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Physical Review A

Polarization-dependent Rabi frequency beats in the coherent response of Tm3+ in YAG

Christoph M. Greiner, B. Boggs, Thomas H. Loftus, Tong Wang, THOMAS W. MOSSBERG

Published Oct 1, 1999• 24 citations
Publisher

Abstract

We experimentally and theoretically investigate the coherent response of ${\mathrm{Tm}}^{3+}$ ions in yttrium aluminum garnet (YAG). Working on the ${}^{3}{H}_{6}{(1)}^{3}{H}_{4}(1)$ transition we observe optical nutation signals that exhibit multiple distinct Fourier components having polarization-dependent frequencies and weights. This phenomenon is caused by the presence of six different transition-dipole moment orientations of ${\mathrm{Tm}}^{3+}$ ions in YAG and a resultant dependence of ion-field coupling on field-propagation direction and polarization. Experimental data shown are in excellent agreement with simulation results based on numerical integration of the Maxwell-Bloch equations.

DOI
10.1103/physreva.60.r2657

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We experimentally and theoretically investigate the coherent response of Tm3+{\mathrm{Tm}}^{3+}Tm3+ ions in yttrium aluminum garnet (YAG). Working on the 3H6(1)3H4(1){}^{3}{H}_{6}{(1)}^{3}{H}_{4}(1)3H6​(1)3H4​(1) transition we observe optical nutation signals that exhibit multiple distinct Fourier components having polarization-dependent frequencies and weights. This phenomenon is caused by the presence of six different transition-dipole moment orientations of Tm3+{\mathrm{Tm}}^{3+}Tm3+ ions in YAG and a resultant dependence of ion-field coupling on field-propagation direction and polarization. Experimental data shown are in excellent agreement with simulation results based on numerical integration of the Maxwell-Bloch equations.
The spectra of luminescence and magnetic circular polarization of luminescence in the 1 D 2 → 3 F 4 emission band in thulium:yttrium-aluminum garnet Tm3+:YAG (Tm3+:Y3Al5O12) have been investigated at temperatures T = 78 and 293 K, respectively. Based on the analysis of the magnetooptical and optical spectra, the optical transitions between the Stark sublevels of the 3 F 4 and 1 D 2 multiplets in Tm3+:YAG were identified. It is shown that the symmetry and energies of the Stark sublevels of the 3 F 4, 1 D 2, and 3 H 6 multiplets, found experimentally from magnetic and magnetooptical studies, confirm the results of theoretical calculations of the energy spectrum of the rare earth Tm3+ ion in YAG.
We report an experimental study of the $1.064\text{ }\ensuremath{\mu}\text{m}$ transition dipoles in neodymium-doped yttrium aluminum garnet (Nd:YAG) by measuring the coupling constant between two orthogonal modes of a laser cavity for different cuts of the YAG gain crystal. We propose a theoretical model in which the transition dipoles, slightly elliptic, are oriented along the crystallographic axes. Our experimental measurements show a very good quantitative agreement with this model and predict a dipole ellipticity between 2% and 3%. This work provides an experimental evidence for the simple description in which transition dipoles and crystallographic axes are collinear in Nd:YAG (with an accuracy better than $1\ifmmode^\circ\else\textdegree\fi{}$), a point that has been discussed for years.
Spectroscopic studies and the efficiency of optical coherent transient devices can be adversely affected by interference arising from several distinct Rabi frequencies associated with crystallographically equivalent but orientationally inequivalent crystal sites. General symmetry principles have been used to find light field directions that guarantee both optimum single-Rabi-frequency interaction and the most efficient coherent transient generation in arbitrary crystals. This theoretical analysis has been applied experimentally to a wide range of rare earth crystals, many of which are important for technological applications. Site interference in optical nutation provides a simple illustration of this effect. Optimum single-Rabi-frequency nutation signal was obtained for the 3H6(1){}^{3}{H}_{6}(1)3H6​(1) to 3H4(1){}^{3}{H}_{4}(1)3H4​(1) transition of 0.1% Tm3+:Y3Al5O12{\mathrm{Tm}}^{3+}:{\mathrm{Y}}_{3}{\mathrm{Al}}_{5}{\mathrm{O}}_{12}Tm3+:Y3​Al5​O12​ when the light $\stackrel{\ensuremath{\rightarrow}}{E}$ vector is along special crystal directions 〈111〉〈111〉〈111〉 or 〈001〉.〈001〉.〈001〉. Quantitative comparison of nutation frequencies for light polarized along different directions allowed the determination of the optical transition dipole moment to be along 〈110〉〈110〉〈110〉 for this transition. The transition dipole moment derived from the nutation signal agrees within 15% with that obtained from absorption experiments. Other applications of nutation measurements are discussed, including a procedure for determining site occupancy in crystals with crystallographically inequivalent sites.
We report an experimental study of the 1.064 ¹m transition dipoles in neodymium doped yttrium aluminum garnet (Nd-YAG) by measuring the coupling constant between two orthogonal modes of a laser cavity for different cuts of the YAG gain crystal. We propose a theoretical model in which the transition dipoles, slightly elliptic, are oriented along the crystallographic axes. Our experimental measurements show a very good quantitative agreement with this model, and predict a dipole ellipticity between 2% and 3%. This work provides an experimental evidence for the simple description in which transition dipoles and crystallographic axes are collinear in Nd-YAG (with an accuracy better than 1 deg), a point that has been discussed for years.
The response of a Nd3+{\text{Nd}}^{3+}Nd3+-doped yttrium-aluminum-garnet laser is examined experimentally when the pump polarization direction is abruptly changed from one to the other stress-induced principal axis of the cavity. As a result, the laser output polarization changes direction but only after a significant delay. We numerically solve rate equations that describe the evolution of the two polarization fields coupled to the population inversion. The simulations indicate that the polarization switching (PS) delay depends on two successive processes that we analyze using multi-time-scale techniques. The analysis predicts two qualitatively different PS responses depending on how close the laser is from its threshold. Finally, we compare quantitatively the experimental and theoretical estimates of the PS delay.
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.