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Measurement of linewidths and permanent electric dipole moment change of the Ce 4 f -5d transition in Y2SiO5 for qubit readout scheme in rare-earth ion based quantum computing

Ying-yan, LiheZhen, JunXu, JennyKar, LarsRipp, AndreasW, DianaSer, DavidLind, Mats-Erik, StefanKr, Philippe

Published May 30, 2013• 0 citations
OpenAlex

Abstract

In this work the inhomogeneous (zero-phonon line) and homogeneous linewidths and the permanent electric dipole moment change (averaged value of all dipole orientations) for the Ce 4f -5d transition in Y2SiO5 were measured in order to investigate the possibility for using Ce as a sensor to detect the hyperfine state of a spatially close-lying Pr or Eu ion. The experiments were carried out on Ce doped or Ce-Pr co-doped single Y2SiO5 crystals. The homogeneous linewidth is essentially limited by the excited state lifetime. Based on the linewidth measurements, the oscillator strength, absorption cross section, and saturation intensity were calculated to be about 6.2(±1.7) × 10？7, 4.5(±1.3) × 10？19 m2, and 1.4(±0.4) × 107 W/m2, respectively. The difference in permanent dipole moment, μCe, between the ground and excited states of the Ce ion was measured as 9.6(±5.3) × 10？30 C m. These measurements indicate that Ce is a promising readout ion to probe a single-ion qubit state for the quantum computing scheme using rare-earth ions.

Related papers

Measurement of linewidths and permanent electric dipole moment change of the Ce 4f - 5d transition in Y 2 SiO 5 for qubit readout scheme in rare-earth ion based quantum computing

Ying Lin Yan, Jenny Karlsson, Lars Rippe +8 more

In this work the inhomogeneous (zero-phonon line) and homogeneous linewidths and the permanent electric dipole moment change (averaged value of all dipole orientations) for the Ce $4f$-$5d$ transition in Y${}_{2}$SiO${}_{5}\phantom{\rule{0.16em}{0ex}}$ were measured in order to investigate the possibility for using Ce as a sensor to detect the hyperfine state of a spatially close-lying Pr or Eu ion. The experiments were carried out on Ce doped or Ce-Pr co-doped single Y${}_{2}$SiO${}_{5}\phantom{\rule{0.16em}{0ex}}$ crystals. The homogeneous linewidth is essentially limited by the excited state lifetime. Based on the linewidth measurements, the oscillator strength, absorption cross section, and saturation intensity were calculated to be about 6.2$(\ifmmode\pm\else\textpm\fi{}1.7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$, $4.5(\ifmmode\pm\else\textpm\fi{}1.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}\phantom{\rule{0.222222em}{0ex}}$m${}^{2}$, and $1.4(\ifmmode\pm\else\textpm\fi{}0.4)\ifmmode\times\else\texttimes\fi{}{10}^{7}\phantom{\rule{0.222222em}{0ex}}$W/m${}^{2}$, respectively. The difference in permanent dipole moment, $△{\ensuremath{\mu}}_{\mathrm{Ce}}$, between the ground and excited states of the Ce ion was measured as $9.6(\ifmmode\pm\else\textpm\fi{}5.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}30}\phantom{\rule{0.222222em}{0ex}}$C m. These measurements indicate that Ce is a promising readout ion to probe a single-ion qubit state for the quantum computing scheme using rare-earth ions.

arXiv:1303.0877•Physical Review B•May 30, 2013•25 citations

Towards single Ce ion detection in a bulk crystal for the development of a single-ion qubit readout scheme

Ying Lin Yan

The work presented in this thesis was concerned with investigating the relevant spectroscopic properties of Ce ions randomly doped in an Y2SiO5 crystal at low temperatures (around 4 K), in order to develop a technique and an experimental set-up to detect the fluorescence photons emitted by a single Ce ion. The aim of the work was to determine whether a single Ce ion (referred to as the readout ion) can be used as a local probe to sense the quantum state of a neighbouring single-ion qubit via a state-selective interaction between the readout and qubit ion. More precisely, if the qubit ion is in state |1> or |0> state, the single Ce ion will, or will not, emit fluorescence photons. This single ion readout concept is a key step towards single-rare-earth-ion quantum computing, which is believed to be a promising approach for a scalable quantum computer. Rare-earth ion based quantum computing is an attractive scheme for several reasons. Firstly, the qubit coherence time can be on the timescale of a minute while the optical coherence time can be on the millisecond timescale, despite the fact that the ions are in a solid (crystal), which means that more than 10000 optical pulses could be implemented before the system decoheres. Secondly, any sub-ensemble of ions in a frequency interval equal to or larger than the homogeneous linewidth within the inhomogeneously broadened absorption line can be used as a frequency-selectively addressed qubit. The proof of principle of the qubit-qubit interaction has been previously demonstrated. Thirdly, no special material engineering is required, and the crystal is commercially available. Ways of initializing a sub-ensemble of Pr ions as a qubit in the random system, manipulating the quantum state of the ions in a controlled way, and characterizing the quantum state created are presented. In order to achieve better scalability, the idea of letting a single rare-earth ion represent a qubit was investigated. The fidelity of the single-ion readout scheme was briefly studied. The influence of the energy transfer process between two neighbouring ions on quantum computing is discussed. A readout ion should possess a number of specific spectroscopic properties. Therefore, the position and the linewidths of the zero-phonon line of Ce ions were measured using an external cavity diode laser (at 371 nm) as the excitation source. The difference in the permanent dipole moment of the ground and excited states of Ce ions was measured in a photon echo experiment on Pr ions in a Ce-Pr co-doped Y2SiO5 crystal. The last and most important task was to realize single Ce ion detection. Fluorescence of Ce ions has been detected from a crystal, where there is on average 1 ion within 4.6 \micro m$^3$ interacting with the excitation laser at a time. Estimates were made of the number of ions contributing to an observed signal. A trial experiment to investigate whether the signal was emitted by a single Ce ion was carried out, but was unsuccessful. Potential reasons why the experiment failed are presented.

Lund reports on atomic physics•Jan 1, 2013•1 citation

Cerium as a quantum state probe for rare-earth qubits in a crystal

Jenny Karlsson

Rare-earth ions doped into a transparent crystal can have optically excited states with coherence times of milliseconds and hyperfine levels with coherence times of hours when cooled down to liquid helium temperatures. This makes them attractive for developing quantum computing hardware. A quantum transistor can be implemented in a rare-earth-ion-doped crystal by utilizing a dipole blockade effect, where one excited ion prevents nearby ions from being excited. By using single rare-earth ions as qubits, the quantum processor is believed to be scalable to several qubits. In this thesis a readout mechanism for qubits represented by single ions (Eu or Pr) in a Y2SiO5 crystal is explored. A single cerium ion, in the same crystal as the qubits, could potentially be used as an indicator ion for non-demolition quantum state detection of the qubits. Cerium has a strong transition with high fluorescence yield which makes it possible to detect single ions. A cerium ion can be controlled by a qubit via the dipole blockade effect, and fluoresce if the qubit is in state |1> but stay dark if the qubit is in state |0>. Relevant spectroscopic properties of Ce:Y2SiO5 are studied, as well as interactions between cerium ions and qubit ions. The inhomogeneous and homogeneous linewidth of the Ce:Y2SiO5 4f-5d transition is measured and fluorescence spectra for ions in site 1 and site 2 are characterized. The change in electric dipole moment as a cerium ion is brought to the excited state is measured. The static dipole interaction between a single cerium ion and a qubit ion is shown to be strong enough for efficient qubit readout. Energy transfer from cerium to qubit ions is investigated. A lower bound on the cerium-qubit distance is found in order to avoid energy transfer. Satellite lines belonging to cerium-qubit pairs are mapped out. A microscope set-up is built to detect single ions in a crystal. Single ion detection is believed to be within reach.

•Jan 1, 2015•1 citation

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

Single Ion Detection of Cerium in Y2SiO5 Microcrystals

Vassily Kornienko

Quantum computing with single instances of rare earth-ions doped into inorganic crystals shows great promise as a scalable design in the field of quantum information. A detectable and controllable single readout ion is necessary for the scheme proposed in Lund to work. Due to its short excited state lifetime and its cyclable 4f-5d transition, cerium has been deemed suitable for just this purpose. The approach taken in Lund for this single cerium detection is to use a homemade confocal microscopy setup. In previous work using this setup on bulk crystals, it has been assumed that the undetectability of single cerium is due to out of focus ions contributing to a noise floor that is higher than the fluorescence signal from a single one. Hence single ion detection is being attempted in microcrystals. This thesis outlines the process behind converting the confocal microscope into a microcrystal detection setup. Subsequently, Ce3+:Y2SiO5 microcrystal spectroscopy experiments were performed. The energy level structure of cerium is reported to be identical to bulk, with a slight shift in wavelength, and the inhomogenous linewidth has proven to be inconclusive, although it hints towards being much wider than in bulk. Quantifying the homogenous linewidth of the cerium ions using Zeeman hole burning techniques was impervious to our attempts.

•Jan 1, 2019•0 citations

An unconventional approach to quantum computing based on rare-earth-ion doped inorganic crystals, including proof of principle experiments.

Nicklas Ohlsson, Tomas Christiansson, Stefan Kröll +3 more

We present a scheme for quantum computing in rare-earth-ion doped inorganic crystals. We use two of the ground state hyperfine levels as the qubit states, with different qubits absorbing light at different frequencies within an inhomogeneously broadened optical transition. Interaction between different qubits is accomplished using the change in permanent dipole moment that is induced at the optical excitation of the ions. The two most important aspects of the scheme have been accomplished experimentally: The isolation of a single qubit in a pure state and interaction between ions absorbing at different frequencies.

Optical Fiber Communication Conference•Jan 1, 2001•0 citations
In this work the inhomogeneous (zero-phonon line) and homogeneous linewidths and the permanent electric dipole moment change (averaged value of all dipole orientations) for the Ce 4f -5d transition in Y2SiO5 were measured in order to investigate the possibility for using Ce as a sensor to detect the hyperfine state of a spatially close-lying Pr or Eu ion. The experiments were carried out on Ce doped or Ce-Pr co-doped single Y2SiO5 crystals. The homogeneous linewidth is essentially limited by the excited state lifetime. Based on the
linewidth measurements, the oscillator strength, absorption cross section, and saturation intensity were calculated to be about 6.2(±1.7) × 10？7, 4.5(±1.3) × 10？19 m2, and 1.4(±0.4) × 107 W/m2, respectively. The difference
in permanent dipole moment, μCe, between the ground and excited states of the Ce ion was measured as 9.6(±5.3) × 10？30 C m. These measurements indicate that Ce is a promising readout ion to probe a single-ion qubit state for the quantum computing scheme using rare-earth ions.
In this work the inhomogeneous (zero-phonon line) and homogeneous linewidths and the permanent electric dipole moment change (averaged value of all dipole orientations) for the Ce 4f4f4f-5d5d5d transition in Y2{}_{2}2​SiO5{}_{5}\phantom{\rule{0.16em}{0ex}}5​ were measured in order to investigate the possibility for using Ce as a sensor to detect the hyperfine state of a spatially close-lying Pr or Eu ion. The experiments were carried out on Ce doped or Ce-Pr co-doped single Y2{}_{2}2​SiO5{}_{5}\phantom{\rule{0.16em}{0ex}}5​ crystals. The homogeneous linewidth is essentially limited by the excited state lifetime. Based on the linewidth measurements, the oscillator strength, absorption cross section, and saturation intensity were calculated to be about 6.2$(\ifmmode\pm\else\textpm\fi{}1.7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$, $4.5(\ifmmode\pm\else\textpm\fi{}1.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}\phantom{\rule{0.222222em}{0ex}}$m2{}^{2}2, and $1.4(\ifmmode\pm\else\textpm\fi{}0.4)\ifmmode\times\else\texttimes\fi{}{10}^{7}\phantom{\rule{0.222222em}{0ex}}$W/m2{}^{2}2, respectively. The difference in permanent dipole moment, $△{\ensuremath{\mu}}_{\mathrm{Ce}}$, between the ground and excited states of the Ce ion was measured as $9.6(\ifmmode\pm\else\textpm\fi{}5.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}30}\phantom{\rule{0.222222em}{0ex}}$C m. These measurements indicate that Ce is a promising readout ion to probe a single-ion qubit state for the quantum computing scheme using rare-earth ions.
The work presented in this thesis was concerned with investigating the relevant spectroscopic properties of Ce ions randomly doped in an Y2SiO5 crystal at low temperatures (around 4 K), in order to develop a technique and an experimental set-up to detect the fluorescence photons emitted by a single Ce ion. The aim of the work was to determine whether a single Ce ion (referred to as the readout ion) can be used as a local probe to sense the quantum state of a neighbouring single-ion qubit via a state-selective interaction between the readout and qubit ion. More precisely, if the qubit ion is in state |1> or |0> state, the single Ce ion will, or will not, emit fluorescence photons. This single ion readout concept is a key step towards single-rare-earth-ion quantum computing, which is believed to be a promising approach for a scalable quantum computer. Rare-earth ion based quantum computing is an attractive scheme for several reasons. Firstly, the qubit coherence time can be on the timescale of a minute while the optical coherence time can be on the millisecond timescale, despite the fact that the ions are in a solid (crystal), which means that more than 10000 optical pulses could be implemented before the system decoheres. Secondly, any sub-ensemble of ions in a frequency interval equal to or larger than the homogeneous linewidth within the inhomogeneously broadened absorption line can be used as a frequency-selectively addressed qubit. The proof of principle of the qubit-qubit interaction has been previously demonstrated. Thirdly, no special material engineering is required, and the crystal is commercially available. Ways of initializing a sub-ensemble of Pr ions as a qubit in the random system, manipulating the quantum state of the ions in a controlled way, and characterizing the quantum state created are presented. In order to achieve better scalability, the idea of letting a single rare-earth ion represent a qubit was investigated. The fidelity of the single-ion readout scheme was briefly studied. The influence of the energy transfer process between two neighbouring ions on quantum computing is discussed. A readout ion should possess a number of specific spectroscopic properties. Therefore, the position and the linewidths of the zero-phonon line of Ce ions were measured using an external cavity diode laser (at 371 nm) as the excitation source. The difference in the permanent dipole moment of the ground and excited states of Ce ions was measured in a photon echo experiment on Pr ions in a Ce-Pr co-doped Y2SiO5 crystal. The last and most important task was to realize single Ce ion detection. Fluorescence of Ce ions has been detected from a crystal, where there is on average 1 ion within 4.6 \micro m3^33 interacting with the excitation laser at a time. Estimates were made of the number of ions contributing to an observed signal. A trial experiment to investigate whether the signal was emitted by a single Ce ion was carried out, but was unsuccessful. Potential reasons why the experiment failed are presented.
Rare-earth ions doped into a transparent crystal can have optically excited states with coherence times of milliseconds and hyperfine levels with coherence times of hours when cooled down to liquid helium temperatures. This makes them attractive for developing quantum computing hardware. A quantum transistor can be implemented in a rare-earth-ion-doped crystal by utilizing a dipole blockade effect, where one excited ion prevents nearby ions from being excited. By using single rare-earth ions as qubits, the quantum processor is believed to be scalable to several qubits. In this thesis a readout mechanism for qubits represented by single ions (Eu or Pr) in a Y2SiO5 crystal is explored. A single cerium ion, in the same crystal as the qubits, could potentially be used as an indicator ion for non-demolition quantum state detection of the qubits. Cerium has a strong transition with high fluorescence yield which makes it possible to detect single ions. A cerium ion can be controlled by a qubit via the dipole blockade effect, and fluoresce if the qubit is in state |1> but stay dark if the qubit is in state |0>. Relevant spectroscopic properties of Ce:Y2SiO5 are studied, as well as interactions between cerium ions and qubit ions. The inhomogeneous and homogeneous linewidth of the Ce:Y2SiO5 4f-5d transition is measured and fluorescence spectra for ions in site 1 and site 2 are characterized. The change in electric dipole moment as a cerium ion is brought to the excited state is measured. The static dipole interaction between a single cerium ion and a qubit ion is shown to be strong enough for efficient qubit readout. Energy transfer from cerium to qubit ions is investigated. A lower bound on the cerium-qubit distance is found in order to avoid energy transfer. Satellite lines belonging to cerium-qubit pairs are mapped out. A microscope set-up is built to detect single ions in a crystal. Single ion detection is believed to be within reach.
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.
Quantum computing with single instances of rare earth-ions doped into inorganic crystals shows great promise as a scalable design in the field of quantum information. A detectable and controllable single readout ion is necessary for the scheme proposed in Lund to work. Due to its short excited state lifetime and its cyclable 4f-5d transition, cerium has been deemed suitable for just this purpose. The approach taken in Lund for this single cerium detection is to use a homemade confocal microscopy setup. In previous work using this setup on bulk crystals, it has been assumed that the undetectability of single cerium is due to out of focus ions contributing to a noise floor that is higher than the fluorescence signal from a single one. Hence single ion detection is being attempted in microcrystals. This thesis outlines the process behind converting the confocal microscope into a microcrystal detection setup. Subsequently, Ce3+:Y2SiO5 microcrystal spectroscopy experiments were performed. The energy level structure of cerium is reported to be identical to bulk, with a slight shift in wavelength, and the inhomogenous linewidth has proven to be inconclusive, although it hints towards being much wider than in bulk. Quantifying the homogenous linewidth of the cerium ions using Zeeman hole burning techniques was impervious to our attempts.
We present a scheme for quantum computing in rare-earth-ion doped inorganic crystals. We use two of the ground state hyperfine levels as the qubit states, with different qubits absorbing light at different frequencies within an inhomogeneously broadened optical transition. Interaction between different qubits is accomplished using the change in permanent dipole moment that is induced at the optical excitation of the ions. The two most important aspects of the scheme have been accomplished experimentally: The isolation of a single qubit in a pure state and interaction between ions absorbing at different frequencies.