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arXiv:2101.10169 · Applied Physics Letters

Precision measurements of electric-field-induced frequency displacements of an ultranarrow optical transition in ions in a solid

S. Zhang, Nemanja Lučić, Nicolas Galland, Rodolphe Le Targat, Philippe Goldner, Bess Fang, Signe Louise Seidelin, Yann Le Coq

Published Nov 30, 2020• 10 citations
arXivHTMLPDF

Abstract

We report a series of measurements of the effect of an electric field on the frequency of the ultranarrow linewidth F70→ D50 optical transition of Eu3+ ions in an Y2SiO5 matrix at cryogenic temperatures. We provide linear Stark coefficients along two dielectric axes and for the two different substitution sites of the Eu3+ ions, with an unprecedented accuracy and an upper limit for the quadratic Stark shift. The measurements, which indicate that the electric field sensitivity is a factor of seven larger for site 1 relative to site 2 for a particular direction of the electric field, are of direct interest in the context of both quantum information processing and laser frequency stabilization with rare-earth doped crystals, in which electric fields can be used to engineer experimental protocols by tuning transition frequencies.

DOI
10.1063/5.0025356

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Single quantum emitters embedded in solid-state hosts are an ideal platform for realizing quantum information processors and quantum network nodes. Among the currently investigated candidates, Er^{3+} ions are particularly appealing due to their 1.5 μm optical transition in the telecom band as well as their long spin coherence times. However, the long lifetimes of the excited state-generally in excess of 1 ms-along with the inhomogeneous broadening of the optical transition result in significant challenges. Photon emission rates are prohibitively small, and different emitters generally create photons with distinct spectra, thereby preventing multiphoton interference-a requirement for building large-scale, multinode quantum networks. Here we solve this challenge by demonstrating for the first time linear Stark tuning of the emission frequency of a single Er^{3+} ion. Our ions are embedded in a lithium niobate crystal and couple evanescently to a silicon nanophotonic crystal cavity that provides a strong increase of the measured decay rate. By applying an electric field along the crystal c axis, we achieve a Stark tuning greater than the ion's linewidth without changing the single-photon emission statistics of the ion. These results are a key step towards rare earth ion-based quantum networks.

arXiv:2304.14685•Physical Review Letters•Oct 23, 2023•35 citations
We report a series of measurements of the effect of an electric field on the frequency of the ultranarrow linewidth F70→ D50 optical transition of Eu3+ ions in an Y2SiO5 matrix at cryogenic temperatures. We provide linear Stark coefficients along two dielectric axes and for the two different substitution sites of the Eu3+ ions, with an unprecedented accuracy and an upper limit for the quadratic Stark shift. The measurements, which indicate that the electric field sensitivity is a factor of seven larger for site 1 relative to site 2 for a particular direction of the electric field, are of direct interest in the context of both quantum information processing and laser frequency stabilization with rare-earth doped crystals, in which electric fields can be used to engineer experimental protocols by tuning transition frequencies.
We show that the coherence properties of the nuclear spin states of rare-earth ions in solids can be manipulated by small applied electric fields. This was done by measuring the Stark effect on the nuclear quadrupole transitions of 151Eu^{151}\mathrm{Eu}151Eu in Y2SiO5{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}Y2​SiO5​ (YSO) using a combination of Raman heterodyne optical detection and Stark modulated quadrupole echoes to achieve high sensitivity. The measured Stark coefficients were 0.42 and 1.0  Hz cm/V1.0\text{ }\text{ }\mathrm{Hz}\text{ }\mathrm{cm}/\mathrm{V}1.0  Hz cm/V for the two quadrupole transitions at 34.54 and 46.20 MHz, respectively. The long decoherence time of the nuclear spin states (25 ms) allowed us to make the measurements in very low electric fields of $\ensuremath{\sim}10\text{ }\text{ }\mathrm{V}/\mathrm{cm}$, which produced 100% modulation of the nuclear spin echo, and to measure Stark shifts of $\ensuremath{\sim}1\text{ }\text{ }\mathrm{Hz}$ or 20 ppm of the inhomogeneous linewidth.
We report measurements of discrete excitation-induced frequency shifts on the $^{7}F_{0}\ensuremath{\rightarrow}^{5}D_{0}$ transition of the Eu3+{\mathrm{Eu}}^{3+}Eu3+ center in $\mathrm{La}\mathrm{\text{:}}\mathrm{Lu}\mathrm{\text{:}}{\mathrm{EuCl}}_{3}\ifmmode\cdot\else\textperiodcentered\fi{}6{\mathrm{D}}_{2}\mathrm{O}$ resulting from the optical excitation of neighboring Eu3+{\mathrm{Eu}}^{3+}Eu3+ ions. Shifts of up to $46.081\ifmmode\pm\else\textpm\fi{}0.005\text{ }\text{ }\mathrm{MHz}$ were observed. The magnitude of the interaction between neighboring ions was found to be significantly larger than expected from the electric dipole-dipole mechanism often observed in rare earth systems. We show that a large network of interacting and individually addressable centers can be created by lightly doping crystals otherwise stoichiometric in the optically active rare earth ion, and that this network could be used to implement a quantum processor with more than ten qubits.
The photon echo is often the best technique for measuring ultra narrow homogeneous linewidths of an inhomogeneously broadened optical transition for which a higher spectral resolution than the laser bandwidth is required. Homogenous linewidths on the order of one kHz have been measured for Eu3+ and Pr3+ in different host materials at liquid helium temperature from the echo intensity as a function of the delay between the two excitation pulses. These linewidths arc three orders of magnitude narrower than the long term jitter bandwidth of the laser which was used for excitation.1 Here we present a novel spectroscopic method based on the modulation of a 2-pulsc photon echo or a stimulated echo by an externally applied field, for the accurate measurement of frequency shifting perturbations with sub-homogeneous linewidth resolution. This is illustrated by the Stark effect on the 7F0→5D0 transition of Eu3+:YAIO3. The basic idea is that two coherent preparation pulses create an excited state population grating in the frequency domain of an inhomogeneously broadened line, which then gives rise to the echo in the course of the free induction decay of the coherently prepared ions. Since the photon echo can be observed for pulse separations much larger than T2, it is possible to generate frequency gratings which have a periodic spacing smaller than the homogeneous linewidth.2 In the case of a centrosymmetric crystal there are two groups of ions with equal and opposite dipole moments. An applied electric field Es shifts the ground and excited state energy levels through interaction with the electric dipole moments of these states and hence leads to a linear frequency shift, Ω=δμ⇀⋅E⇀s/ℏ, for the two sets of ions in opposite directions, where δμ⇀ is the difference between the ground and excited state dipole moments. If the electric field is applied after the first pulse, the two sets of ions accumulate equal and opposite phase shifts Φ = ± Ωt during the time interval, t. The result of the second pulse is that an excited state population grating is created in the frequency domain with a period (t + τ)-1 where t is the time interval between the pulses and τ is the duration of one pulse. Since there arc two sets of ions with opposite phase shifts, we formally get two population gratings, one with the phase Φ = + Ωt and one with the phase Φ = − Ωt. with respect to the population grating that is caused without an applied field.
Solids containing rare earth (RE) ions have attracted spectroscopists' attention since the beginning of this century.In the last 30 years, their extremely narrow spectral features in combination with the use of non linear spectroscopy have served to sensitively measure ion-solid interactions and to progressively observe narrower homogeneous linewidths.The potential for using RE ion doped crystals as optical storage materials and processors has lately been a driving force in their investigations, Here, the ratio of inhomogeneous to homogeneous linewidth is regarded as an adequate measure of storage density and can become as big as 10 7 at cryogenic temperatures.Therefore, the analysis of line broadening is of fundamental as well as applied interest.This work is concerned with the investigation of interactions of RE ions with their environment.By means of a laser with a kilohertz resolution and non-linear spectroscopy, spectral dynamics as a function of intrinsic, external electric field, or light-pulse induced perturbations are analyzed on different time scales.In the first part, the theoretical background for the spectroscopy of RE ion doped crystals is outlined.The energy levels are presented and it is shown that due to their electronic properties RE ions have spectrally narrow electronic transitions, sometimes in the sub-kHz regime.The investigations of these narrow spectral features on the seconds to minutes time scale require very stable tunable laser sources.At present, such devices are not commercially available.In the second part, the performance of ahorne built laser system is characterized using persistent spectral holes, The results show that frequency selective materials can be used as powerful tools for the high resolution Vlll Abstract spectral analysis of laser sources.Complementary to that, they give a measure for the long term evolution of the spectral holes for the particular hole burning substance.In the third part, the effect of an external electric field on RE ion doped crystals is investigated.It is shown that for these systems the electric field induced frequency shifts are fully reversible.A general theory of Stark splittings of RE doped crystals is introduced and two methods are presented which allow for the determination of the magnitude and orientation of the electric dipole moment differences with sub-degree accuracy.Finally in the last part, spectral line broadening mechanisms of RE ion doped crystals are discussed and investigated by means of two-pulse photon echoes.Through variation of the experimental parameters, a discrimination between the different contributions is partly achieved and characteristic properties for different dephasing mechanisms are presented.In combination with the measurements from the third part, quantitative predictions of the electric dipole-dipole induced broadening are carried out, which are compared to the experimental results,
Single quantum emitters embedded in solid-state hosts are an ideal platform for realizing quantum information processors and quantum network nodes. Among the currently investigated candidates, Er^{3+} ions are particularly appealing due to their 1.5 μm optical transition in the telecom band as well as their long spin coherence times. However, the long lifetimes of the excited state-generally in excess of 1 ms-along with the inhomogeneous broadening of the optical transition result in significant challenges. Photon emission rates are prohibitively small, and different emitters generally create photons with distinct spectra, thereby preventing multiphoton interference-a requirement for building large-scale, multinode quantum networks. Here we solve this challenge by demonstrating for the first time linear Stark tuning of the emission frequency of a single Er^{3+} ion. Our ions are embedded in a lithium niobate crystal and couple evanescently to a silicon nanophotonic crystal cavity that provides a strong increase of the measured decay rate. By applying an electric field along the crystal c axis, we achieve a Stark tuning greater than the ion's linewidth without changing the single-photon emission statistics of the ion. These results are a key step towards rare earth ion-based quantum networks.