Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Inhomogeneous response of an ion ensemble from mechanical stress

Shuo Zhang, Nicolas Galland, Nemanja Lučić, Rodolphe Le Targat, Alban Ferrier, Philippe Goldner, Bess Fang, Yann Le Coq, Signe Louise Seidelin

Published Jan 1, 2020• 11 citations
OpenAlex

Abstract

Material strain has recently received growing attention as a complementary resource to control the energy levels of quantum emitters embedded inside a solid-state environment. Some rare-earth ion dopants provide an optical transition which simultaneously has a narrow linewidth and is highly sensitive to strain. In such systems, the technique of spectral hole burning, in which a transparent window is burned within the large inhomogeneous profile, allows one to benefit from the narrow features, which are also sensitive to strain, while working with large ensembles of ions. However, working with ensembles may give rise to inhomogeneous responses among different ions. We investigate experimentally how the shape of a narrow spectral hole is modified due to external mechanical strain, in particular, the hole broadening as a function of the geometry of the crystal sites and the crystalline axis along which the stress is applied. Studying these effects is essential in order to optimize the existing applications of rare-earth-doped crystals in fields which already profit from the more-well-established coherence properties of these dopants, such as frequency metrology and quantum information processing, or even suggest alternative applications of these materials, for example, as robust devices for force-sensing or highly sensitive accelerometers.Received 24 December 2019Accepted 20 February 2020DOI:https://doi.org/10.1103/PhysRevResearch.2.013306Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasDopantsFine & hyperfine structureOptics & lasersStressPhysical SystemsRare-earth doped crystalsGeneral Physics

Related papers

Inhomogeneous response of an ion ensemble from mechanical stress

S. Zhang, Nicolas Galland, Nemanja Lučić +6 more

Material strain has recently received growing attention as a complementary resource to control the energy levels of quantum emitters embedded inside a solid-state environment.Some rare-earth ion dopants provide an optical transition which simultaneously has a narrow linewidth and is highly sensitive to strain.In such systems, the technique of spectral hole burning, in which a transparent window is burned within the large inhomogeneous profile, allows one to benefit from the narrow features, which are also sensitive to strain, while working with large ensembles of ions.However, working with ensembles may give rise to inhomogeneous responses among different ions.We investigate experimentally how the shape of a narrow spectral hole is modified due to external mechanical strain, in particular, the hole broadening as a function of the geometry of the crystal sites and the crystalline axis along which the stress is applied.Studying these effects is essential in order to optimize the existing applications of rare-earth-doped crystals in fields which already profit from the more-well-established coherence properties of these dopants, such as frequency metrology and quantum information processing, or even suggest alternative applications of these materials, for example, as robust devices for force-sensing or highly sensitive accelerometers.

arXiv:2004.04951•Physical Review Research•Mar 12, 2020•13 citations

Mechanical Tunability of an Ultranarrow Spectral Feature of a Rare-Earth-Doped Crystal via Uniaxial Stress

Nicolas Galland, Nemanja Lučić, Bess Fang +6 more

Rare-earth-doped crystals have numerous applications ranging from frequency metrology to quantum information processing. To fully benefit from their exceptional coherence properties, the effect of mechanical strain on the energy levels of the dopants---whether it is a resource or perturbation---needs to be considered. We demonstrate that by applying uniaxial stress to a rare-earth-doped crystal containing a spectral hole, we can shift the hole by a controlled amount that is larger than the width of the hole. We deduce the sensitivity of $\mathrm{Eu}$${}^{3+}$ ions in an $\mathrm{Y}$${}_{2}$$\mathrm{Si}\mathrm{O}$${}_{5}$ matrix as a function of the crystal site and the crystalline axis along which the stress is applied.

arXiv:1912.10885•Physical Review Applied•Apr 8, 2020•24 citations

Dispersive coupling between light and a rare-earth-ion–doped mechanical resonator

Klaus Mølmer, Yann Le Coq, Signe Louise Seidelin

By spectrally hole burning an inhomogeneously broadened ensemble of ions while applying a controlled perturbation, one can obtain spectral holes that are functionalized for maximum sensitivity to different perturbations. We propose to use such hole-burned structures for the dispersive optical interaction with rare-earth-ion dopants whose frequencies are sensitive to crystal strain due to the bending motion of a crystal cantilever. A quantitative analysis shows that good optical sensitivity to the bending motion is obtained if a magnetic-field gradient is applied across the crystal during hole burning and that the resulting optomechanical coupling strength is sufficient for observing quantum features such as zero-point vibrations.

arXiv:1608.00804•Physical Review A•Nov 2, 2016•28 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.

arXiv:cond-mat/0408515•Physical Review B•Dec 30, 2004•201 citations

Investigations of spectral dynamics in rare earth ion doped crystals using high resolution laser techniques

Graf, Felix R.

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,

•Jan 1, 1998•5 citations

Light-Matter Interaction and Quantum Computing in Rare-Earth-Ion-Doped Crystals

Adam Kinos

In this thesis, crystals of yttrium orthosilicate (Y2SiO5) that are randomly doped with another rare-earth element, such as praseodymium (Pr), europium (Eu), or cerium (Ce), are investigated with lasers locked to ultra-stable cavities using the Pound-Drever-Hall locking technique. Many of these rare-earth elements have long-lived 4f-4f transitions, hundreds of microseconds to a few milliseconds, with even longer ground hyperfine lifetimes of up to several days. The coherence properties are, to the best of the author's knowledge, the longest achieved for any material, currently with a record of six hours for the nuclear spin states of Eu3+:Y2SiO5 measured at cryogenic temperatures. Furthermore, due to natural trapping and differences in the local environments, each dopant ion experiences a slightly different crystal field, and thus an inhomogeneity in the 4f-4f transition exists between all ions in a crystal. Since the homogeneous linewidth is in the order of kHz or below, whereas the inhomogeneous profile can be several GHz wide, these materials have dense storing capabilities.This thesis explores how light interacts with such rare-earth-ion-doped crystals; how the absorption and light polarization varies during propagation; how spectral features in the inhomogeneous absorption profile can be tailored to create narrowband spectral filters; how the speed of light is slowed down significantly in such narrow transmission windows; and how that can be used to either frequency shift incoming light, control its group velocity, or temporally compress pulses. It also uses rare-earth-ions to research quantum computing, the field of using quantum mechanical effects such as superpositions and entanglements to outperform classical computers on certain specific problems. This is done by examining how two-color pulses can be used to rapidly induce coherence from an initially mixed state; how qubit-qubit interactions can be performed experimentally using ensemble qubits, which opens the door to two-qubit experiments such as the CNOT-gate and entanglements; how a scalable quantum computer might be constructed using a single ion qubit approach with a dedicated readout ion and buffer ion(s) to improve readout fidelity; and how cerium is investigated as a candidate for such a dedicated readout ion.

•Feb 5, 2018•0 citations
Material strain has recently received growing attention as a complementary resource to control the energy levels of quantum emitters embedded inside a solid-state environment. Some rare-earth ion dopants provide an optical transition which simultaneously has a narrow linewidth and is highly sensitive to strain. In such systems, the technique of spectral hole burning, in which a transparent window is burned within the large inhomogeneous profile, allows one to benefit from the narrow features, which are also sensitive to strain, while working with large ensembles of ions. However, working with ensembles may give rise to inhomogeneous responses among different ions. We investigate experimentally how the shape of a narrow spectral hole is modified due to external mechanical strain, in particular, the hole broadening as a function of the geometry of the crystal sites and the crystalline axis along which the stress is applied. Studying these effects is essential in order to optimize the existing applications of rare-earth-doped crystals in fields which already profit from the more-well-established coherence properties of these dopants, such as frequency metrology and quantum information processing, or even suggest alternative applications of these materials, for example, as robust devices for force-sensing or highly sensitive accelerometers.Received 24 December 2019Accepted 20 February 2020DOI:https://doi.org/10.1103/PhysRevResearch.2.013306Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasDopantsFine & hyperfine structureOptics & lasersStressPhysical SystemsRare-earth doped crystalsGeneral Physics
Material strain has recently received growing attention as a complementary resource to control the energy levels of quantum emitters embedded inside a solid-state environment.Some rare-earth ion dopants provide an optical transition which simultaneously has a narrow linewidth and is highly sensitive to strain.In such systems, the technique of spectral hole burning, in which a transparent window is burned within the large inhomogeneous profile, allows one to benefit from the narrow features, which are also sensitive to strain, while working with large ensembles of ions.However, working with ensembles may give rise to inhomogeneous responses among different ions.We investigate experimentally how the shape of a narrow spectral hole is modified due to external mechanical strain, in particular, the hole broadening as a function of the geometry of the crystal sites and the crystalline axis along which the stress is applied.Studying these effects is essential in order to optimize the existing applications of rare-earth-doped crystals in fields which already profit from the more-well-established coherence properties of these dopants, such as frequency metrology and quantum information processing, or even suggest alternative applications of these materials, for example, as robust devices for force-sensing or highly sensitive accelerometers.
Rare-earth-doped crystals have numerous applications ranging from frequency metrology to quantum information processing. To fully benefit from their exceptional coherence properties, the effect of mechanical strain on the energy levels of the dopants---whether it is a resource or perturbation---needs to be considered. We demonstrate that by applying uniaxial stress to a rare-earth-doped crystal containing a spectral hole, we can shift the hole by a controlled amount that is larger than the width of the hole. We deduce the sensitivity of Eu\mathrm{Eu}Eu3+{}^{3+}3+ ions in an Y\mathrm{Y}Y2{}_{2}2​SiO\mathrm{Si}\mathrm{O}SiO5{}_{5}5​ matrix as a function of the crystal site and the crystalline axis along which the stress is applied.
By spectrally hole burning an inhomogeneously broadened ensemble of ions while applying a controlled perturbation, one can obtain spectral holes that are functionalized for maximum sensitivity to different perturbations. We propose to use such hole-burned structures for the dispersive optical interaction with rare-earth-ion dopants whose frequencies are sensitive to crystal strain due to the bending motion of a crystal cantilever. A quantitative analysis shows that good optical sensitivity to the bending motion is obtained if a magnetic-field gradient is applied across the crystal during hole burning and that the resulting optomechanical coupling strength is sufficient for observing quantum features such as zero-point vibrations.
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 Pr3+{\mathrm{Pr}}^{3+}Pr3+ in Y2SiO5{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}Y2​SiO5​. Information on the hyperfine structure and relative transition strengths of the $^{3}H_{4}\text{\ensuremath{-}}^{1}D_{2}$ hyperfine transitions in Pr3+:Y2SiO5{\mathrm{Pr}}^{3+}:{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}Pr3+:Y2​SiO5​ has been obtained from frequency-resolved absorption measurements, in combination with coherent and incoherent driving of the transitions.
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,
In this thesis, crystals of yttrium orthosilicate (Y2SiO5) that are randomly doped with another rare-earth element, such as praseodymium (Pr), europium (Eu), or cerium (Ce), are investigated with lasers locked to ultra-stable cavities using the Pound-Drever-Hall locking technique. Many of these rare-earth elements have long-lived 4f-4f transitions, hundreds of microseconds to a few milliseconds, with even longer ground hyperfine lifetimes of up to several days. The coherence properties are, to the best of the author's knowledge, the longest achieved for any material, currently with a record of six hours for the nuclear spin states of Eu3+:Y2SiO5 measured at cryogenic temperatures. Furthermore, due to natural trapping and differences in the local environments, each dopant ion experiences a slightly different crystal field, and thus an inhomogeneity in the 4f-4f transition exists between all ions in a crystal. Since the homogeneous linewidth is in the order of kHz or below, whereas the inhomogeneous profile can be several GHz wide, these materials have dense storing capabilities.This thesis explores how light interacts with such rare-earth-ion-doped crystals; how the absorption and light polarization varies during propagation; how spectral features in the inhomogeneous absorption profile can be tailored to create narrowband spectral filters; how the speed of light is slowed down significantly in such narrow transmission windows; and how that can be used to either frequency shift incoming light, control its group velocity, or temporally compress pulses. It also uses rare-earth-ions to research quantum computing, the field of using quantum mechanical effects such as superpositions and entanglements to outperform classical computers on certain specific problems. This is done by examining how two-color pulses can be used to rapidly induce coherence from an initially mixed state; how qubit-qubit interactions can be performed experimentally using ensemble qubits, which opens the door to two-qubit experiments such as the CNOT-gate and entanglements; how a scalable quantum computer might be constructed using a single ion qubit approach with a dedicated readout ion and buffer ion(s) to improve readout fidelity; and how cerium is investigated as a candidate for such a dedicated readout ion.