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Kluwer Academic Publishers eBooks

Towards Quantum Computation with Trapped Calcium Ions

Dietrich G. Leibfried, Christian F. Roos, P. Barton, H. J. Rohde, S. Guide, A.B. Mundt, Ferdinand Schmidt‐Kaler, Jürgen Eschner, R. Blatt

Published Feb 24, 2006• 0 citations
Publisher

Abstract

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.

DOI
10.1007/0-306-47114-0_29

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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.

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arXiv:quant-ph/0003096•Journal of Modern Optics•Nov 1, 2000•25 citations
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.
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.
Ground state cooling and coherent manipulation of ions in a rf-(Paul) trap is the prerequisite for quantum information experiments with trapped ions. In our experiments a single /sup 40/Ca/sup +/ ion in a conventional Paul trap has been cooled to the ground state of vibration with 99.9% (98%) probability in the axial (radial) trap direction, We use a continuous resolved sideband method where we drive the S/sub 1/2/-D/sub 5/2/ quadrupole transition (@729 nm) and repump the ion to the ground state via the D/sub 5/2/-P/sub 3/2/ dipole transition. Efficient cooling is achieved on the timescale of a few ms.
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.
Summary form only given. Ground state cooling and coherent manipulation of ions in a rf-(Paul) trap is the prerequisite for quantum information experiments with trapped ions. In our experiments a single /sup 40/Ca/sup +/ ion in a conventional Paul trap has been cooled to the ground state of vibration with 99.9% (98%) probability in the axial (radial) trap direction. We use a continuous resolved sideband method where we drive the S/sub 1/2/-D/sub 5/2/ quadrupole transition (@ 729nm) and repump the ion to the ground state via the D/sub 5/2/-P/sub 3/2/ dipole transition. Efficient cooling is achieved on the timescale of a few 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.