The temporal dependence of the fluorescence line shape of Pr ion diluted in La
F3 has been studied in detail. The line-shape study is based on the assumption that the cross relaxation between Pr ions dominates the nonradiative process. The ion-ion interaction has been directly probed by the two-ion cooperative absorption process under which a
3P0 level lifetime dilation has been observed. The dilation effect can be suppressed when the spectral energy transfer is switched on by raising the temperature of the host crystal. The temporal behavior of the fluorescence line shape of the
1D2 level has been systematically investigated. The "inhomogeneous" linewidth is found to be composed of a main central peak and a series of ion-pair satellites. The shorter decay lifetime of the ion-pair states results in the narrowing of the emission line shape at later times. The energy positions of the ion-pair states have been measured from the
1D2 ion pairs up-conversion fluorescence process. The lifetime of the ion-pair states is determined by the coupling strength of the cross relaxation from an excited ion to its partner ion and hence varies according to the ion-pair separation. The decay under the inhomogeneous width is nonexponential in general. Based on the number of the distinguished ion pair levels, a concept of the sphere of influence is introduced. Following this model, an approach has been developed which allows us to study the decay characteristics. Systematical trends emerge from such analysis. The cross-relaxation coupling constants for ion pairs have been extracted from the decay curves and profiles of the ion-pairs line shape have been mapped out. Their peak positions agree with those obtained from
1D2 ion-pair up-conversion fluorescence measurements.
Up to now, only quantum computing using few quantum bits have been realized [1]. Main obstacles to increase the size of quantum register are fast decoherence and difficulties to control many-qubits entanglement. The clusters of the Nd3+ions formed in the Nd3+:LaF3crystal can be a candidate for many-qubit CNOT-gate, because of their entangled states due to strong coherent interaction (Davydov's splitting; bright and dark states with their own lifetimes τ and ra), weak electron-phonon coupling and long coherence time of the excited states. It was shown earlier that satellite lines of the main spectral line for single-site optical center of absorption [2, 3] and fluorescence excitation spectra [2] of Nd3+:LaF3crystals can be attributed to Nd3+ion pairs. The direct measurement of the fluorescence decay times for various classes of Nd3+pairs was made [2] since the pairs are well selected by fluorescence excitation wavelength.
We present optical linewidth and line-shape studies of transitions of
4f impurity ions in doubly doped systems and show that interactions which involve excitation transfer between the impurity systems produce homogeneous broadening and line-shape changes in the optical transitions. In particular, we have studied the behavior of the 5985-\AA{} line of
Pr3+ in doubly doped La
F3:
Pr3+,
Nd3+ as a function of
Nd3+ concentration. The 5985-\AA{}
Pr3+ transition at 4.2\ifmmode^\circ\else\textdegree\fi{}K involves two long-lived electronic states of the
Pr3+ ion; it follows that in the singly doped La
F3:
Pr3+ the transition shows a Gaussian shape which is characteristic of inhomogeneous strain and imperfection broadening. As
Nd3+ is added to the system, a broader Lorentzian component begins to appear in the 5985-\AA{}
Pr3+ transition and eventually (at
Nd3+ concentrations of \ensuremath{\sim}1% or above) completely dominates the width and shape of the transition. The Lorentzian component of the transition line shape was successfully separated using a Fourier-transform technique and the width of this component was studied as a function of the
Nd3+ concentration. The width is found to increase linearly with increasing
Nd3+ concentration up to concentrations of 2%; at higher concentrations, the linewidth saturates and approaches an asymptotic value of \ensuremath{\sim}2 ${\mathrm{cm}}^{\ensuremath{-}1}$. We construe this homogeneous component to be evidence of a rapid short-range energy transfer mechanism between the
Pr3+ and
Nd3+ systems at the terminating
(3H6)1 level of the 5985-\AA{}
Pr3+ transition. Various mechanisms are investigated as causes of the energy transfer process; it is concluded that the spin-exchange interaction is the most probable cause for the transfer. Results of other spectroscopic measurements on the doubly doped La
F3:
Pr3+,
Nd3+ system are also presented.
Using the energy level shift induced by a Nd3+ ion on a neighbour ion, the selective excitation of a class of (Nd, Nd) pairs is possible in weakly doped samples with a spectrally narrow laser. The observation of an anti-Stokes fluorescence shows that a pair can absorb two photons. From experiments with a magnetic field, it is shown that using a single laser, the double excitation of moderatly coupled pairs is essentially induced by a double quantum process by which two photons are simultaneously absorbed. The strongly coupled pairs, on the contrary, can only be doubly excited by two lasers of different frequencies. Orders of magnitude of the coupling strength between the two ions are deduced from the difference between these frequencies.
4fn ⇒ 4fn transitions of trivalent rare earth ions doped in crystals frequently give sharp spectral lines. The transitions associated with the higher levels of a multiplet can be relatively sharp, 10-1000 GHz, where the width is determined by the decay rate of the levels by spontaneous phonon emission to lower levels. The transitions and their linewidth can be determined using conventional absorption or excitation techniques. On the other hand the transitions associated with the meta-stable lower levels typically give much sharper features with linewidths of 1 - 100 GHz and the widths are determined by the inhomogeneities of the crystal field. These inhomogeneous linewdths can be obtained by conventional spectroscopic techniques but the homogeneous linewidth requires more innovative techniques such as optical holeburning or photon echoes. The time domain photon echo measurements do not requiring a high resolution source and have frequently been used to establish that the homogeneous linewidth of such transitions. The lines can be very narrow down to the kHz regime [1,2]. Should complimentary measurements be attempted in the frequency domain utilising holeburning a special frequency stabilised lasers is required and one has been developed in association with the current work [3].