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arXiv:1009.4346 · Physical Review B

Adiabatic refocusing of nuclear spins in Tm 3+ :YAG

Romain Lauro, T. Chanelière, J.-L. Le Gouët

Published Jan 24, 2011• 16 citations
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Abstract

We show that the optical absorbance detection of nuclear spin echo gives direct access to the spin concentration, unlike most coherent signal detection techniques where the signal intensity/amplitude is difficult to connect experimentally with the spin concentration. This way we measure the spin-refocusing efficiency in a crystal of Tm${}^{3+}$:YAG. Given the large inhomogeneous broadening of the spin transition in this material, rephasing the spins with the usual hard pulse procedure would require excessively high radiofrequency power. Instead we resort to an adiabatic pulse sequence that perfectly returns the spins to their initial common orientation, at low power cost.

DOI
10.1103/physrevb.83.035124

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We show that the optical absorbance detection of nuclear spin echo gives direct access to the spin concentration, unlike most coherent signal detection techniques where the signal intensity/amplitude is difficult to connect experimentally with the spin concentration. This way we measure the spin-refocusing efficiency in a crystal of Tm3+{}^{3+}3+:YAG. Given the large inhomogeneous broadening of the spin transition in this material, rephasing the spins with the usual hard pulse procedure would require excessively high radiofrequency power. Instead we resort to an adiabatic pulse sequence that perfectly returns the spins to their initial common orientation, at low power cost.
In low-concentration Tm3+{}^{3+}3+:YAG, we observe efficient adiabatic rapid passage (ARP) of thulium nuclear spin over flipping times much longer than T2{T}_{2}T2​. Efficient ARP with long flipping time has been observed in monoatomic solids for decades and has been analyzed in terms of spin temperature and of the thermodynamic equilibrium of a coupled spin ensemble. In low-concentration impurity-doped crystals the spin temperature concept may be questioned. A single spin model should be preferred since the impurity ions are weakly coupled together but interact with the numerous off-resonant matrix ions that originate the spin-spin relaxation. The experiment takes place in the context of quantum information investigation, involving impurity-doped crystals, spin hyperpolarization by optical pumping, and optical detection of the spin evolution.
We report on the experimental demonstration of stimulated Raman adiabatic passage in a Tm3+:YAG{\text{Tm}}^{3+}:\text{YAG}Tm3+:YAG crystal. Tm3+:YAG{\text{Tm}}^{3+}:\text{YAG}Tm3+:YAG is a promising material for use in quantum information processing applications, but as yet there are few experimental investigations of coherent Raman processes in this material. We investigate the effect of inhomogeneous broadening and Rabi frequency on the transfer efficiency and the width of the two-photon spectrum. Simulations of the complete Tm3+:YAG{\text{Tm}}^{3+}:\text{YAG}Tm3+:YAG system are presented along with the corresponding experimental results.
Coherence rephasing is an essential step in quantum storage protocols that use echo-based strategies. We present a thorough analysis on how two adiabatic rapid passages (ARPs) are able to rephase atomic coherences in an inhomogeneously broadened ensemble. We consider both optical and spin coherences, rephased by optical or radio-frequency (rf) ARPs, respectively. We show how a rephasing sequence consisting of two ARPs in a double-echo scheme is equivalent to the identity operator ( any state can be recovered), as long as certain conditions are fulfilled. Our mathematical treatment of the ARPs leads to a very simple geometrical interpretation within the Bloch sphere that permits a visual comprehension of the rephasing process. We also identify the conditions that ensure the rephasing, finding that the phase of the optical or rf ARP fields plays a key role in the ability of the sequence to preserve the phase of the superposition state. This settles a difference between optical and rf ARPs, since field phase control is not readily guaranteed in the former case. We also provide a quantitative comparison between π -pulse and ARP rephasing efficiencies, showing the superiority of the latter. We experimentally verify the conclusions of our analysis through rf ARP rephasing sequences performed on the rare-earth ion-doped crystal Tm 3+ :YAG, of interest in quantum memories.
Highly efficient two-pulse and stimulated photon echoes are experimentally demonstrated in an absorbing medium. Recall efficiencies of 235% and 150% with excellent signal contrast are measured for two-pulse and stimulated photon echoes, respectively, in a Tm:YAG crystal with an absorption length of 3.8. The reported efficiencies do not include any correction for decay or beam profile. We believe that this is the first demonstration of an uncorrected echo efficiency greater than 100% with good signal fidelity in an optically thick medium.
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 $(172\ifmmode\pm\else\textpm\fi{}30)$ $\ensuremath{\mu}$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.
Echo-based spectroscopy of the superhyperfine interaction of an electronic spin with nuclear spins in its surroundings enables detailed insights into the microscopic magnetic environment of spins in solids. Still, it is an outstanding challenge to resolve individual nuclear spins in a dense bath, in which many of them exhibit a comparable coupling strength. This simultaneously requires a high spectral resolution and a large signal-to-noise ratio. However, when probing spin ensembles, dipolar interactions between the dopants can lead to a concentration-dependent trade-off between resolution and signal. Here, we fully eliminate this limitation of previous optical-echo-envelope-modulation spectroscopy experiments by integrating the emitters into a high-finesse resonator, which allows for strong optical echoes even at very low concentrations. To demonstrate its potential, the technique is applied to erbium dopants in yttrium orthosilicate ( Er : YSO ). Achieving an unprecedented spectral resolution enables precise measurements of the superhyperfine interaction with four of the Y nuclear spins densely surrounding each emitter. The achieved boost of the signal, enabled by the resonator, allows for extending the approach to the lowest concentration possible—to the level of single dopants, thereby providing a tool for detecting and studying individual nuclear spins. Thus, our technique paves the way for an improved understanding of dense nuclear-spin baths in solids.