The application of rare earth (RE) doped crystals in quantum information processing has attracted more and more attention in the past decade. How to change the clock transitions of RE ion in crystal and control their lifetime of maintaining coherent quantum state is a valuable question. In this work, the trigonal 171Yb3+ centers in lithium niobate (LN) crystal are investigated theoretically to obtain their accurate ground and excited hyperfine sublevels under external magnetic field B by a combined method of density functional theory-based geometric optimization and parametric effective Hamiltonian modeling. An optical clock transition at |B| = 45.73 mT along the c axis of the LN crystal is successfully found by calculation. To show the pressure-dependent behavior of optical clock transition, the variation of such transition under hydrostatic pressure up to 3 GPa is also obtained theoretically. The calculated results show that applying external pressure is an effective way to control these transitions of RE ion doped crystal. Moreover, the optical coherence time T2 at zero magnetic field for 171Yb3+ ion with C3 symmetry in the LN crystal is estimated by our calculations. The calculated results indicate that if the magnetic field noise is 33 μT in the LN crystal, it is possible to find an optical clock transition with long coherence time T2 (≈382 μs) at the zero magnetic field. The present methods of seeking optical clock transition and calculating its coherence time T2 caused by a fluctuating magnetic field noise in the host crystal can be applied to other Kramers RE ions doped materials.
The application of rare earth (RE) doped crystals in quantum information processing has attracted more and more attention in the past decade. How to change the clock transitions of RE ion in crystal and control their lifetime of maintaining coherent quantum state is a valuable question. In this work, the trigonal 171Yb3+ centers in lithium niobate (LN) crystal are investigated theoretically to obtain their accurate ground and excited hyperfine sublevels under external magnetic field B by a combined method of density functional theory-based geometric optimization and parametric effective Hamiltonian modeling. An optical clock transition at |B| = 45.73 mT along the c axis of the LN crystal is successfully found by calculation. To show the pressure-dependent behavior of optical clock transition, the variation of such transition under hydrostatic pressure up to 3 GPa is also obtained theoretically. The calculated results show that applying external pressure is an effective way to control these transitions of RE ion doped crystal. Moreover, the optical coherence time T2 at zero magnetic field for 171Yb3+ ion with C3 symmetry in the LN crystal is estimated by our calculations. The calculated results indicate that if the magnetic field noise is 33 μT in the LN crystal, it is possible to find an optical clock transition with long coherence time T2 (≈382 μs) at the zero magnetic field. The present methods of seeking optical clock transition and calculating its coherence time T2 caused by a fluctuating magnetic field noise in the host crystal can be applied to other Kramers RE ions doped materials.
Clock transitions play an important role in extending the coherence time of rare-earth (RE) ion-doped crystals. It is still a challenge to accurately obtain the hyperfine structure of these crystals to determine their clock transitions and establish a proper solid-state quantum memory system. In this work, a nonspin-Hamiltonian method combining density functional theory (DFT)-based geometric optimization and effective Hamiltonian is utilized to obtain the hyperfine sublevels and clock transitions under an external magnetic field for the Kramers RE ion in crystals. To show clearly, the 173 Yb 3+:Y 2 SiO 5 crystal is first investigated to demonstrate that the complicated hyperfine structure of the Kramers RE ion can be correctly calculated by the complete diagonalization (of energy) matrix (CDM) formalism. Second, optical and angular-dependent electron paramagnetic resonance (EPR) spectra of the 171 Yb 3+:Lu 2 Si 2 O 7 crystal are studied by fitting calculations based on the DFT-optimized geometric structure. By reliable fitting parameters, the external magnetic field at clock transitions is determined successfully. Such two case studies indicate that the hyperfine structure and clock transitions of the Kramers RE ion in the crystal can be accurately predicted by the present approach. This is very useful for designing and searching practical RE-based quantum memory materials with longer optical or spin coherence time.
Various spectroscopic properties of Yb 3+ -doped Y 2 SiO 5 crystal have been extensively investigated due to its promising application in quantum information processing. However, the local structure, electronic structure of Yb 3+:Y 2 SiO 5 crystal, and its optical and magnetic properties have not been comprehensively studied from a theoretical viewpoint. In this work, the geometric and electronic structures of Yb 3+ that replaces two crystallographic Y 3+ sites in the Y 2 SiO 5 crystal are first obtained by the method of density functional theory (DFT). Then, the optical, electron paramagnetic resonance (EPR), and optically detected magnetic resonance (ODMR) spectra for 171 Yb 3+ (nuclear spin I = 1/2) at such two sites are simultaneously calculated in the framework of the complete diagonalization (of energy) matrix (CDM) based on the optimized local structure around 171 Yb 3+ ion by DFT. The various calculated spectroscopic properties by such combined theoretical approach are consistent with the experimental ones, which demonstrates that CDM is effective and particularly suitable for calculating hyperfine A -tensors under zero, low, and intermediate magnetic field. More importantly, based on the obtained accurate hyperfine structure of 171 Yb 3+ in Y 2 SiO 5 crystal, the possible “clock transitions”, which can enhance the optical coherence time, can be assigned or predicted by the present approach. This study successfully explains the spectroscopic properties of 171 Yb 3+ -doped Y 2 SiO 5 and provides a feasible method to design and search for practical rare-earth-doped quantum information materials for the community.
Rare-earth ion-doped crystals are promising systems for quantum communication and quantum information processing. In particular, paramagnetic rare-earth centers can be utilized to realize quantum coherent interfaces simultaneously for optical and microwave photons. In this paper, we study hyperfine and magnetic properties of a Y2SiO5 crystal doped with 171Yb3+ ions. This isotope is particularly interesting since it is the only rare--earth ion having electronic spin S=21 and nuclear spin I=21, which results in the simplest possible hyperfine level structure. In this work, we determine the hyperfine tensors for the ground and excited states on the optical $^{2}\mathrm{F}_{7/2}(0)\ensuremath{\longleftrightarrow}^{2}\mathrm{F}_{5/2}(0)$ transition by combining spectral hole burning and optically detected magnetic resonance techniques. The resulting spin Hamiltonians correctly predict the magnetic-field dependence of all observed optical-hyperfine transitions, from zero applied field up to fields where the Zeeman interaction is dominating the hyperfine interaction. Using the optical absorption spectrum, we can also determine the order of the hyperfine levels in both states. These results pave the way for realizing solid-state optical and microwave quantum memories based on a 171Yb3+:Y2SiO5 crystal.
The influence of magnetic interactions in rare-earth-doped crystals under an external magnetic field has been studied in order to obtain an efficient three-level $\ensuremath{\Lambda}$ system with the hyperfine levels of the rare earth. Nuclear Zeeman effect under the action of an external magnetic field removes the nuclear degeneracy. This interaction does not provide an efficient $\ensuremath{\Lambda}$ system because nuclear-spin flipping such as $\ensuremath{\mid}{M}_{I}⟩=\ifmmode\pm\else\textpm\fi{}\frac{1}{2}\ensuremath{\rightarrow}\ensuremath{\mid}{M}_{I}⟩=\ensuremath{\mp}\frac{1}{2}$ (MI is the nuclear-spin projection) cannot be induced by an optical transition. However, this selection rule only applies to pure nuclear Zeeman effect. Indeed, it is shown that the coupling of the electronic Zeeman and of the hyperfine interactions releases the nuclear-spin selection rules $\ensuremath{\Delta}{M}_{I}=0$. This can be described in terms of a pseudonuclear Zeeman effect induced by an effective magnetic field. The relative strengths of the two optical transitions involved in the three-level system can be controlled by the orientation of the external magnetic field. The particular case of the Tm3+ ion in the Y3Al5O12 host (YAG) is discussed. Tm3+ hyperfine structure is determined using a complete Hamiltonian including free-ion, crystal-field, and magnetic interactions. A good three-level $\ensuremath{\Lambda}$ system is obtained in Tm:YAG with a transition strength ratio of 0.24 $(\ensuremath{\sim}1:4)$ between the two optical transitions. An analytical analysis based on a spin-Hamiltonian approach is proposed to explain the results of the complete crystal-field calculations. Finally, an experimental protocol that makes a crystal similar to the atomic samples used in previous quantum information investigations, with the additional benefits of absence of motion and long coherence time, is described.
Rare-earth doped insulators have been widely recognized as excellent candidate materials for optical quantum computing and information processing. This is principally due to a combination of optical coherence times of up to milliseconds and ground-state hyperfine coherence times of seconds exhibited by rare-earth 4𝑓 𝑁 states. A key contender among rare-earth doped materials is Er3+:Y2SiO5, for which homogeneous linewidths as narrow as 50 Hz have been reported, and for which transitions between the ground and first excited states fall within the 1.5 𝜇m telecommunications wavelength band. However, attempts to utilize this material for spin-wave storage have been hampered by the complexity of the excited-state hyperfine structure, which inhibits the necessary theoretical work required to predict the location of zero first-order zeeman transitions. To address this, a novel crystal-field fitting method was developed to allow an accurate analysis of the 𝐶1 point-group symmetry sites of Y2SiO5. This work was complemented with spectral hole-burning spectroscopy, which revealed ground-state hyperfine level storage with a lifetime of 1.6 ± 0.4 seconds for the 4I15/2𝑍1 → 4F9/2𝐷1 transition. This type of storage time is uncharacteristic for erbium without an external magnetic field, since spin-flips of the unpaired electron in nearby Er3+ ions are typically understood to lead to fast hole filling. The development process of the theoretical and experimental tools required to perform the above work enabled several additional investigations. In particular, the novel crystal-field fitting methods were applied to the 𝑆4 site of Ce3+:LiYF4 and to the 𝐶2𝑣 site of Sm3+:Na+/Li+:CaF2/SrF2. These studies consisted of excellent tests for the developed methods yet also amounted to interesting investigations in their own respect. Similarly, the experimental work afforded an opportunity to directly determine the hyperfine splittings of the 5I8𝑍1 → 5F5𝐷1 transition in Ho3+:KY3F10. This was achieved using high-resolution excitation spectroscopy. Furthermore, the experimentally determined hyperfine structure could be accurately reproduced using a crystal field model. Finally, a lifetime measurement of the 6H7/2 state of Sm3+:LiYF4 was conducted. By utilizing an infrared free-electron laser, pico-second pump-probe spectroscopy allowed for a direct measurements of one of the shortest lifetimes of an RE3+ doped insulator reported in the literature to date. This confirmed the previously suggested two-gradient modification required for the energy-gap law at very short time scales.
Recent progress in the realization of high-quality optical resonators and waveguides along with the possibility to incorporate rare-earth ions, make lithium niobate a promising material to build integrated platforms for quantum information processing. 171Yb3+ is a particularly attractive system because it can show long coherence lifetimes at zero magnetic field thanks to transitions insensitive to magnetic field fluctuations. In this paper, we investigate the optical and spin properties of 171Yb3+ ions in LiNbO3 bulk crystals as well as implanted waveguides. Using hole-burning spectroscopy and optically detected magnetic resonance, we studied ground and excited state hyperfine structures and probed optical and spin spectral holes. Importantly, the hole linewidths suggest that part of the ions in the waveguides are in a similar environment as in the bulk sample. We furthermore characterized spin population relaxation and coherence lifetimes of 171Yb3+ ions in the bulk crystal at temperatures between 50 mK and 9 K. At low temperatures, T2 up to 9.5 $\ensuremath{\mu}\mathrm{s}$ (34 kHz homogeneous linewidth) and spin relaxation rates as long as $\ensuremath{\approx}100$ ms were measured. Our results show that 171Yb3+:LiNbO3 is a system that exhibits narrow optical homogeneous linewidths over a 50 GHz bandwidth together with an electron spin degree of freedom. This is of interest for a variety of applications in integrated quantum photonics such as quantum memories or quantum processors.