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Physical Review A

Investigating a qubit candidate: Spectroscopy on the S1/2 to D5/2 transition of a trapped calcium ion in a linear Paul trap

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

Published Jan 7, 2000• 82 citations
Publisher

Abstract

A single ${}^{40}{\mathrm{Ca}}^{+}$ ion is confined in a linear Paul trap and Doppler-cooled on the ${S}_{1/2}$ to ${P}_{1/2}$ dipole transition. Then the narrow quadrupole ${S}_{1/2}$ to ${D}_{5/2}$ transition at 729 nm is probed. The observed spectrum is interpreted in terms of the Zeeman substructure superimposed with oscillation sidebands due to the harmonic motion in the trap. The height of the motional sidebands provides a sensitive method to determine the ion's temperature and thus allows us to test sub-Doppler laser cooling schemes needed for quantum state preparation and quantum computation. We also observe the dynamics induced by Rabi oscillations on a carrier transition and interpret it in terms of the thermal state which is reached after Doppler cooling.

DOI
10.1103/physreva.61.023405

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Towards quantum computation with trapped Ca+ ions

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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.

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Sideband cooling an ion to the quantum ground state in a Penning trap with very low heating rate

Joseph F. Goodwin, G. Stutter, Richard Claude Thompson +1 more

We report the laser cooling of a single $^{40}\text{Ca}^+$ ion in a Penning trap to the motional ground state in one dimension. Cooling is performed in the strong binding limit on the 729-nm electric quadrupole $S_{1/2}\leftrightarrow D_{5/2}$ transition, broadened by a quench laser coupling the $D_{5/2}$ and $P_{3/2}$ levels. We find the final phonon number to be $\bar{n}=0.014\pm0.009$. We measure the heating rate of the trap to be very low with $\dot{\bar{n}}=2.5\pm 0.3\textrm{s}^{-1}$ and a scaled spectral noise density of $\omega S_{E}(\omega)\sim1.6^{-8}\textrm{V}^2\textrm{m}^{-2}\textrm{Hz}^{-1}\textrm{s}^{-1}$, which is consistent with the large ion-electrode distance. We perform Rabi oscillations on the sideband-cooled ion and observe a coherence time of $0.7\pm 0.1\textrm{ms}$, noting that the practical performance is currently limited by the intensity noise of the probe laser.

•Jul 23, 2014•0 citations
A single 40Ca+{}^{40}{\mathrm{Ca}}^{+}40Ca+ ion is confined in a linear Paul trap and Doppler-cooled on the S1/2{S}_{1/2}S1/2​ to P1/2{P}_{1/2}P1/2​ dipole transition. Then the narrow quadrupole S1/2{S}_{1/2}S1/2​ to D5/2{D}_{5/2}D5/2​ transition at 729 nm is probed. The observed spectrum is interpreted in terms of the Zeeman substructure superimposed with oscillation sidebands due to the harmonic motion in the trap. The height of the motional sidebands provides a sensitive method to determine the ion's temperature and thus allows us to test sub-Doppler laser cooling schemes needed for quantum state preparation and quantum computation. We also observe the dynamics induced by Rabi oscillations on a carrier transition and interpret it in terms of the thermal state which is reached after Doppler cooling.
We investigate the spectra of the electric quadrupole 4 2 S 1/2 →3 2 D 5/2 transitions in a single 40 Ca + ion confined in a home-built linear trap. We probe the transitions with an ultra-narrow bandwidth laser at 729 nm. In a weak magnetic field, the quadrupole transition splits into ten components with the maximal line strength proportional to their squared Clebsch—Gordan factors. In a magnetic field of the order of Gauss, the observed equidistant sideband reflects the Zeeman substructure modulated by the quantized oscillation due to the secular motion in the trap. The temperature of the trapped ion can be determined by the envelope of the sideband spectrum. We also demonstrate the Rabi oscillation in a carrier transition after the ion has been Doppler cooled, which can be fitted by the model with the thermal state of motion.
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.
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.
The use of cold trapped ions for quantum information processing requires the preparation of linear strings of ions at low temperatures and the coherent manipulation by laser light of the quantum state of individual ions in the string. In our experiment, 40Ca+ ions are trapped in a linear Paul trap, forming crystallized linear strings when laser cooled. These strings are observed by fluorescence detection on the S1/2-P1/2 dipole transition at 397 nm using a photomultiplier and a CCD camera. The narrow S1/2-D5/2 quadrupole transition at 729 nm is used to investigate and manipulate the vibrational motion of the ion in the trap. The spectral resolution obtained up to now on this transition is 2 · 10—12, proving long coherence time of the two-level system. Addressing of individual ions in the string is achieved, using a tightly focused laser beam at 729 nm, and detected by the observation of quantum jumps from the S1/2 to the D5/2 level. These experimental techniques make ions in a superposition of their S1/2 and D5/2 states suitable as qubits for quantum information processing. The realization of a two-ion quantum gate furthermore requires ground-state cooling of the string. The status of current experiments is reviewed and techniques to achieve ground-state cooling of ion strings are discussed.
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 report the laser cooling of a single 40Ca+^{40}\text{Ca}^+40Ca+ ion in a Penning trap to the motional ground state in one dimension. Cooling is performed in the strong binding limit on the 729-nm electric quadrupole S1/2↔D5/2S_{1/2}\leftrightarrow D_{5/2}S1/2​↔D5/2​ transition, broadened by a quench laser coupling the D5/2D_{5/2}D5/2​ and P3/2P_{3/2}P3/2​ levels. We find the final phonon number to be nˉ=0.014±0.009\bar{n}=0.014\pm0.009nˉ=0.014±0.009. We measure the heating rate of the trap to be very low with nˉ˙=2.5±0.3s−1\dot{\bar{n}}=2.5\pm 0.3\textrm{s}^{-1}nˉ˙=2.5±0.3s−1 and a scaled spectral noise density of ωSE(ω)∼1.6−8V2m−2Hz−1s−1\omega S_{E}(\omega)\sim1.6^{-8}\textrm{V}^2\textrm{m}^{-2}\textrm{Hz}^{-1}\textrm{s}^{-1}ωSE​(ω)∼1.6−8V2m−2Hz−1s−1, which is consistent with the large ion-electrode distance. We perform Rabi oscillations on the sideband-cooled ion and observe a coherence time of 0.7±0.1ms0.7\pm 0.1\textrm{ms}0.7±0.1ms, noting that the practical performance is currently limited by the intensity noise of the probe laser.