Physical Review B

Hyperfine structure and hyperfine coherent properties of praseodymium in single-crystalline La2(WO4)3 by hole-burning and photon-echo techniques

O. Guillot-Noël, Philippe Goldner, Florian Beaudoux, Y. Le Du, Julien Lejay, A. Amari, Andreas Walther, Lars Rippe, Stefan Kröll

Published Apr 27, 2009• 30 citations

Publisher

Abstract

We studied the hyperfine structure and hyperfine coherent properties of the ${^{3}\text{H}}_{4}(0)\ensuremath{\rightarrow}{^{1}\text{D}}_{2}(0)$ transition of ${\text{Pr}}^{3+}$ ions in a tungstate single crystal ${\text{La}}_{2}{({\text{WO}}_{4})}_{3}$ by hole-burning and photon-echo techniques. This work is motivated by the search of an efficient three level $\ensuremath{\Lambda}$ system in this new compound with which we could build up a quantum memory. By nonconventional hole-burning experiments, the ordering of the hyperfine splittings in the ${^{3}\text{H}}_{4}(0)$ ground state and in the ${^{1}\text{D}}_{2}(0)$ excited state is obtained. The hyperfine splittings are thus ordered: 24.6 and 14.9 MHz for the ${^{3}\text{H}}_{4}(0)$ level and 5.0 and 7.3 MHz for the ${^{1}\text{D}}_{2}(0)$ level. The relative and absolute transition strengths of individual hyperfine transitions are determined by comparing absorption strengths and by measuring the Rabi flopping frequency as the transition is coherently driven. Free induction and Raman echo decays give inhomogeneous and homogeneous hyperfine linewidths of $57\ifmmode\pm\else\textpm\fi{}2$ and $1.25\ifmmode\pm\else\textpm\fi{}0.1\text{ }\text{kHz}$, respectively.

DOI: 10.1103/physrevb.79.155119

Related papers

Hyperfine structure, optical dephasing, and spectral-hole lifetime of single-crystalline Pr3+:La2(WO4)3

O. Guillot-Noël, Philippe Goldner, Y. Le Du +4 more

Physical Review BMay 15, 200719 citations

Hyperfine structure and homogeneous broadening in Pr3+:KY(WO4)2

H. L. Xu, M. Nilsson, S. Ohser +4 more

Physical Review BDec 30, 20048 citations

Concentration dependence of absorption and optical and hyperfine transition dynamics in Pr 3 + :La 2 (WO 4 ) 3

Florian Beaudoux, O. Guillot-Noël, Julien Lejay +2 more

Journal of Physics B Atomic Molecular and Optical PhysicsJun 8, 20128 citations

Hole-burning techniques for isolation and study of individual hyperfine transitions in inhomogeneously broadened solids demonstrated in Pr3+:Y2SiO5

Mattias Nilsson, Lars Rippe, Stefan Kröll +2 more

arXiv:cond-mat/0408515Physical Review BDec 30, 2004201 citations

Hyperfine characterization and spin coherence lifetime extension in Pr 3 + :La 2 (WO 4 ) 3

Marko Lovrić, Philipp Glasenapp, Dieter Suter +6 more

arXiv:1107.2274Physical Review BSep 12, 201154 citations

Spectroscopic and relaxation character of the P03−H43 transition in La F3 : Pr3+ measured by photon echoes

Y.C. Chen, Kophu P. Chiang, Sven R. Hartmann

Physical review. B, Condensed matterJan 1, 198064 citations

Physical Review B

Hyperfine structure and hyperfine coherent properties of praseodymium in single-crystalline La2(WO4)3 by hole-burning and photon-echo techniques

O. Guillot-Noël, Philippe Goldner, Florian Beaudoux, Y. Le Du, Julien Lejay, A. Amari, Andreas Walther, Lars Rippe, Stefan Kröll

Published Apr 27, 2009• 30 citations

Publisher

Abstract

We studied the hyperfine structure and hyperfine coherent properties of the

{^{3}\text{H}}_{4}(0)\ensuremath{\rightarrow}{^{1}\text{D}}_{2}(0)

transition of

{\text{Pr}}^{3+}

ions in a tungstate single crystal

{\text{La}}_{2}{({\text{WO}}_{4})}_{3}

by hole-burning and photon-echo techniques. This work is motivated by the search of an efficient three level

\ensuremath{\Lambda}

system in this new compound with which we could build up a quantum memory. By nonconventional hole-burning experiments, the ordering of the hyperfine splittings in the

{^{3}\text{H}}_{4}(0)

ground state and in the

{^{1}\text{D}}_{2}(0)

excited state is obtained. The hyperfine splittings are thus ordered: 24.6 and 14.9 MHz for the

{^{3}\text{H}}_{4}(0)

level and 5.0 and 7.3 MHz for the

{^{1}\text{D}}_{2}(0)

level. The relative and absolute transition strengths of individual hyperfine transitions are determined by comparing absorption strengths and by measuring the Rabi flopping frequency as the transition is coherently driven. Free induction and Raman echo decays give inhomogeneous and homogeneous hyperfine linewidths of

57\ifmmode\pm\else\textpm\fi{}2

and

1.25\ifmmode\pm\else\textpm\fi{}0.1\text{ }\text{kHz}

, respectively.

DOI: 10.1103/physrevb.79.155119

Related papers

Hyperfine structure, optical dephasing, and spectral-hole lifetime of single-crystalline Pr3+:La2(WO4)3

O. Guillot-Noël, Philippe Goldner, Y. Le Du +4 more

Most of the experiments related to quantum information applications, involving rare-earth doped inorganic crystals, are performed on yttrium orthosilicate single crystals. The work presented here is motivated by the search of new compounds which can be used in the field of quantum computing and/or quantum storage. Relaxation times and hyperfine structure of the $^{3}H_{4}(0)\ensuremath{\rightarrow}^{1}D_{2}(0)$ transition in 1.4% ${\mathrm{Pr}}^{3+}:{\mathrm{La}}_{2}{(\mathrm{W}{\mathrm{O}}_{4})}_{3}$ at $4\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ have been measured by photon-echo and spectral-hole-burning techniques. The hyperfine splittings of the ground $^{3}H_{4}(0)$ and the excited $^{1}D_{2}(0)$ states are $14.9\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$, $24.6\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$ and $5.0\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$, $7.3\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$, respectively. An inhomogeneous linewidth of $18.8\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$ was measured. A homogeneous linewidth of $25.3\ifmmode\pm\else\textpm\fi{}2.0\phantom{\rule{0.3em}{0ex}}\mathrm{kHz}$ was obtained with or without an external magnetic field of about $14\phantom{\rule{0.3em}{0ex}}\mathrm{mT}$ . The fluorescence dynamics of the $^{1}D_{2}$ level obtained by a direct excitation in the $^{3}H_{4}\ensuremath{\rightarrow}^{1}D_{2}$ transition gives a nonexponential decay which indicates energy-transfer processes. This decay can be accurately fitted by the Inokuti-Hirayama model [J. Chem. Phys. 43, 1978 (1965)] with a radiative lifetime of $61\ifmmode\pm\else\textpm\fi{}1\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$ giving a minimal homogeneous linewidth of $2.6\phantom{\rule{0.3em}{0ex}}\mathrm{kHz}$ . The spectral-hole lifetime due to population redistribution within the ground hyperfine levels is $16\ifmmode\pm\else\textpm\fi{}2\phantom{\rule{0.3em}{0ex}}\mathrm{s}$. The results obtained for the ${\mathrm{La}}_{2}{(\mathrm{W}{\mathrm{O}}_{4})}_{3}$ compound make this crystal an interesting host for quantum applications.Most of the experiments related to quantum information applications, involving rare-earth doped inorganic crystals, are performed on yttrium orthosilicate single crystals. The work presented here is motivated by the search of new compounds which can be used in the field of quantum computing and/or quantum storage. Relaxation times and hyperfine structure of the $^{3}H_{4}(0)\ensuremath{\rightarrow}^{1}D_{2}(0)$ transition in 1.4% ${\mathrm{Pr}}^{3+}:{\mathrm{La}}_{2}{(\mathrm{W}{\mathrm{O}}_{4})}_{3}$ at $4\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ have been measured by photon-echo and spectral-hole-burning techniques. The hyperfine splittings of the ground $^{3}H_{4}(0)$ and the excited $^{1}D_{2}(0)$ states are $14.9\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$, $24.6\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$ and $5.0\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$, $7.3\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$, respectively. An inhomogeneous linewidth of $18.8\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$ was measured. A homogeneous linewidth of $25.3\ifmmode\pm\else\textpm\fi{}2.0\phantom{\rule{0.3em}{0ex}}\mathrm{kHz}$ was obtained with or without an external magnetic field of about $14\phantom{\rule{0.3em}{0ex}}\mathrm{mT}$. The fluorescence dynamics of the $^{1}D_{2}$ level obtained by a direct excitation in the $^{3}H_{4}\ensuremath{\rightarrow}^{1}D_{2}$ transition gives a nonexponential decay which indicates energy-transfer processes. This decay can be accurately fitted by the Inokuti-Hirayama model [J. Chem. Phys. 43, 1978 (1965)] with a radiative lifetime of $61\ifmmode\pm\else\textpm\fi{}1\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$ giving a minimal homogeneous linewidth of $2.6\phantom{\rule{0.3em}{0ex}}\mathrm{kHz}$. The spectral-hole lifetime due to population redistribution within the ground hyperfine levels is $16\ifmmode\pm\else\textpm\fi{}2\phantom{\rule{0.3em}{0ex}}\mathrm{s}$. The results obtained for the ${\mathrm{La}}_{2}{(\mathrm{W}{\mathrm{O}}_{4})}_{3}$ compound make this crystal an interesting host for quantum applications.

Physical Review BMay 15, 200719 citations

Hyperfine structure and homogeneous broadening in Pr3+:KY(WO4)2

H. L. Xu, M. Nilsson, S. Ohser +4 more

As part of a search for suitable materials for coherent quantum operations, relaxation times and hyperfine structure of the $^{1}D_{2}(1)\text{\ensuremath{-}}^{3}H_{4}(1)$ transition in ${\mathrm{Pr}}^{3+}:\mathrm{KY}{({\mathrm{WO}}_{4})}_{2}$ (0.29 at. %) at 4 K have been obtained using photon-echo and spectral hole burning techniques. The homogeneous linewidth and the effect of excitation-induced dephasing were measured using two-pulse photon-echo techniques. Linewidths of $23.4\ifmmode\pm\else\textpm\fi{}1.0$ and $17.6\ifmmode\pm\else\textpm\fi{}0.9\phantom{\rule{0.3em}{0ex}}\mathrm{kHz}$ were obtained in the absence and presence of an external magnetic field of about 9 mT. The radiative lifetime $({T}_{1})$ of the $^{1}D_{2}$ state was measured to be $43\ifmmode\pm\else\textpm\fi{}2\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$ using time-resolved laser-induced fluorescence and three-pulse photon-echo measurements. The transmission hole spectra were measured and directly yielded the quadrupole level splitting in the $^{1}D_{2}$ ($3.77\ifmmode\pm\else\textpm\fi{}0.03$ and $4.58\ifmmode\pm\else\textpm\fi{}0.04\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$) and $^{3}H_{4}$ ($17.1\ifmmode\pm\else\textpm\fi{}0.1$ and $33.2\ifmmode\pm\else\textpm\fi{}0.3\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$) states. The spectral hole lifetime due to population redistribution between the ground-state nuclear levels was also determined to be $70\ifmmode\pm\else\textpm\fi{}10\phantom{\rule{0.3em}{0ex}}\mathrm{ms}$. A strong dipole-dipole interaction observed in this crystal opens for potential applications in quantum computing schemes for performing quantum logic operations, but the short dephasing time makes it less useful in data storage applications.As part of a search for suitable materials for coherent quantum operations, relaxation times and hyperfine structure of the $^{1}D_{2}(1)\text{\ensuremath{-}}^{3}H_{4}(1)$ transition in ${\mathrm{Pr}}^{3+}:\mathrm{KY}{({\mathrm{WO}}_{4})}_{2}$ (0.29 at. %) at 4 K have been obtained using photon-echo and spectral hole burning techniques. The homogeneous linewidth and the effect of excitation-induced dephasing were measured using two-pulse photon-echo techniques. Linewidths of $23.4\ifmmode\pm\else\textpm\fi{}1.0$ and $17.6\ifmmode\pm\else\textpm\fi{}0.9\phantom{\rule{0.3em}{0ex}}\mathrm{kHz}$ were obtained in the absence and presence of an external magnetic field of about 9 mT. The radiative lifetime $({T}_{1})$ of the $^{1}D_{2}$ state was measured to be $43\ifmmode\pm\else\textpm\fi{}2\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$ using time-resolved laser-induced fluorescence and three-pulse photon-echo measurements. The transmission hole spectra were measured and directly yielded the quadrupole level splitting in the $^{1}D_{2}$ ($3.77\ifmmode\pm\else\textpm\fi{}0.03$ and $4.58\ifmmode\pm\else\textpm\fi{}0.04\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$) and $^{3}H_{4}$ ($17.1\ifmmode\pm\else\textpm\fi{}0.1$ and $33.2\ifmmode\pm\else\textpm\fi{}0.3\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$) states. The spectral hole lifetime due to population redistribution between the ground-state nuclear levels was also determined to be $70\ifmmode\pm\else\textpm\fi{}10\phantom{\rule{0.3em}{0ex}}\mathrm{ms}$. A strong dipole-dipole interaction observed in this crystal opens for potential applications in quantum computing schemes for performing quantum logic operations, but the short dephasing time makes it less useful in data storage applications.

Physical Review BDec 30, 20048 citations

Concentration dependence of absorption and optical and hyperfine transition dynamics in Pr 3 + :La 2 (WO 4 ) 3

Florian Beaudoux, O. Guillot-Noël, Julien Lejay +2 more

Optical and hyperfine parameters of the 3H4–1D2 transition are investigated in Pr3 +:La2(WO4)3 for doping concentrations ranging from 0.02 to 3 at.%, at liquid helium temperatures. This includes optical inhomogeneous and homogeneous linewidths, peak absorption, excited-state population decays, spectral hole lifetime and inhomogeneous and homogeneous hyperfine linewidths. Optical inhomogeneous broadening with increasing Pr3 + concentration is limited due to close atomic radii between Pr3 + and La3 +. The peak absorption coefficient increases with increasing Pr3 + doping, reaching up to 28 cm−1. At the highest Pr3 + concentration, optical coherence lifetime is 4.6 μs and hole lifetime 2 s, which should allow one to transfer coherences and tailor the optical inhomogeneous linewidth, as required for rare earth-based optical quantum memories. Raman echo experiments show that hyperfine inhomogeneous linewidth and coherence lifetime (50 kHz and 250 μs respectively) are independent of Pr3 + concentration. These results suggest that highly doped crystals are useful for efficient and long-storage time quantum memories.Optical and hyperfine parameters of the 3H4–1D2 transition are investigated in Pr3 +:La2(WO4)3 for doping concentrations ranging from 0.02 to 3 at.%, at liquid helium temperatures. This includes optical inhomogeneous and homogeneous linewidths, peak absorption, excited-state population decays, spectral hole lifetime and inhomogeneous and homogeneous hyperfine linewidths. Optical inhomogeneous broadening with increasing Pr3 + concentration is limited due to close atomic radii between Pr3 + and La3 +. The peak absorption coefficient increases with increasing Pr3 + doping, reaching up to 28 cm−1. At the highest Pr3 + concentration, optical coherence lifetime is 4.6 μs and hole lifetime 2 s, which should allow one to transfer coherences and tailor the optical inhomogeneous linewidth, as required for rare earth-based optical quantum memories. Raman echo experiments show that hyperfine inhomogeneous linewidth and coherence lifetime (50 kHz and 250 μs respectively) are independent of Pr3 + concentration. These results suggest that highly doped crystals are useful for efficient and long-storage time quantum memories.

Journal of Physics B Atomic Molecular and Optical PhysicsJun 8, 20128 citations

Hole-burning techniques for isolation and study of individual hyperfine transitions in inhomogeneously broadened solids demonstrated in Pr3+:Y2SiO5

Mattias Nilsson, Lars Rippe, Stefan Kröll +2 more

Due to their narrow homogeneous linewidths, rare-earth ions in inorganic crystals at low temperatures have recently been given considerable attention as test materials for experiments in coherent quantum optics. Because these narrow linewidth transitions have been buried in a wide inhomogeneous line, the scope of experiments that could be carried out in these materials has been limited. However, here we present spectroscopic techniques, based on spectral hole burning and optical pumping, which allow hyperfine transitions that are initially buried within an inhomogeneously broadened absorption line to be studied with no background absorption from other transitions. A sequence of hole-burning pulses is used to isolate selected transitions between hyperfine levels, which makes it possible to directly study properties of the transitions, e.g., transition strengths, and gives access to information that is difficult to obtain in standard hole-burning spectroscopy, such as the ordering of hyperfine levels. The techniques introduced are applicable to absorbers in a solid with long-lived sublevels in the ground state and where the homogeneous linewidth and sublevel separations are smaller than the inhomogeneous broadening of the optical transition. In particular, this includes rare-earth ions doped into inorganic crystals and in the present work the techniques are demonstrated in spectroscopy of ${\mathrm{Pr}}^{3+}$ in ${\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$ . Information on the hyperfine structure and relative transition strengths of the $^{3}H_{4}\text{\ensuremath{-}}^{1}D_{2}$ hyperfine transitions in ${\mathrm{Pr}}^{3+}:{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$ has been obtained from frequency-resolved absorption measurements, in combination with coherent and incoherent driving of the transitions.Due to their narrow homogeneous linewidths, rare-earth ions in inorganic crystals at low temperatures have recently been given considerable attention as test materials for experiments in coherent quantum optics. Because these narrow linewidth transitions have been buried in a wide inhomogeneous line, the scope of experiments that could be carried out in these materials has been limited. However, here we present spectroscopic techniques, based on spectral hole burning and optical pumping, which allow hyperfine transitions that are initially buried within an inhomogeneously broadened absorption line to be studied with no background absorption from other transitions. A sequence of hole-burning pulses is used to isolate selected transitions between hyperfine levels, which makes it possible to directly study properties of the transitions, e.g., transition strengths, and gives access to information that is difficult to obtain in standard hole-burning spectroscopy, such as the ordering of hyperfine levels. The techniques introduced are applicable to absorbers in a solid with long-lived sublevels in the ground state and where the homogeneous linewidth and sublevel separations are smaller than the inhomogeneous broadening of the optical transition. In particular, this includes rare-earth ions doped into inorganic crystals and in the present work the techniques are demonstrated in spectroscopy of ${\mathrm{Pr}}^{3+}$ in ${\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$. Information on the hyperfine structure and relative transition strengths of the $^{3}H_{4}\text{\ensuremath{-}}^{1}D_{2}$ hyperfine transitions in ${\mathrm{Pr}}^{3+}:{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$ has been obtained from frequency-resolved absorption measurements, in combination with coherent and incoherent driving of the transitions.

arXiv:cond-mat/0408515Physical Review BDec 30, 2004201 citations

Hyperfine characterization and spin coherence lifetime extension in Pr 3 + :La 2 (WO 4 ) 3

Marko Lovrić, Philipp Glasenapp, Dieter Suter +6 more

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 Pr ${}^{3+}$ :La ${}_{2}$ (WO ${}_{4}$ ) ${}_{3}$ , 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 ( ${}^{3}$ $H$ ${}_{4}$ ) and one excited state ( ${}^{1}$ $D$ ${}_{2}$ ) 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 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 Pr${}^{3+}$:La${}_{2}$(WO${}_{4}$)${}_{3}$, 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}$$H$${}_{4}$) and one excited state (${}^{1}$$D$${}_{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.

arXiv:1107.2274Physical Review BSep 12, 201154 citations

Spectroscopic and relaxation character of the P03−H43 transition in La F3 : Pr3+ measured by photon echoes

Y.C. Chen, Kophu P. Chiang, Sven R. Hartmann

The hyperfine structure and relaxation character of the terminal levels of the $^{3}P_{0}\ensuremath{-}^{3}H_{4}$ (4777 \AA{}) transition in La ${\mathrm{F}}_{3}$ : ${\mathrm{Pr}}^{3+}$ (0.03 at.%) were studied using the photon-echo technique. Using two independent nitrogen-laser pumped dye lasers we have observed modulated photon echoes for pulse separations over a \ensuremath{\sim}10-\ensuremath{\mu}sec range. In this interval our modulated photon echoes decay in a simple exponential manner by a factor of ${10}^{5}$ and yield a homogeneous linewidth of 70 kHz [full width at half maximum (FWHM)]. Fourier transformation of the echo-modulation data yields directly the nuclear level splittings and their associated linewidths in the $^{3}P_{0}$ and $^{3}H_{4}$ states. In the $^{3}P_{0}(^{3}H_{4})$ state the nuclear splittings are 0.73 and 1.12 MHz (8.48 and 16.68 MHz). The measurements for the nuclear level splittings and associated linewidths in the $^{3}H_{4}$ state are in excellent agreement with those obtained from the optical-rf double-resonance experiments of Erickson. We find that the calculated echo modulation is a sensitive function of the relative orientation of the principal axes associated with the ground-and excited-state Hamiltonians. By comparing our experimental and calculated echo-modulation patterns we are able to determine their relative orientations.The hyperfine structure and relaxation character of the terminal levels of the $^{3}P_{0}\ensuremath{-}^{3}H_{4}$ (4777 \AA{}) transition in La${\mathrm{F}}_{3}$: ${\mathrm{Pr}}^{3+}$ (0.03 at.%) were studied using the photon-echo technique. Using two independent nitrogen-laser pumped dye lasers we have observed modulated photon echoes for pulse separations over a \ensuremath{\sim}10-\ensuremath{\mu}sec range. In this interval our modulated photon echoes decay in a simple exponential manner by a factor of ${10}^{5}$ and yield a homogeneous linewidth of 70 kHz [full width at half maximum (FWHM)]. Fourier transformation of the echo-modulation data yields directly the nuclear level splittings and their associated linewidths in the $^{3}P_{0}$ and $^{3}H_{4}$ states. In the $^{3}P_{0}(^{3}H_{4})$ state the nuclear splittings are 0.73 and 1.12 MHz (8.48 and 16.68 MHz). The measurements for the nuclear level splittings and associated linewidths in the $^{3}H_{4}$ state are in excellent agreement with those obtained from the optical-rf double-resonance experiments of Erickson. We find that the calculated echo modulation is a sensitive function of the relative orientation of the principal axes associated with the ground-and excited-state Hamiltonians. By comparing our experimental and calculated echo-modulation patterns we are able to determine their relative orientations.

Physical review. B, Condensed matterJan 1, 198064 citations

We studied the hyperfine structure and hyperfine coherent properties of the

{^{3}\text{H}}_{4}(0)\ensuremath{\rightarrow}{^{1}\text{D}}_{2}(0)

transition of

{\text{Pr}}^{3+}

ions in a tungstate single crystal

{\text{La}}_{2}{({\text{WO}}_{4})}_{3}

by hole-burning and photon-echo techniques. This work is motivated by the search of an efficient three level

\ensuremath{\Lambda}

system in this new compound with which we could build up a quantum memory. By nonconventional hole-burning experiments, the ordering of the hyperfine splittings in the

{^{3}\text{H}}_{4}(0)

ground state and in the

{^{1}\text{D}}_{2}(0)

excited state is obtained. The hyperfine splittings are thus ordered: 24.6 and 14.9 MHz for the

{^{3}\text{H}}_{4}(0)

level and 5.0 and 7.3 MHz for the

{^{1}\text{D}}_{2}(0)

57\ifmmode\pm\else\textpm\fi{}2

and

1.25\ifmmode\pm\else\textpm\fi{}0.1\text{ }\text{kHz}

, respectively.

{\mathrm{Pr}}^{3+}:{\mathrm{La}}_{2}{(\mathrm{W}{\mathrm{O}}_{4})}_{3}

4\phantom{\rule{0.3em}{0ex}}\mathrm{K}

have been measured by photon-echo and spectral-hole-burning techniques. The hyperfine splittings of the ground

^{3}H_{4}(0)

and the excited

^{1}D_{2}(0)

states are $14.9\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$, $24.6\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$ and $5.0\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$, $7.3\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$, respectively. An inhomogeneous linewidth of $18.8\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$ was measured. A homogeneous linewidth of $25.3\ifmmode\pm\else\textpm\fi{}2.0\phantom{\rule{0.3em}{0ex}}\mathrm{kHz}$ was obtained with or without an external magnetic field of about

14\phantom{\rule{0.3em}{0ex}}\mathrm{mT}

. The fluorescence dynamics of the

^{1}D_{2}

level obtained by a direct excitation in the $^{3}H_{4}\ensuremath{\rightarrow}^{1}D_{2}$ transition gives a nonexponential decay which indicates energy-transfer processes. This decay can be accurately fitted by the Inokuti-Hirayama model [J. Chem. Phys. 43, 1978 (1965)] with a radiative lifetime of $61\ifmmode\pm\else\textpm\fi{}1\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$ giving a minimal homogeneous linewidth of

2.6\phantom{\rule{0.3em}{0ex}}\mathrm{kHz}

. The spectral-hole lifetime due to population redistribution within the ground hyperfine levels is $16\ifmmode\pm\else\textpm\fi{}2\phantom{\rule{0.3em}{0ex}}\mathrm{s}$. The results obtained for the

{\mathrm{La}}_{2}{(\mathrm{W}{\mathrm{O}}_{4})}_{3}

compound make this crystal an interesting host for quantum applications.

As part of a search for suitable materials for coherent quantum operations, relaxation times and hyperfine structure of the $^{1}D_{2}(1)\text{\ensuremath{-}}^{3}H_{4}(1)$ transition in

{\mathrm{Pr}}^{3+}:\mathrm{KY}{({\mathrm{WO}}_{4})}_{2}

(0.29 at. %) at 4 K have been obtained using photon-echo and spectral hole burning techniques. The homogeneous linewidth and the effect of excitation-induced dephasing were measured using two-pulse photon-echo techniques. Linewidths of $23.4\ifmmode\pm\else\textpm\fi{}1.0$ and $17.6\ifmmode\pm\else\textpm\fi{}0.9\phantom{\rule{0.3em}{0ex}}\mathrm{kHz}$ were obtained in the absence and presence of an external magnetic field of about 9 mT. The radiative lifetime

({T}_{1})

of the

^{1}D_{2}

state was measured to be $43\ifmmode\pm\else\textpm\fi{}2\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$ using time-resolved laser-induced fluorescence and three-pulse photon-echo measurements. The transmission hole spectra were measured and directly yielded the quadrupole level splitting in the

^{1}D_{2}

($3.77\ifmmode\pm\else\textpm\fi{}0.03$ and $4.58\ifmmode\pm\else\textpm\fi{}0.04\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$) and

^{3}H_{4}

($17.1\ifmmode\pm\else\textpm\fi{}0.1$ and $33.2\ifmmode\pm\else\textpm\fi{}0.3\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$) states. The spectral hole lifetime due to population redistribution between the ground-state nuclear levels was also determined to be $70\ifmmode\pm\else\textpm\fi{}10\phantom{\rule{0.3em}{0ex}}\mathrm{ms}$. A strong dipole-dipole interaction observed in this crystal opens for potential applications in quantum computing schemes for performing quantum logic operations, but the short dephasing time makes it less useful in data storage applications.

{\mathrm{Pr}}^{3+}

{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}

. Information on the hyperfine structure and relative transition strengths of the $^{3}H_{4}\text{\ensuremath{-}}^{1}D_{2}$ hyperfine transitions in

{\mathrm{Pr}}^{3+}:{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}

has been obtained from frequency-resolved absorption measurements, in combination with coherent and incoherent driving of the transitions.

{}^{3+}

:La

{}_{2}

(WO

{}_{4}

)

{}_{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}

H

{}_{4}

) and one excited state (

{}^{1}

D

{}_{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.

The hyperfine structure and relaxation character of the terminal levels of the $^{3}P_{0}\ensuremath{-}^{3}H_{4}$ (4777 \AA{}) transition in La

{\mathrm{F}}_{3}

{\mathrm{Pr}}^{3+}

(0.03 at.%) were studied using the photon-echo technique. Using two independent nitrogen-laser pumped dye lasers we have observed modulated photon echoes for pulse separations over a \ensuremath{\sim}10-\ensuremath{\mu}sec range. In this interval our modulated photon echoes decay in a simple exponential manner by a factor of

{10}^{5}

and yield a homogeneous linewidth of 70 kHz [full width at half maximum (FWHM)]. Fourier transformation of the echo-modulation data yields directly the nuclear level splittings and their associated linewidths in the

^{3}P_{0}

and

^{3}H_{4}

states. In the

^{3}P_{0}(^{3}H_{4})

state the nuclear splittings are 0.73 and 1.12 MHz (8.48 and 16.68 MHz). The measurements for the nuclear level splittings and associated linewidths in the

^{3}H_{4}

state are in excellent agreement with those obtained from the optical-rf double-resonance experiments of Erickson. We find that the calculated echo modulation is a sensitive function of the relative orientation of the principal axes associated with the ground-and excited-state Hamiltonians. By comparing our experimental and calculated echo-modulation patterns we are able to determine their relative orientations.