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arXiv:1203.3753 · Physical Review B

Adiabatic passage with spin locking in Tm 3+ :YAG

M. F. Pascual-Winter, R.-C. Tongning, Romain Lauro, Anne Louchet-Chauvet, T. Chanelière, J.-L. Le Gouët

Published Aug 6, 2012• 9 citations
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Abstract

In low-concentration Tm${}^{3+}$:YAG, we observe efficient adiabatic rapid passage (ARP) of thulium nuclear spin over flipping times much longer than ${T}_{2}$. 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.

DOI
10.1103/physrevb.86.064301

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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 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.
The spin relaxation dynamics of Ce3+{\mathrm{Ce}}^{3+}Ce3+ ions in heavily cerium-doped YAG crystals is studied using pulse-electron paramagnetic resonance and time-resolved pump-probe Faraday rotation. Both techniques address the 4f4f4f ground state, while pump-probe Faraday rotation also provides access to the excited 5d5d5d state. We measure a millisecond spin-lattice relaxation time T1{T}_{1}T1​, a microsecond spin coherence time T2{T}_{2}T2​, and a $\ensuremath{\sim}10$ ns inhomogeneous spin dephasing time T2∗{T}_{2}^{*}T2∗​ for the Ce3+{\mathrm{Ce}}^{3+}Ce3+ ground state at low temperatures. The spin-lattice relaxation of Ce3+{\mathrm{Ce}}^{3+}Ce3+ ions is due to modified Raman processes involving the optical phonon mode at $\ensuremath{\sim}\phantom{\rule{0.16em}{0ex}}125\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$. The relaxation at higher temperature goes through a first excited level of the 2F52^{2}\mathrm{F}_{\frac{5}{2}}2F25​​ term at about $\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{\approx}228\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$. Effects provided by the hyperfine interaction of the Ce3+{\mathrm{Ce}}^{3+}Ce3+ with the 27Al^{27}\mathrm{Al}27Al nuclei are observed.
Rare-earth-doped crystals have been used for optical signal processing and storage applications. In this dissertation, their potential for quantum computing applications is explored. In one quantum computing scheme, information is stored in nuclear spin states and this information is then processed by using optical pulses through the coupling of these nuclear spin states to a common electronic level. To implement this scheme, nuclear spin states and coupling of these nuclear spin states to a common electronic level is required. Preliminary work in rare-earth materials like Pr3+ and Eu3+ has shown promising results regarding their suitability for quantum computing applications. One particular problem with these materials is that their transition wavelengths are only accessible with dye lasers. These lasers are inherently unstable, and currently few available systems exhibit the stability required for quantum computing applications. An alternative choice was to investigate other rare-earth ions like thulium. Thulium has a transition wavelength that can be accessed with diode lasers, which are commercially available, easy to stabilize, and compact. This dissertation is based on our investigations of Tm3+:YAG for quantum computing applications. Investigations involved a detailed characterization of the material. Nuclear spin states, in Tm3+:YAG, were obtained by applying an external magnetic field to the sample. First, interaction of an external magnetic field with the thulium ions at various sites in the crystal was analyzed. This analysis was used to measure the magnetic anisotropy in the material. These results show that it is possible, with the suitable choice of the magnetic orientation and the site in the crystal, to build a working 3-level quantum system. In the demonstration of single qubit operations in Tm3+:YAG, we first theoretically studied the effect of Gaussian spatial beam on the single qubit operations. Later on, we experimentally prepared a single isolated ensemble of ions in the inhomogeneously broadened absorption profile of the medium. This single isolated ensemble of ions was used as a test-bed to implement the single qubit operations. We also isolated two ensembles of ions in the inhomogeneous absorption profile of the medium. The interaction between these two isolated ensembles of ions was also studied.
The frequency-field and orientation dependences of the electron paramagnetic resonance (EPR) spectra are measured for impurity Tm 3+ ions in yttrium orthosilicate (Y 2 SiO 5 ) single crystals by stationary EPR spectroscopy in the frequency range of 50–100 GHz at 4.2 K. The position of the impurity ion in the crystal lattice and its magnetic characteristics are determined. The temperature dependences of the spin–lattice and phase relaxation times are measured by pulse EPR methods in the temperature range of 5–15 K and the high efficiency of the direct single-phonon mechanism of spin–lattice relaxation is established. This greatly shortens the spin–lattice relaxation time at low temperatures and makes impurity Tm 3+ ions in Y 2 SiO 5 a promising basis for the implementation of high-speed quantum memory based on rare-earth ions in dielectric crystals.