This work has demonstrated that hyperfine decoherence times sufficiently long for QIP and quantum optics applications are achievable in rare earth ion centres. Prior to this work there were several QIP proposals using rare earth hyperfine states for long term coherent storage of optical interactions. The very long T_1 (~weeks ) observed for rare-earth hyperfine transitions appears promising but hyperfine T_2s were only a few ms, comparable to rare earth optical transitions and therefore the usefulness of such proposals was doubtful. ¶ This work demonstrated an increase in hyperfine T_2 by a factor of 7 × 10^4 compared to the previously reported hyperfine T_2 for Pr^[3+]:Y_2SiO_5 through the application of static and dynamic magnetic field techniques. This increase in T_2 makes previous QIP proposals useful and provides the first solid state optically active Lamda system with very long hyperfine T_2 for quantum optics applications. ¶ ...
This work has demonstrated that hyperfine decoherence times sufficiently long for QIP and quantum optics applications are achievable in rare earth ion centres. Prior to this work there were several QIP proposals using rare earth hyperfine states for long term coherent storage of optical interactions. The very long T_1 (~weeks ) observed for rare-earth hyperfine transitions appears promising but hyperfine T_2s were only a few ms, comparable to rare earth optical transitions and therefore the usefulness of such proposals was doubtful. ¶ This work demonstrated an increase in hyperfine T_2 by a factor of 7 × 10^4 compared to the previously reported hyperfine T_2 for Pr^[3+]:Y_2SiO_5 through the application of static and dynamic magnetic field techniques. This increase in T_2 makes previous QIP proposals useful and provides the first solid state optically active Lamda system with very long hyperfine T_2 for quantum optics applications. ¶ ...
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.
Rare earth ions (REI) in solid materials are among the leading systems for quantum technology applications. However, developing practical REI quantum devices with long-lived coherent states remains challenging due to great difficulties in growing high-quality REI materials and incomplete understanding of their decoherence mechanisms. In this work, we report a long optical coherence time of 422 ± 11 μs for the 7F0 → 5D0 transition, as well as a lifetime exceeding 30 hours for the 7F0 hyperfine spin states in Eu3+:Y2O3 optical ceramics. We identify the absence of two-level-system induced optical decoherence in short-range-ordered crystals and a decoherence mechanism caused by perturbing magnetic centers that were not detected previously below 1.5 K. Furthermore, we demonstrate coherent light storage over 5 μs by using the atomic frequency comb protocol. These results provide a promising proof-of-principle demonstration of quantum memory using Eu3+:Y2O3 optical ceramic system, highlighting its significant potential for practical quantum applications. Rare earth ions (REI) in solids are promising for quantum technologies. Here, the authors demonstrate a record optical coherence lifetime and the absence of two-level-system induced decoherence in Eu3+:Y2O3 optical ceramics. These findings advance the optimization of REI-based quantum systems and enable tailored material designs.
Light-matter interaction at single quantum object level is a long-lived challenge and dream of physicists. From the 1970s, the development of single ion spectroscopy and the observation of single photon states pave a way to a new era of detecting, and coherently manipulating quantum objects with electromagnetic field at single-ion levels. Later on, the invention of single molecular spectroscopy offers a new approach to investigate single quantum objects in condensed matter, where the sophisticated trapping systems like in ions and cold atoms are not needed, resulting in the discovery of various of single photon emitters embedded in solids. Among all, single quantum dots and single negatively charged nitrogen-vacancy centers in diamond attract most attentions, since their single spins can be coherently manipulated and entangled by the light field giving rise to numerous applications from nanoscale sensing to quantum computing. They are intensively studied as the most promising candidates for the realization of solid-state quantum bits. However, these systems coupled to a complex environment which can result in rapid loss of spin coherence or optical instability. Finding an alternative solid-state single system with remarkable optical and spin properties is the motivation of this dissertation. Rare earth ions doped in inorganic crystal hosts provide promises not only by the high quality factor 4f-4f optical transitions but also by the well preserved and long-lived spin states, with the applications from solid-state laser spectroscopy to quantum information processing. However, for almost three decades, not being able to identify single rare earth elements in solids is the obstacle to achieve their full potential functionality. We demonstrated the first direct optical detection of single rare earth ions (praseodymium) in solids in 2012. This research was covered in my Master Degree Thesis. This dissertation presents experimental progress in optically detecting other single rare earth species in crystals, understanding their fundamental spectroscopy properties and coherently controlling them, which is mainly focused on single trivalent cerium ions in different host materials. Following the optical detection of single cerium ions in yttrium aluminum garnet (YAG), the optical and spin properties of single Ce ions are investigated. Single Ce ions show good photostability under the pulsed laser excitation. Still, like in other solid emitters, photo-induced dynamics of single Ce ions is observed, however, in a counterintuitive way under the continuous laser irradiation. To understand this behavior, we proposed a charge dynamics model, and developed a novel method to suppress this undesired charge dynamics. With this approach, we obtain the photoluminescence excitation spectrum of single Ce ions in YAG under a CW laser excitation. Narrow (~80 MHz) and spectrally stable optical transitions between the lowest Kramers doublets of the ground and the excited states are observed. In comparison with the large inhomogeneous broadening (500 GHz), narrow resonant transitions provide the good selectivity in the spectral domain. Moreover, the single Ce ground spin state presents a spin 1/2 system with anisotropy g factor. It results in the optical selection rules dependent on the directions of the external magnetic field. Under parallel external magnetic field with respect to the quantization axis, only the spin-flip transitions are allowed with high transition contrast. It gives the opportunity to optically initialize the ground spin state of single Ce ions with 97.5% fidelity. The coherent spin properties of single Ce ions can be investigated, after the successful optical initialization. By scanning the microwave frequency, we obtain the electron spin resonance of single Ce spin transitions. We show the spin state has a coherence time of 290 ns, which is dominated by the surrounding aluminum nuclear spin bath and impurities induced electron spin bath. The coherence time can be extended to 2 ms through dynamical decoupling method, which approaches closely to the upper limit 4.5 ms due to spin-lattice relaxation. This result indicates single Ce electron spin can be a good solid-state qubit. With the combination of optical and spin manipulations of single Ce ions, a quantum interface between a single spin and a single photon is observed by monitoring the temporal behavior of circularly polarized emission photons from the ion. We obtain the Larmor precession of the excited spin state, indicating the direct mapping of the excited spin states of single Ce ions onto the polarization states of the fluorescence photons. Furthermore, with both optical and spin access, we all-optically demonstrate coherent population trapping of a single Ce spin qubit. To scale up the system for further applications, we present the nano-scale engineering of rare earth species in YAG crystal, with the acquirement of the production yield of Ce and Pr implantation (53 and 91% respectively). The optical and spin properties of single implanted Ce ions show fairly good performance, which paves the way towards coherent coupling of single rare earth qubits in a small volume. Besides the study of single Ce ions, the spectroscopy properties of single praseodymium ions in YAG crystal are investigated. We obtain the photoluminescence excitation spectrum and the hyperfine splitting of a single praseodymium ion. All-optical control of a single praseodymium ion is achieved. In this dissertation, we solve the key problem of optically detecting, spectrally studying and coherently manipulating single rare earth ions in solids. The developed methods including optical detection, initialization, readout, coherent control and nanoscale production of single rare earth elements in crystals offer novel and powerful tools for understanding and exploring the fundamental spectroscopy properties of single rare earth elements in solids. It paves a way towards constructing scalable quantum network based on single rare earth solid-state qubits.
Ultralong-lived Coherent States in Eu3+:Y2O3 Optical Ceramics for Quantum Memories
Rare earth ions (REI) in solid materials are among the leading systems for quantum technology applications. However, developing practical REI quantum devices with long-lived coherent states remains challenging due to great growth difficulties of high-quality REI materials and a lack of comprehensive understanding of REI's decoherence mechanisms. Here we realize a record optical coherence time of 421.5 ± 10.5 μs for the 7F0→5D0 transition and more than 30 hours lifetime for the 7F0 hyperfine spin states in Eu3+:Y2O3 optical ceramics. We report the elimination of two-level-system induced optical decoherence in short-range ordered crystals. Meanwhile, a new decoherence mechanism caused by new kinds of perturbing magnetic centers is identified below 1.5 K. We further demonstrate the coherent light storage over 5 μs by using the atomic frequency comb protocol. These results open up prospects for the realization of practical quantum memories and large scale quantum communications with REI optical ceramics.
This thesis investigates the potential of Er:YSO and Er:Si for quantum communication and computation applications. Erbium uniquely possess optical transitions in the 1.5 um region, making it suitable for both fibre telecommunication and silicon photonics. The properties of the I15/2↔I13/2 optical transition in Er:YSO have already been extensively studied. Over two decades ago, improvements in Er3+ dephasing time at 1.5 um were achieved by applying a 5T field along the D1 axis. More recently, a record 4.4 ms coherence time on the same optical transition was achieved using a 7T field. These investigations, among others, illustrate that large Er electron spins become thermally polarised with sufficient magnetic field. However, no long lived and coherent spin transitions associated with the Er ions had previously been identified, and such transitions are necessary for on-demand quantum state storage. To address this requirement, the optical and hyperfine transition properties of 167-Er:YSO were investigated in large magnetic fields. In a field of 7T, spectral hole lifetimes of 1 minute and hyperfine population lifetimes of 12 minutes were observed. These measurements illustrate the effect of spin-lattice relaxation in this system, and how it can be mitigated. Efficient spin-polarisation of the entire 167-Er hyperfine ensemble is also demonstrated. This is the first such demonstration in rare earth systems, and a key requirement for broadband optical storage. Moreover, a 1.3 second coherence time was recorded for an 167-Er:YSO hyperfine transition at 7T and 1.4 K. This is an improvement of several orders-of-magnitude over previous coherence measurements on spin-transitions in Er doped solids. This is also sufficient for maximal entanglement rates in quantum repeater networks that span distances of 1000 km or greater. With an optical transition at 1.5 um, Er is also an ideal candidate to connect silicon based quantum computers to the future quantum Internet. In particular, single Er:Si ions could be used to develop an optical-spin bus between P:Si qubits and fibre based quantum networks. Presented here is the first spectroscopic investigation of single Er:Si ions. This required a novel opto-electronic approach to single ion detection, where the Er ions are implanted into a nanometre scale fin-shaped Field Effect Transistor. With this approach it was possible to develop high resolution optical spectra, where both the electronic and hyperfine levels of individual Er ions were resolved. Long optical and spin coherence times are also important requirements for an optical-spin bus. To address the first requirement, an investigation of the optical lineshape was undertaken. Here it was determined that sources of Stark noise external to the transistor channel contribute a significant amount to optical homogeneous linewidth. However, the dominant noise contribution was determined to be short-range (from within the 30 nm wide channel) and the total homogeneous linewidth was measured to be 50 MHz. The site structure of an individual Er:Si ion was then analysed, using magnetic field rotation patterns and optical transitions between multiple crystal field levels. This site was determined to have approximately axial (C3) symmetry. The purpose of this study was to determine a magnetic field regime in which the Er electrons spin can be polarised, which is necessary for realising of long hyperfine lifetimes and coherence times.
Without using any trapping lasers, rare-earth (RE) ions can be doped into some nanofabricated materials in form of nanocrystals in a solid state matrix, thus rendering a natural trap for potential application as a quantum computing device. In particular, passive nuclear spin states of RE ions can be utilized as (i) optical quantum memory (with huge density as yielded from nanocrystals), (ii) qubits by encoding in ground hyperfine states and operated as (iii) two-qubit gate when transferring them to active magnetized electronic states. A feasible implementation of qubits is realised by using those doped RE ions whose open-shell (for inner highly shielded 4f shell electrons) energy levels and statevectors are well described by the crystal field (CF) interaction and hyperfine coupling in which the Hamiltonian is composed of various freeion interactions, the CF potential, electronic and nuclear Zeeman effects as well as the hyperfine interaction. For those qubit encoded in the two ground hyperfine states of RE ions, they can have fairly long lifetimes of days and coherence times (from 1.3s for Er3+ to 6 hours for Eu3+) due to the unique spectroscopic properties of RE ions. Because of the recent progress in optical single-ion detection for addressing individual qubits with a specific frequency channel, RE ions could be packed in a solid state 3D matrix at nanometer spacing, hence rendering very high qubit densities for quantum memories. Meanwhile, this configure also leads to strong dipole-dipole interactions (or high connectivity) between qubits which are not nearest neighbors. In this study, Kramers ions like 167Er and 171Yb doped in yttrium orthosilicate Y2SiO5 (YSO) nanocrystals will be investigated as a promising system for quantum computing because of their weak spin bath and possibility for being directly milled in single nanocrystals as nano-resonators. By using the famous Wien2k package to carry out the first-principles calculations, we can obtain the CF parameters and hyperfine constants as well as various electronic properties like energy gap and band structure for those Kramers RE ions doped in YSO. We shall present some essential findings from first-principles calculations to obtain various properties of the ground and excited CF and hyperfine states for those RE ions with an aim to optimize RE ions doping in YSO nanocrystals for quantum memories and qubits, contributing to scalable quantum computing architectures.