Photon-echo measurements are reported for the trivalent thulium ion, which differs from all other rare-earth ions in having a single isotope of nuclear spin 1/2. Echo decays on the 3H6(1) ↔ 3H4(1) transition of LaF3:Tm3+ and YAG:Tm3+ were magnetic-field dependent at 1.5 K, showing that the dephasing originates from spin fluctuations of nuclei in the host crystals. Coherence times in the range of 7 to 100 μs were measured, corresponding to homogeneous linewidths of tens of kilohertz. The echo decays were nonexponential, providing evidence for spectral diffusion that is due to a distribution of 19F and 27A1 nuclear spin-flip times in the respective hosts.
Photon-echo measurements are reported for the trivalent thulium ion, which differs from all other rare-earth ions in having a single isotope of nuclear spin 1/2. Echo decays on the 3H6(1) ↔ 3H4(1) transition of LaF3:Tm3+ and YAG:Tm3+ were magnetic-field dependent at 1.5 K, showing that the dephasing originates from spin fluctuations of nuclei in the host crystals. Coherence times in the range of 7 to 100 μs were measured, corresponding to homogeneous linewidths of tens of kilohertz. The echo decays were nonexponential, providing evidence for spectral diffusion that is due to a distribution of 19F and 27A1 nuclear spin-flip times in the respective hosts.
The optical spectroscopy and dynamics of three materials; Eu^3+:Y2SiO5, Pr^3+:Y2SiO5, and Tm^3+:Y2SiO5 that are of interest for application in persistent spectral holeburning optical memory and signal processing devices were investigated using linear and nonlinear spectroscopic techniques.Two-pulse photon echoes have been used to measure the homogeneous linewidths.The effects of instantaneous spectral diffusion were systematically studied to allow accurate determination of the optical resonance widths, and external magnetic fields were applied to characterize the effects of fluctuating nuclear spins of the host lattice on dephasing of the dopant ion.The 7F0 → 5D0 transition of 0.1% Eu^3+ in the two crystallographic sites of Y2SiO5 was studied using photon echoes.Using this material, we succeeded in measuring the narrowest optical resonance in a solid by shielding the crystal from stray electromagnetic fields and using sufficiently low laser power to minimize contributions from instantaneous diffusion.The homogeneous linewidths measured in a magnetic field of 100 G are 122 Hz (site 1) and 167 Hz (site 2).These widths are dominated by population decay, but up to 20 Hz is attributed to 89Y spin fluctuations which have been reduced by the applied magnetic field.Similar studies were performed to determine the contributions to the homogeneous linewidth of the 3H4(1) → 1D2(1) transition for both sites of 0.02% Pr^3+ in Y2SiO5.Linewidths of 2.1 kHz (site 1) and 0.85 kHz (site 2) were obtained with an applied magnetic field of 77 G.A significant contribution of 89Y nuclear spin fluctuations to the zero-field homogeneous linewidth was found.Optically detected nuclear magnetic resonance measurements determined the hyperfine structure of the 3H4 ground state for each site, and photon echo nuclear double resonance was used to determine the hyperfine levels of the lowest component of the 1D2 manifold. 3) 2.1? Ec,2S
Photon echo measurements made at 2 °K on the 3H4 - 1D2 transition in Pr3+:LaF3 show that magnetic dipolar couplings between the Pr and F nuclei account for the 56 kHz homogeneous linewidth of this transition.1 The homogeneous broadening arises from the enhanced 141Pr nuclear moment (I=5/2) interacting with the local field fluctuations of the 19F nuclear moments undergoing mutual spin flip transitions. Such resonant fluctuations should, in the absence of a fluorine spin diffusion barrier, produce a homogeneous linewidth of about 200 kHz which is, in fact, roughly what is observed for the inhomogeneous broadening of the Pr3+ hyperfine levels and is considerably broader than that obtained by the photon echo measurements. Shelby et al2 proposed a simple model analogous to the spin diffusion barriers responsible for narrowing the homogeneous lines in certain electron paramagnetic resonance transitions3. In such systems, the field produced by the electron magnetic dipole moment (2-3 orders of magnitude larger than the enhanced nuclear moment associated with the ground state of Pr3+ in LaF3) de-tunes the nearest neighbors from each other, prohibiting mutual spin flips among them. Thus, the fields produced by the neighboring spins are static and their interaction with the paramagnetic ion contributes to the inhomogeneous linewidth and not to homogeneous broadening. The de-tuned neighbors are referred to as the "frozen core." Application of this picture to the case of Pr3+:LaF3 is supported by the calculation of Devoe et al.4 Their Monte Carlo calculation of the Pr3+ optical dephasing times shows that the observed homogeneous linewidth could be explained by deleting the nearest neighbor F spins from the lattice of rapidly fluctuating fluorine moments, in effect, treating them as part of a frozen core.
The zero-phonon line (ZPL) between the two excited-state manifolds 3F4 and 3H4 of the trivalent thulium ion in yttrium aluminum perovskite (Tm3+:YAlO3) lies within the telecom E-band at around 1451 nm and exhibits an optical coherence time of a few μs at cryogenic temperatures. To improve this time in view of potential applications, e.g. single-photon sources and optical quantum memory, we characterized the magnetic properties of the lowest Stark levels of these two manifolds. Varying the external magnetic field amplitude and orientation, we measured the enhanced nuclear Zeeman splitting by probing the field-dependent frequency detuning of side holes created by means of spectral hole burning, and we characterized the inhomogeneous line shift caused by the quadratic Zeeman interaction. Together, this allowed us to establish the spin Hamiltonians for the lowest Stark level of the 3F4 and 3H4 manifolds, and to predict optical clock transitions for particular orientations and magnitudes of the magnetic field
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.
Photon-echo-relaxation measurements made on the 3H4${\mathrm{\ensuremath{-}}}^{3}$P0 transition of 0.01 at. % Pr3+:YAG (where YAG represents yttrium aluminum garnet), 3H4${\mathrm{\ensuremath{-}}}^{1}$D2 transition in 0.1 at. % Pr3+:YAlO3, and 7F0${\mathrm{\ensuremath{-}}}^{5}$D0 transition in 0.25 at. % Eu3+:YAlO3 show that the photon-echo relaxation rate increases when the intensities of the excitation pulses are increased. Although a part of the relaxation-rate increase in Pr3+:YAG may be attributed to an instantaneous spectral diffusion (ISD) in which the presence of excited neighboring Pr3+ ions change the local field and the absorption frequency of the rare-earth ions, our data deviate significantly from the ISD-model predictions. An additional intensity-dependent relaxation mechanism is required to explain the results.
The photon echo experiment is a method of measuring the homogeneous dephasing time (T2) from which the homogeneous linewidth of an optical transition can be calculated.In this thesis, the theories of linewidths of transitions and of the development of a photon echo are presented.Also discussed is the experimental setup by which the first photon echoes in the rare-earth terbium were observed and measured.The decays of echo intensity with laser pulse separation at the externally applied fields of 45 KG and 25 KG were plotted and from these plots a homogeneous dephasing time of HO nanoseconds was calculated.Data at 15 KG were taken, but because of the non-exponential behavior of the decay, Tj was not calculated.At 0 KG, no echo was observed, implying a decrease of the dephasing time below 15 KG.