamically decoupling the thulium spins from their magnetic environment. The coherence lifetime reached with a Carr-Purcell-Meiboom-Gill sequence revealed a 450-fold extension [\ensuremath{\sim}$$(230\ifmmode\pm\else\textpm\fi{}30) ms] with respect to previously measured values. Comparison to a simple theoretical model allowed us to estimate the correlation time of the fluctuations of the ground-level transition frequency to (172\ifmmode±\else\textpm\fi30)(172\ifmmode\pm\else\textpm\fi{}30)(172\ifmmode±\else\textpm\fi30) \ensuremathμ\ensuremath{\mu}\ensuremathμs at 1.7 K. For attaining efficient decoupling sequences, we developed a strategy inspired by the zero-first-order Zeeman effect to minimize the large inhomogeneous broadening of the ground-level spin transition.
We investigate the scaling of coherence time T2{T}_{2}T2​ with the number of $\ensuremath{\pi}$ pulses ${n}_{\ensuremath{\pi}}$ in a singlet-triplet spin qubit using Carr-Purcell-Meiboom-Gill (CPMG) and concatenated dynamical decoupling (CDD) pulse sequences. For an even numbers of CPMG pulses, we find a power law ${T}_{2}\ensuremath{\propto}({n}_{\ensuremath{\pi}}{)}^{{\ensuremath{\gamma}}_{e}}$, with ${\ensuremath{\gamma}}_{e}=0.72\ifmmode\pm\else\textpm\fi{}0.01$, essentially independent of the envelope function used to extract T2{T}_{2}T2​. From this surprisingly robust value, a power-law model of the noise spectrum of the environment, $S(\ensuremath{\omega})\ensuremath{\sim}{\ensuremath{\omega}}^{\ensuremath{-}\ensuremath{\beta}}$, yields $\ensuremath{\beta}={\ensuremath{\gamma}}_{e}/(1\ensuremath{-}{\ensuremath{\gamma}}_{e})=2.6\ifmmode\pm\else\textpm\fi{}0.1$. Model values for ${T}_{2}\left({n}_{\ensuremath{\pi}}\right)$ using $\ensuremath{\beta}=2.6$ for CPMG with both even and odd ${n}_{\ensuremath{\pi}}$ up to 32 and CDD orders 3 through 6 compare very well with the experiment.
We report a low-temperature spectroscopic characterization of the ground-state hyperfine transitions in 151Eu3+:Y2SiO5{}^{151}\mathrm{Eu}{}^{3+}{\mathrm{:Y}}_{2}{\mathrm{SiO}}_{5}151Eu3+:Y2​SiO5​ via coherent Raman scattering. Inhomogeneous linewidths of 21 and 38 kHz were measured for the ${I}_{z}=\ifmmode\pm\else\textpm\fi{}\frac{1}{2}$ $\ensuremath{\leftrightarrow}$ $\ifmmode\pm\else\textpm\fi{}\frac{3}{2}$ and the $\ifmmode\pm\else\textpm\fi{}\frac{3}{2}$ $\ensuremath{\leftrightarrow}$ $\ifmmode\pm\else\textpm\fi{}\frac{5}{2}$ ground-state transitions, respectively. Spin-echo decays were recorded for the ${I}_{z}=\ifmmode\pm\else\textpm\fi{}\frac{1}{2}$ $\ensuremath{\leftrightarrow}$ $\ifmmode\pm\else\textpm\fi{}\frac{3}{2}$ transition at zero field and for a small static magnetic field. In the latter case, analysis by a simple model gave an amplitude of 284 Hz and a correlation time of 3.5 ms for the transition frequency fluctuations. Application of a dynamical decoupling sequence resulted in coherence lifetimes up to 474 ms, an 18-fold increase compared to the spin intrinsic phase memory time of 26 ms.
Long coherence times are an essential prerequisite for implementations of quantum information technology. This requires techniques to control perturbing processes and hence prolong coherence times in quantum systems. In our work, we present systematic experimental investigations on prolongation of spin coherence times in a rare-earth ion-doped crystal. The approach is based on a combination of established coherence control techniques (i.e., zero first-order Zeeman shifts and simple dynamical decoupling), supported by automatic optimization of experimental control parameters, as well as precise characterization of the optimization loop and the strongly modified complex level structure by spin echoes and high-resolution Raman heterodyne spectroscopy. The spin-echo and Raman heterodyne data clearly prove successful optimization towards proper conditions of zero first-order Zeeman shifts, finally yielding a coherence time of 1 min, i.e., close to the theoretical limit set by the population lifetime in Pr3+{\text{Pr}}^{3+}Pr3+:Y2{\text{Y}}_{2}Y2​SiO5{\text{SiO}}_{5}SiO5​.
We obtained a long-time-storage mechanism for spectral features in thulium ions doped into YAG by applying a magnetic field that splits the electronic ground state. We show experimentally that the storage time can be more than 30 s, which is 3 orders of magnitude longer than that of the metastable state that normally is used for information storage in this material. Level splitting and storage lifetimes for various magnetic field strengths of as much as 5 T were investigated. This storage mechanism will be relevant in the many coherent transient-based signal-processing schemes in which Tm:YAG is being used, and we demonstrate long-time storage in a basic data storage application.
We demonstrate the use of dynamic decoupling techniques to extend the coherence time of a single memory qubit by nearly two orders of magnitude. By extending the Hahn spin-echo technique to correct for unknown, arbitrary polynomial variations in the qubit precession frequency, we show analytically that the required sequence of π-pulses is identical to the Uhrig dynamic decoupling (UDD) sequence. We compare UDD and Carr–Purcell–Meiboom–Gill (CPMG) sequences applied to a single 43 Ca + trapped-ion qubit and find that they afford comparable protection in our ambient noise environment.