Quantum information transfer from light to atom ensembles and vice versa has both basic and practical importance. Among the relevant topics let us mention entanglement and decoherence of macroscopic systems, together with applications to quantum memory for long distance quantum cryptography. Although the first experimental demonstrations have been performed in atomic vapors and clouds, rare earth ion doped crystals are also interesting media for such processes. In this paper we address Tm3+ ions capability to behave as three-level lambda systems, a key ingredient to convert optical excitation into a spontaneous- emission-free spin wave. Indeed Tm3+ falls within reach of light sources that can be stabilized easily to the required degree. In the absence of zero-field hyperfine structure we apply an external magnetic field to lift the nuclear spin degeneracy in Tm3+:YAG. We experimentally determine the gyromagnetic tensor components with the help of spectral hole-burning techniques. Then appropriate orientation of the applied field enables us to optimize the transition probability ratio along the two legs of the lambda. The resulting three-level lambda system should suit quantum information processing requirements.
Quantum information transfer from light to atom ensembles and vice versa has both basic and practical importance. Among the relevant topics let us mention entanglement and decoherence of macroscopic systems, together with applications to quantum memory for long distance quantum cryptography. Although the first experimental demonstrations have been performed in atomic vapors and clouds, rare earth ion doped crystals are also interesting media for such processes. In this paper we address Tm3+ ions capability to behave as three-level lambda systems, a key ingredient to convert optical excitation into a spontaneous- emission-free spin wave. Indeed Tm3+ falls within reach of light sources that can be stabilized easily to the required degree. In the absence of zero-field hyperfine structure we apply an external magnetic field to lift the nuclear spin degeneracy in Tm3+:YAG. We experimentally determine the gyromagnetic tensor components with the help of spectral hole-burning techniques. Then appropriate orientation of the applied field enables us to optimize the transition probability ratio along the two legs of the lambda. The resulting three-level lambda system should suit quantum information processing requirements.
Quantum information transfer from light to atom ensembles and vice versa has both basic and practical importance. Among the relevant topics let us mention entanglement and decoherence of macroscopic systems, together with applications to quantum memory for long distance quantum cryptography. Although the first experimental demonstrations have been performed in atomic vapors and clouds, rare earth ion doped crystals are also interesting media for such processes. In this paper we address Tm3+ ions capability to behave as three-level $\ensuremath{\Lambda}$ systems, a key ingredient to convert optical excitation into a spontaneous-emission-free spin wave. Indeed Tm3+ falls within reach of light sources that can be stabilized easily to the required degree. In the absence of zero-field hyperfine structure we apply an external magnetic field to lift the nuclear spin degeneracy in Tm3+:YAG. We experimentally determine the gyromagnetic tensor components with the help of spectral hole-burning techniques. Then appropriate orientation of the applied field enables us to optimize the transition probability ratio along the two legs of the $\ensuremath{\Lambda}$. The resulting three-level $\ensuremath{\Lambda}$ system should suit quantum information processing requirements.
A three-level $\ensuremath{\Lambda}$ system in Tm3+ doped YAG crystal is experimentally investigated in the prospect of quantum information processing. Zeeman effect is used to lift the nuclear spin degeneracy of this ion. In a previous paper [de Seze et al., Phys. Rev. B 73, 085112 (2006)] we measured the gyromagnetic tensor components and concluded that adequate magnetic field orientation could optimize the optical connection of both ground state sublevels to each one of the excited state sublevels, thus generating $\ensuremath{\Lambda}$ systems. Here we report on the direct measurement of the transition probability ratio along the two legs of the $\ensuremath{\Lambda}$. Measurement techniques combine frequency selective optical pumping with optical nutation or photon echo processes.
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 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.
This thesis describes investigations of the use of cryogenically cooled rare-earth-ion-doped crystals for quantum information processing and quantum optics. Several aspects of the coherent interaction between light and rare-earth ions in solids are addressed. Quantum information science has given physicists new views of quantum mechanics. The transmission of quantum states has already found practical use and full scale quantum computers may one day perform computations and simulations that would be impossible on a conventional computer. The work presented in this thesis can be seen as a part of a broad effort to learn how to control and manipulate quantum mechanical systems, which will become necessary as science and technology continue to push ever deeper into the nanoscopic world. Coherent radiation, such as laser light, provides us with an ideal tool for these investigations and, along the way, we may also learn more about the quantum nature of light. Rare-earth ions in inorganic crystals have several unusual properties that are interesting for applications within quantum information science, including long coherence times and long-lived ground state sublevels that can be used for storage of quantum and classical information. As part of the work presented in this thesis, new materials have been investigated with respect to these properties, and ways to enhance the useful properties of the materials were explored. In one investigation, the lifetime of information stored in the ground state population distribution of Tm3 ions in YAG was shown to increase by several orders of magnitude with the application of a magnetic field. It is demonstrated how the optical inhomogeneous absorption profile can be prepared, so that the light only interacts with a selected group of ions, absorbing on a specific transition. Narrow absorbing structures, with widths approaching the optical homogeneous linewidth, have been prepared with no absorption in the surrounding spectral interval. This thesis addresses the use of such structures as hardware for quantum bits. Tailored pulses, capable of inducing controlled changes in the quantum states of the ions (qubits), even in the presence of unknown variations of coupling strengths and frequencies, have been realised experimentally and used for multiple transfer of ions between energy levels. Ion-ion interactions, which can be used for performing quantum logic operations, have been investigated in some detail. Techniques for selecting strongly interacting ions, by transferring weakly interacting ions to auxiliary states, have been demonstrated. A scheme for storing the quantum state of light in a solid, using photon-echo-like techniques, is proposed and analysed. In the proposed scheme, an optical wave packet is absorbed and subsequently re-emitted by an inhomogeneous absorption profile, which is tailored and externally controlled by the application of an electric field Additionally, an accumulated photon echo experiment has been performed using faint optical pulses. The experiment can be viewed as a demonstration of delayed self-interference of a single photon and as a demonstration of how a single photon can act as two of the fields in a photon echo process.
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.