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Physical review. B, Condensed matter

Site interference in Stark-modulated photon echoes

Felix R. Graf, Alois Renn, Urs P. Wild, Masaharu Mitsunaga

Published May 1, 1997• 27 citations
Publisher

Abstract

We show that Stark-pulse-modulated photon echoes in an impurity-ion-doped crystal are generally characterized by a complex oscillatory behavior with two or more frequency components which results from the interference of the static dipole moment differences of ions located at inequivalent sites. We analyze this phenomenon using group theory and present experimental evidence for a ${\mathrm{Pr}}^{3+}$- and ${\mathrm{Eu}}^{3+}$-codoped ${\mathrm{YAlO}}_{3}$ and a ${\mathrm{Pr}}^{3+}$-doped ${\mathrm{Y}}_{2}$${\mathrm{SiO}}_{5}$ crystal. It is demonstrated that the orientations of the dipole moments and of the crystal axes can be determined with subdegree accuracy.

DOI
10.1103/physrevb.55.11225

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Effect of a hybrid transition moment on Stark-modulated photon echoes in Er3+:Y2SiO5

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The 1538-nm ${}^{4}{\mathrm{I}}_{15/2} \ensuremath{\rightarrow} {}^{4}{\mathrm{I}}_{13/2}$ transition of ${\mathrm{Er}}^{3+}$ has an unusual hybrid electric-magnetic dipole character, and signatures of the hybrid moment can be expected in coherent transient measurements. Here, we investigate the effect of the hybrid moment in both sites of ${\mathrm{Er}}^{3+}$:${\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}$ on Stark-modulated photon echo measurements, showing that it results in a reduction of visibility of the modulated signal as well as phase and polarization shifts. We interpret these effects using a simple optical Bloch equation model, showing that site 1 has a strongly mixed moment and site 2 is predominantly magnetic dipole. We discuss the implications of the hybrid moment for quantum information applications of quantum memories. We also use the echo measurements to extract the Stark shift of the optical transition along three orthogonal directions, finding values between 10.50 and $11.93\phantom{\rule{4pt}{0ex}}\mathrm{kHz}\phantom{\rule{0.16em}{0ex}}{\mathrm{V}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}\mathrm{cm}$ for site 1 and 1.61 and $15.35\phantom{\rule{4pt}{0ex}}\mathrm{kHz}\phantom{\rule{0.16em}{0ex}}{\mathrm{V}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}\mathrm{cm}$ for site 2, dependent on the direction of the electric field. We observe a modification of the Zeeman shift by the electric field in both sites and discuss how this may be used to electrically control ${\mathrm{Er}}^{3+}$ spin qubits.

Physical review. B./Physical review. B•Nov 13, 2023•1 citation
We show that Stark-pulse-modulated photon echoes in an impurity-ion-doped crystal are generally characterized by a complex oscillatory behavior with two or more frequency components which results from the interference of the static dipole moment differences of ions located at inequivalent sites. We analyze this phenomenon using group theory and present experimental evidence for a Pr3+{\mathrm{Pr}}^{3+}Pr3+- and Eu3+{\mathrm{Eu}}^{3+}Eu3+-codoped YAlO3{\mathrm{YAlO}}_{3}YAlO3​ and a Pr3+{\mathrm{Pr}}^{3+}Pr3+-doped {\mathrm{Y}}_{2}$${\mathrm{SiO}}_{5} crystal. It is demonstrated that the orientations of the dipole moments and of the crystal axes can be determined with subdegree accuracy.
We study the photon-echo attenuation by various dynamical processes in rare-earth-ion-doped crystals. The experimental investigations concentrate on a Pr3+:Eu3+:Nd3+{\mathrm{Pr}}^{3+}:{\mathrm{Eu}}^{3+}:{\mathrm{Nd}}^{3+}Pr3+:Eu3+:Nd3+ codoped Y2SiO5{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}Y2​SiO5​ crystal at low temperatures. Two-pulse photon-echo intensities are measured as a function of the pulse intensities when either the Pr3+{\mathrm{Pr}}^{3+}Pr3+ or the Eu3+{\mathrm{Eu}}^{3+}Eu3+ ions are excited. For the quantitative interpretation we consider primarily excitation-induced frequency shifts (EFS) by diagonal and off-diagonal interactions and show that for the systems under consideration EFS are dominated by diagonal interactions. The observed echo attenuation by EFS is compared with the predictions calculated from independent Stark-field measurements and reasonable agreement is obtained. The broadening by spin-ion interactions, by nonequilibrium phonons and the dependence of the echo attenuation on the frequency position in the inhomogeneously broadened band are further investigated.
We study the optical properties of rare-earth-ion-doped inorganic crystals with an emphasis on the dependence of two-pulse photon echoes on the excitation density in the system. The experimental investigations concentrate on Pr3+{\mathrm{Pr}}^{3+}Pr3+:Nd3+{\mathrm{Nd}}^{3+}Nd3+:Eu3+{\mathrm{Eu}}^{3+}Eu3+ codoped Y2{\mathrm{Y}}_{2}Y2​SiO5{\mathrm{O}}_{5}O5​ and YAlO3{\mathrm{O}}_{3}O3​ crystals at low temperatures. With two pulses of one laser the echo is induced in one ion species and with a third, "scrambler" pulse of a second laser another species is excited. These scrambler excitations lead to a dephasing and thus to an echo attenuation which depends on the strength, frequency, and time of the scrambler pulse. The spectral sensitivity of the echo attenuation is used for a spectroscopic technique: "photon-echo attenuation spectroscopy." As a function of the delay time ts{t}_{s}ts​ between the scrambler pulse and the onset of the two-pulse echo sequence the attenuation shows a very specific behavior dictated by the excitation-induced frequency shifts (EFS's). For ts{t}_{s}ts​ between the two echo-inducing pulses the echo intensity is partially regained by the "dephasing-rephasing balancing" of the reversible EFS's. For the theoretical description a stochastic model is introduced and the dephasing by excitation-induced lattice vibrations and by EFS's are analyzed in detail. The present results are discussed in the light of previous experimental and theoretical investigations.
When the intensity of photon echo in a two-level system is measured as a function of delay time of the two input pulses, one obtains a simple exponential decay with the characteristic phase relaxation time. When the two levels contain hyperfine structures, the interference among the hyperfine levels gives rise to modulation of the decay envelope. The Fourier transform of the modulation pattern reveals the hyperfine structure of the rare-earth ions. The hyperfine structure, and therefore the modulation pattern, are both sensitively affected by the crystal environment of the ionic site. We extend photon-echo modulation spectroscopy to three-pulse, stimulated photon-echo modulation, and we find that the stimulated echo modulation patterns are quite distinct from the two-pulse, photon-echo case and are affected by a different set of atomic and crystal interaction parameters. The modulation is measured, in several photon-echo transitions of praseodymium ions in lanthanum trifluoride and yttrium aluminum garnet crystals, as functions of delay times between first and second pulses and between first and third pulses. Comparison of the experimental results with density-matrix calculations allows us to determine hyperfine parameters that are not easily observed with two-pulse echo modulation.
The recently developed technique of Raman heterodyne detection has unveiled a new interference effect in the Zeeman spectrum of hyperfine transitions of impurity-ion solids. An earlier theory had been developed to explain the basic Raman heterodyne process which involves the resonant interaction of a three-level quantum system with coherent optical-frequency and radiofrequency fields. However, it was not realized that impurity-ion crystals can generate more than one type of Raman heterodyne signal and that these signals can interfere. This article describes two examples of interference where one originates from two or more inequivalent nuclear sites and the other from a single site that exhibits interference among Zeeman transitions. An analytical theory covering these two cases is presented and compared to observations for the impurity-ion crystals Pr3+{\mathrm{Pr}}^{3+}Pr3+:YAlO3{\mathrm{YAlO}}_{3}YAlO3​ and Pr3+{\mathrm{Pr}}^{3+}Pr3+:LaF3{\mathrm{LaF}}_{3}LaF3​, the interference behavior in the two being dramatically different.
The 1538-nm ${}^{4}{\mathrm{I}}_{15/2} \ensuremath{\rightarrow} {}^{4}{\mathrm{I}}_{13/2}$ transition of Er3+{\mathrm{Er}}^{3+}Er3+ has an unusual hybrid electric-magnetic dipole character, and signatures of the hybrid moment can be expected in coherent transient measurements. Here, we investigate the effect of the hybrid moment in both sites of Er3+{\mathrm{Er}}^{3+}Er3+:Y2SiO5{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}Y2​SiO5​ on Stark-modulated photon echo measurements, showing that it results in a reduction of visibility of the modulated signal as well as phase and polarization shifts. We interpret these effects using a simple optical Bloch equation model, showing that site 1 has a strongly mixed moment and site 2 is predominantly magnetic dipole. We discuss the implications of the hybrid moment for quantum information applications of quantum memories. We also use the echo measurements to extract the Stark shift of the optical transition along three orthogonal directions, finding values between 10.50 and $11.93\phantom{\rule{4pt}{0ex}}\mathrm{kHz}\phantom{\rule{0.16em}{0ex}}{\mathrm{V}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}\mathrm{cm}$ for site 1 and 1.61 and $15.35\phantom{\rule{4pt}{0ex}}\mathrm{kHz}\phantom{\rule{0.16em}{0ex}}{\mathrm{V}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}\mathrm{cm}$ for site 2, dependent on the direction of the electric field. We observe a modification of the Zeeman shift by the electric field in both sites and discuss how this may be used to electrically control Er3+{\mathrm{Er}}^{3+}Er3+ spin qubits.