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Physical Review A

Coherence time extension in Pr 3 + : Y 2 SiO 5 by self-optimized magnetic fields and dynamical decoupling

Georg Heinze, Christian Hubrich, Thomas Halfmann

Published May 15, 2014• 19 citations
Publisher

Abstract

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 ${\text{Pr}}^{3+}$:${\text{Y}}_{2}$${\text{SiO}}_{5}$.

DOI
10.1103/physreva.89.053825

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Development of Persistent Quantum Memories

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This thesis investigates the coherence properties of the hyperfine transitions of the 151Eu3+ ions in Eu3+:Y2SiO5 and evaluates the potential of developing quantum memories using these transitions. Quantum memories for light with long storage times are required for quantum commu- nication applications. For these memories to be useful they need to have storage times long compared to the transmission times across the communication network. For a global optical communication network this requires storage time longer than 100 ms. Rare-earth doped crystals have been identified as a suitable storage material. The storage time of these systems is limited by the coherence time of the hyperfine transitions of the optically active rare-earth ions. In previous work it had been demonstrated that coherence times as long as 1.4 seconds could be achieved for hyperfine transitions in Pr3+:Y2SiO5 by ap- plying a particular magnetic field such that the first order Zeeman shift of the transition nulled. This technique is known as zero first-order Zeeman (ZEFOZ). Due to the relatively large second order Zeeman efficient of the transitions in Pr3+:Y2SiO5, an extension of the coherence time, significantly beyond the 1.4 second mark using ZEFOZ, is not expected. However, it has been predicted that coherence times more than two orders of magnitude longer could be achieved in Eu3+:Y2SiO5 due to the smaller second order Zeeman shifts associated with the relevant hyperfine transitions. The dominant decoherence mechanism for the hyperfine transitions in diluted Eu3+:Y2SiO5 is the magnetic field perturbations caused by the random spin reconfigu- ration of the Y3+ ions in the host. By applying the ZEFOZ technique, previously used in Pr3+:Y2SiO5, the sensitivity of the transition’s frequency to environmental magnetic field perturbations was significantly reduced. Further, this strong ZEFOZ magnetic field was also shown to induce a frozen core around the Eu3+ ion, which resulted in a signifi- cant suppression of the reconfiguration of the nearby Y3+ spins. The combined effect of the reduced sensitivity and frozen core effect allowed a decoherence rate of 8 × 10−5 s−1 over 100 milliseconds to be demonstrated. The observed decoherence rate is at least an order of magnitude lower than that of any other system suitable for an optical quantum memory. Furthermore, by employing dynamic decoherence control, a coherence time of 370 ± 60 minutes was achieved. This 6 hour coherence time observed here opens up the possibility of distributing quantum entanglement via the physical transport of memories as an alternative to optical communications. It was found that even at the critical point alignment the observed coherence times showed that the Y3+ spin flips remain the dominant decoherence mechanism. To aid in the development of future strategies to further extend the coherence time beyond 6 hours, a study of the Y3+ spin dynamics in the frozen core was conducted. Four of the Y3+ sites were resolved and a complete mapping of all frozen-core Y3+ sites was limited by the inhomogeneity of the applied magnetic field. The Rabi frequency, the coherence time and lifetime as well as the interaction strength with the Eu3+ ion of one of these Y3+ ions were measured. The observed lifetime of the Y3+ ion is 27 s, which is four orders of magnitude longer than the low field value. With the technique developed, a detailed understanding of the frozen-core dynamics is possible, which would allow an extension of the hyperfine coherence time of the Eu3+ ion towards the lifetime limit. In summary, this thesis provides a detailed characterisation of the decoherence mecha- nisms of the hyperfine transitions in Eu3+:Y2SiO5. The potential of using rare-earth doped crystals for the long-term storage of quantum information with applications to long-range quantum communications is identified. The demonstrated long coherence time of the quantum transitions for information storage allows a new way of entanglement distribu- tion: entanglement is transported by physically transporting the memory crystal rather than the light. This approach opens a new regime for both quantum communication and fundamental tests of quantum mechanics.

•Jan 1, 2017•3 citations
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+:{\text{Y}}_{2}$${\text{SiO}}_{5}.
In many important situations, the dominant dephasing mechanism in cryogenic rare-earth-metal-ion--doped systems is due to magnetic field fluctuations from spins in the host crystal. Operating at a magnetic field where a transition has a zero first-order Zeeman (ZEFOZ) shift can greatly reduce this dephasing. Here we identify the location of transitions with a zero first-order Zeeman shift for optical transitions in Pr3+{}^{3+}3+:YAG and for spin transitions in Er3+{}^{3+}3+:Y2{}_{2}2​SiO5{}_{5}5​. The long coherence times that ZEFOZ can enable would make Pr3+{}^{3+}3+:YAG a strong candidate for achieving the strong-coupling regime of cavity QED, and would be an important step forward in creating long-lived telecommunications wavelength quantum memories in Er3+{}^{3+}3+:Y2{}_{2}2​SiO5{}_{5}5​. This work relies mostly on published spin-Hamiltonian parameters, but Raman heterodyne spectroscopy was performed on Pr3+{}^{3+}3+:YAG to measure the parameters for the excited state.
Rare-earth ions in dielectric crystals are interesting candidates for storing quantum states of photons. A limiting factor on the optical density and thus the conversion efficiency is the distortion introduced in the crystal by doping elements of one type into a crystal matrix of another type. Here we investigate the system Pr3+{}^{3+}3+:La2{}_{2}2​(WO4{}_{4}4​)3{}_{3}3​, where the similarity of the ionic radii of Pr and La minimizes distortions due to doping. We characterize the praseodymium hyperfine interaction of the ground-state (3{}^{3}3HHH4{}_{4}4​) and one excited state (1{}^{1}1DDD2{}_{2}2​) and determine the spin Hamiltonian parameters by numerical analysis of Raman-heterodyne spectra, which were collected for a range of static external magnetic-field strengths and orientations. On the basis of a crystal-field analysis, we discuss the physical origin of the experimentally determined quadrupole and Zeeman tensor characteristics. We show the potential for quantum memory applications by measuring the spin coherence lifetime in a magnetic field that is chosen such that additional magnetic fields do not shift the transition frequency in first order. Experimental results demonstrate a spin coherence lifetime of 158 ms --- almost 3 orders of magnitude longer than in zero field.
Rare-earth ions in dielectric crystals play an important role in high-resolution laser spectroscopy and are interesting candidates for storing quantum states of photons. We characterize the praseodymium hyperfine interaction of the ground-state (3{}^{3}3H4{}_{4}4​) and one excited-state (1{}^{1}1D2{}_{2}2​) for two important compounds: praseodymium doped in yttrium aluminum perovskite and praseodymium doped in yttrium orthosilicate. The spin Hamiltonian parameters are determined by numerical analysis of Raman-heterodyne spectra, which were collected for a range of static external magnetic field strengths and orientations. For Pr3+{}^{3+}3+:YAlO3{}_{3}3​, we present a full analysis without restrictions for the Zeeman and quadrupole tensors, and our new characterization for Pr3+{}^{3+}3+:Y2{}_{2}2​SiO5{}_{5}5​ resolves a controversy in the literature.
Dense rare-earth spin ensembles in solids offer strong collective light-matter coupling for scalable quantum technologies but are typically incompatible with long coherence times due to strong dipolar interactions. Here we challenge this paradigm by showing long-lived coherence in such systems. In a stoichiometric EuCl_{3}·6H_{2}O crystal, we achieve hyperfine coherence times T_{2}^{CPMG} of up to 15 s at 4 K, extending the zero-field value T_{2} of 1.28 ms by more than four orders of magnitude using dynamical decoupling at a zero-first-order Zeeman (ZEFOZ) transition. Homogeneous linewidth measurements reveal a substantial suppression of resonant Eu^{3+}-Eu^{3+} spin interactions introduced by the full concentration near the ZEFOZ point. Coherence remains resilient to strong local perturbations, with a 32 ms coherence time for Eu^{3+} ions adjacent to Er^{3+} dopants. These results establish stoichiometric rare-earth crystals as a promising platform for quantum memories and spin-photon interfaces, demonstrating that intrinsically high optical depth and long-lived spin coherence can coexist in a fully concentrated ensemble.
Rare earth ion doped crystals are state-of-the-art platforms for processing quantum information, particularly thanks to their excellent optical and spin coherence properties at cryogenic temperatures. Experimental observations have shown that the application of a static magnetic bias field significantly improves the coherence times in the rare earth ions ensemble, but only a few studies have focused on its dependency as a function of both magnetic field direction and amplitude. This is especially true for magnetic field amplitudes under the mT, and for low magnetic dipole moment ions. In this paper, we investigate the relationship between the magnetic field parameters and the decoherence caused by magnetic dipole-dipole coupling with the nearest-neighbor nuclear spins in the crystal. The primary non-Kramers rare earth ions investigated here are europium and praseodymium, but we also extend our study to the ytterbium Kramers ion due to its low magnetic dipole in the mT range. We perform theoretical investigations and simulations of the energy structure and coherence time evolution and identify good correspondences between experimental and simulated spin echo data. This work allows us to pinpoint the most relevant decoherence mechanisms in the considered magnetic field regime, and to predict favorable magnetic configurations.
This thesis investigates the coherence properties of the hyperfine transitions of the 151Eu3+ ions in Eu3+:Y2SiO5 and evaluates the potential of developing quantum memories using these transitions. Quantum memories for light with long storage times are required for quantum commu- nication applications. For these memories to be useful they need to have storage times long compared to the transmission times across the communication network. For a global optical communication network this requires storage time longer than 100 ms. Rare-earth doped crystals have been identified as a suitable storage material. The storage time of these systems is limited by the coherence time of the hyperfine transitions of the optically active rare-earth ions. In previous work it had been demonstrated that coherence times as long as 1.4 seconds could be achieved for hyperfine transitions in Pr3+:Y2SiO5 by ap- plying a particular magnetic field such that the first order Zeeman shift of the transition nulled. This technique is known as zero first-order Zeeman (ZEFOZ). Due to the relatively large second order Zeeman efficient of the transitions in Pr3+:Y2SiO5, an extension of the coherence time, significantly beyond the 1.4 second mark using ZEFOZ, is not expected. However, it has been predicted that coherence times more than two orders of magnitude longer could be achieved in Eu3+:Y2SiO5 due to the smaller second order Zeeman shifts associated with the relevant hyperfine transitions. The dominant decoherence mechanism for the hyperfine transitions in diluted Eu3+:Y2SiO5 is the magnetic field perturbations caused by the random spin reconfigu- ration of the Y3+ ions in the host. By applying the ZEFOZ technique, previously used in Pr3+:Y2SiO5, the sensitivity of the transition’s frequency to environmental magnetic field perturbations was significantly reduced. Further, this strong ZEFOZ magnetic field was also shown to induce a frozen core around the Eu3+ ion, which resulted in a signifi- cant suppression of the reconfiguration of the nearby Y3+ spins. The combined effect of the reduced sensitivity and frozen core effect allowed a decoherence rate of 8 × 10−5 s−1 over 100 milliseconds to be demonstrated. The observed decoherence rate is at least an order of magnitude lower than that of any other system suitable for an optical quantum memory. Furthermore, by employing dynamic decoherence control, a coherence time of 370 ± 60 minutes was achieved. This 6 hour coherence time observed here opens up the possibility of distributing quantum entanglement via the physical transport of memories as an alternative to optical communications. It was found that even at the critical point alignment the observed coherence times showed that the Y3+ spin flips remain the dominant decoherence mechanism. To aid in the development of future strategies to further extend the coherence time beyond 6 hours, a study of the Y3+ spin dynamics in the frozen core was conducted. Four of the Y3+ sites were resolved and a complete mapping of all frozen-core Y3+ sites was limited by the inhomogeneity of the applied magnetic field. The Rabi frequency, the coherence time and lifetime as well as the interaction strength with the Eu3+ ion of one of these Y3+ ions were measured. The observed lifetime of the Y3+ ion is 27 s, which is four orders of magnitude longer than the low field value. With the technique developed, a detailed understanding of the frozen-core dynamics is possible, which would allow an extension of the hyperfine coherence time of the Eu3+ ion towards the lifetime limit. In summary, this thesis provides a detailed characterisation of the decoherence mecha- nisms of the hyperfine transitions in Eu3+:Y2SiO5. The potential of using rare-earth doped crystals for the long-term storage of quantum information with applications to long-range quantum communications is identified. The demonstrated long coherence time of the quantum transitions for information storage allows a new way of entanglement distribu- tion: entanglement is transported by physically transporting the memory crystal rather than the light. This approach opens a new regime for both quantum communication and fundamental tests of quantum mechanics.