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

arXiv:quant-ph/9909038 · Physical Review Letters

Quantum State Engineering on an Optical Transition and Decoherence in a Paul Trap

Christian F. Roos, Th. Zeiger, H. J. Rohde, Hanns‐Christoph Nägerl, Jürgen Eschner, Dietrich G. Leibfried, Ferdinand Schmidt‐Kaler, R. Blatt

Published Dec 6, 1999• 405 citations
arXivHTMLPDF

Abstract

A single ${\mathrm{Ca}}^{+}$ ion in a Paul trap has been cooled to the ground state of vibration with up to $99.9%$ probability. Starting from this Fock state $|n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0〉$ we have demonstrated coherent quantum state manipulation on an optical transition. Up to 30 Rabi oscillations with 1.4 ms have been observed. We find a similar number of Rabi oscillations after preparation of the ion in the $|n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1〉$ Fock state. The coherence of optical state manipulation is limited only by laser and ambient magnetic field fluctuations. Motional heating has been measured to be as low as one vibrational quantum in 190 ms.

DOI
10.1103/physrevlett.83.4713

Related papers

Ground state cooling, quantum state engineering and study of decoherence of ions in Paul traps

Ferdinand Schmidt‐Kaler, Christian F. Roos, Hanns‐Christoph Nägerl +12 more

We investigate single ions of 40Ca+ in Paul traps for quantum information processing. Superpositions of the S½ electronic ground state and the metastable D5/2; state are used to implement a qubit. Laser light on the S½ ↔ D5/2 transition is used for the manipulation of the ion's quantum state. We apply sideband cooling to the ion and reach the ground state of vibration with up to 99.9% probability. Starting from this Fock state (n = 0), we demonstrate coherent quantum state manipulation. A large number of Rabi oscillations and a ms-coherence time is observed. Motional heating is measured to be as low as one vibrational quantum in 190ms. We also report on ground state cooling of two ions.

Journal of Modern Optics•Nov 20, 2000•8 citations

Ground state cooling, quantum state engineering and study of decoherence of ions in Paul traps

Ferdinand Schmidt‐Kaler, Christian F. Roos, Hanns‐Christoph Nägerl +12 more

We investigate single ions of 40Ca+ in Paul traps for quantum information processing. Superpositions of the S½ electronic ground state and the metastable D5/2; state are used to implement a qubit. Laser light on the S½ ↔ D5/2 transition is used for the manipulation of the ion's quantum state. We apply sideband cooling to the ion and reach the ground state of vibration with up to 99.9% probability. Starting from this Fock state (n = 0), we demonstrate coherent quantum state manipulation. A large number of Rabi oscillations and a ms-coherence time is observed. Motional heating is measured to be as low as one vibrational quantum in 190ms. We also report on ground state cooling of two ions.

arXiv:quant-ph/0003096•Journal of Modern Optics•Nov 1, 2000•25 citations

Towards quantum computation with trapped Ca+ ions

Ferdinand Schmidt‐Kaler, Christian F. Roos, H. J. Rohde +5 more

Single ions in Paul traps are investigated for quantum information processing. Superpositions of the S1/2 and the D5/2 states are used to implement a qubit. The ions are optically cooled and fluorescence light at 397 nm on the S1/2-P1/2 transition is monitored for a state measurement by the “electron shelving” technique. The S1/2-D5/2 quadrupole transition at 729 nm is excited for sideband cooling and for quantum state preparation and manipulation. Individual ions in a linear string are addressed by a tightly focused 729 nm laser beam. A single Ca+ ion has been cooled in the spherical Paul trap to the ground state of vibration with up to 99.9% probability. Cooling is achieved in all three dimensions simultaneously as well as ground state cooling of two ions. Starting from a Fock state |n=0> coherent quantum state manipulation on the S1/2-D5/2 transition is achieved. The data show that decoherence is negligible on the time scale of a few oscillations, i.e. during the time required for a quantum gate operation. The measured several decoherence time of a few ms is attributed to residual laser and magnetic field fluctuations. Heating of the motional degrees of freedom has been measured directly and appears at a rate of 1 phonon per 190 ms (70 ms) at the secular frequencies ωaxial (ωradial). A novel type of ground state laser cooling of a single trapped ion is achieved using a technique which tailors the absorption profile for the cooling laser by exploiting electromagnetically induced transparency in the Zeeman structure of the S1/2–P1/2 dipole transition. This new method is robust, easy to implement and proves particularly useful for cooling several motional degrees of freedom simultaneously, which is of great practical importance for the implementation of quantum logic schemes with trapped ions.

Optical Fiber Communication Conference•Jun 13, 2001•1 citation

Experiments towards quantum information with trapped Calcium ions

Dietrich G. Leibfried

Ground state cooling and coherent manipulation of ions in an rf-(Paul) trap is the prerequisite for quantum information experiments with trapped ions. With resolved sideband cooling on the optical S1/2−D5/2 quadrupole transition we have cooled one and two 40Ca+ ions to the ground state of vibration with up to 99.9% probability. With a novel cooling scheme utilizing electromagnetically induced transparency on the S1/2−P1/2 manifold we have achieved simultaneous ground state cooling of two motional sidebands 1.7 MHz apart. Starting from the motional ground state we have demonstrated coherent quantum state manipulation on the S1/2−D5/2 quadrupole transition at 729 nm. Up to 30 Rabi oscillations within 1.4 ms have been observed in the motional ground state and in the n=1 Fock state. In the linear quadrupole rf-trap with 700 kHz trap frequency along the symmetry axis (2 MHz in radial direction) the minimum ion spacing is more than 5 μm for up to 4 ions. We are able to cool two ions to the ground state in the trap and individually address the ions with laser pulses through a special optical addressing channel.

arXiv:quant-ph/0009105•AIP conference proceedings•Jan 1, 2001•9 citations

Ground state cooling, quantum state engineering and study of decoherence of ions in Paul traps

Ferdinand Schmidt‐Kaler, Christian F. Roos, H. J. Rohde +5 more

Summary form only given. Single ions in Paul traps are investigated for quantum information processing. Superpositions of the S/sub 1/2/ and the D/sub 5/2/ states are used to implement a qubit. Single /sup 40/Ca/sup +/ ions are either held in a spherical Paul trap or alternatively, in a linear Paul trap. The ions are optically cooled and fluorescence light at 397 nm on the S/sub 1/2/-P/sub 1/2/ transition is monitored for a state measurement by the electron shelving technique. The S/sub 1/2/-D/sub 5/2/ quadrupole transition at 729 nm is excited for sideband cooling and for quantum state preparation. Individual ions in a linear string are addressed by a tightly focused 729 nm laser beam. In the spherical Paul trap (4.5 MHz trap frequency) a single Ca/sup +/ ion has been cooled to the ground state of vibration with a probability of up to 99.9%. Starting from this Fock state |n=0> coherent quantum state manipulation on the S/sub 1/2/-D/sub 5/2/ transition is achieved.

Conference on Lasers and Electro-Optics•Aug 29, 2005•1 citation

Towards Quantum Computation with Trapped Calcium Ions

Dietrich G. Leibfried, Christian F. Roos, P. Barton +6 more

For quantum information experiments we have cooled one and two 40 Ca + ions to the ground state of vibration with up to 99.9% probability, using resolved sideband cooling on the optical S 1/2 -D 5/2 quadrupole transition. Implementing a novel cooling scheme based on electromagnetically induced transparency on the S ↓/2 -P ↓/2 manifold we have achieved simultaneous ground state cooling of two motional sidebands 1.7 MHz apart. Coherent quantum state manipulation on the S 1/2 -D 5/2 quadrupole transition at 729 nm was demonstrated and up to 30 Rabi oscillations within 1.4 ms have been observed starting from the motional ground state and from the n=1 Fock state. In a linear rf-trap two ions were cooled to the ground state of motion and individual addressing of the ions with laser pulses is achieved.

Kluwer Academic Publishers eBooks•Feb 24, 2006•0 citations
A single Ca+{\mathrm{Ca}}^{+}Ca+ ion in a Paul trap has been cooled to the ground state of vibration with up to 99.999.9%99.9 probability. Starting from this Fock state ∣n=0〉|n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0〉∣n=0〉 we have demonstrated coherent quantum state manipulation on an optical transition. Up to 30 Rabi oscillations with 1.4 ms have been observed. We find a similar number of Rabi oscillations after preparation of the ion in the ∣n=1〉|n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1〉∣n=1〉 Fock state. The coherence of optical state manipulation is limited only by laser and ambient magnetic field fluctuations. Motional heating has been measured to be as low as one vibrational quantum in 190 ms.
We investigate single ions of 40Ca+ in Paul traps for quantum information processing. Superpositions of the S½ electronic ground state and the metastable D5/2; state are used to implement a qubit. Laser light on the S½ ↔ D5/2 transition is used for the manipulation of the ion's quantum state. We apply sideband cooling to the ion and reach the ground state of vibration with up to 99.9% probability. Starting from this Fock state (n = 0), we demonstrate coherent quantum state manipulation. A large number of Rabi oscillations and a ms-coherence time is observed. Motional heating is measured to be as low as one vibrational quantum in 190ms. We also report on ground state cooling of two ions.
We investigate single ions of 40Ca+ in Paul traps for quantum information processing. Superpositions of the S½ electronic ground state and the metastable D5/2; state are used to implement a qubit. Laser light on the S½ ↔ D5/2 transition is used for the manipulation of the ion's quantum state. We apply sideband cooling to the ion and reach the ground state of vibration with up to 99.9% probability. Starting from this Fock state (n = 0), we demonstrate coherent quantum state manipulation. A large number of Rabi oscillations and a ms-coherence time is observed. Motional heating is measured to be as low as one vibrational quantum in 190ms. We also report on ground state cooling of two ions.
Single ions in Paul traps are investigated for quantum information processing. Superpositions of the S1/2 and the D5/2 states are used to implement a qubit. The ions are optically cooled and fluorescence light at 397 nm on the S1/2-P1/2 transition is monitored for a state measurement by the “electron shelving” technique. The S1/2-D5/2 quadrupole transition at 729 nm is excited for sideband cooling and for quantum state preparation and manipulation. Individual ions in a linear string are addressed by a tightly focused 729 nm laser beam. A single Ca+ ion has been cooled in the spherical Paul trap to the ground state of vibration with up to 99.9% probability. Cooling is achieved in all three dimensions simultaneously as well as ground state cooling of two ions. Starting from a Fock state |n=0> coherent quantum state manipulation on the S1/2-D5/2 transition is achieved. The data show that decoherence is negligible on the time scale of a few oscillations, i.e. during the time required for a quantum gate operation. The measured several decoherence time of a few ms is attributed to residual laser and magnetic field fluctuations. Heating of the motional degrees of freedom has been measured directly and appears at a rate of 1 phonon per 190 ms (70 ms) at the secular frequencies ωaxial (ωradial). A novel type of ground state laser cooling of a single trapped ion is achieved using a technique which tailors the absorption profile for the cooling laser by exploiting electromagnetically induced transparency in the Zeeman structure of the S1/2–P1/2 dipole transition. This new method is robust, easy to implement and proves particularly useful for cooling several motional degrees of freedom simultaneously, which is of great practical importance for the implementation of quantum logic schemes with trapped ions.
Ground state cooling and coherent manipulation of ions in an rf-(Paul) trap is the prerequisite for quantum information experiments with trapped ions. With resolved sideband cooling on the optical S1/2−D5/2 quadrupole transition we have cooled one and two 40Ca+ ions to the ground state of vibration with up to 99.9% probability. With a novel cooling scheme utilizing electromagnetically induced transparency on the S1/2−P1/2 manifold we have achieved simultaneous ground state cooling of two motional sidebands 1.7 MHz apart. Starting from the motional ground state we have demonstrated coherent quantum state manipulation on the S1/2−D5/2 quadrupole transition at 729 nm. Up to 30 Rabi oscillations within 1.4 ms have been observed in the motional ground state and in the n=1 Fock state. In the linear quadrupole rf-trap with 700 kHz trap frequency along the symmetry axis (2 MHz in radial direction) the minimum ion spacing is more than 5 μm for up to 4 ions. We are able to cool two ions to the ground state in the trap and individually address the ions with laser pulses through a special optical addressing channel.
Summary form only given. Single ions in Paul traps are investigated for quantum information processing. Superpositions of the S/sub 1/2/ and the D/sub 5/2/ states are used to implement a qubit. Single /sup 40/Ca/sup +/ ions are either held in a spherical Paul trap or alternatively, in a linear Paul trap. The ions are optically cooled and fluorescence light at 397 nm on the S/sub 1/2/-P/sub 1/2/ transition is monitored for a state measurement by the electron shelving technique. The S/sub 1/2/-D/sub 5/2/ quadrupole transition at 729 nm is excited for sideband cooling and for quantum state preparation. Individual ions in a linear string are addressed by a tightly focused 729 nm laser beam. In the spherical Paul trap (4.5 MHz trap frequency) a single Ca/sup +/ ion has been cooled to the ground state of vibration with a probability of up to 99.9%. Starting from this Fock state |n=0> coherent quantum state manipulation on the S/sub 1/2/-D/sub 5/2/ transition is achieved.
For quantum information experiments we have cooled one and two 40 Ca + ions to the ground state of vibration with up to 99.9% probability, using resolved sideband cooling on the optical S 1/2 -D 5/2 quadrupole transition. Implementing a novel cooling scheme based on electromagnetically induced transparency on the S ↓/2 -P ↓/2 manifold we have achieved simultaneous ground state cooling of two motional sidebands 1.7 MHz apart. Coherent quantum state manipulation on the S 1/2 -D 5/2 quadrupole transition at 729 nm was demonstrated and up to 30 Rabi oscillations within 1.4 ms have been observed starting from the motional ground state and from the n=1 Fock state. In a linear rf-trap two ions were cooled to the ground state of motion and individual addressing of the ions with laser pulses is achieved.