Quantum state manipulation of trapped atomic ions

A single laser-cooled and trapped 9Be+ ion is used to investigate methods of coherent quantum-state synthesis and quantum logic. We create and characterize nonclassical states of motion including "Schroedinger-cat" states. A fundamental quantum logic gate is realized which uses two states of the quantized ion motion and two ion internal states as qubits. We explore some of the applications for, and problems in realizing, quantum computation based on multiple trapped ions.Comment: Postscript only. 21 pages text, 5 figures., Proc. Workshop on Quantum Computing, Santa Barbara, CA, Dec. 1996, Submitted to Proc. Roy. Soc.

Observation of power-law scaling for phase transitions in linear trapped ion crystals

We report an experimental confirmation of the power-law relationship between the critical anisotropy parameter and ion number for the linear-to-zigzag phase transition in an ionic crystal. Our experiment uses laser cooled calcium ions confined in a linear radio-frequency trap. Measurements for up to 10 ions are in good agreement with theoretical and numeric predictions. Implications on an upper limit to the size of data registers in ion trap quantum computers are discussed.Comment: Physical Review Letters in press, 4 pages, 4 figure

Quantum control of 88^{88}Sr+^+ in a miniature linear Paul trap

We report on the construction and characterization of an apparatus for quantum information experiments using $^{88}$Sr$^+$ ions. A miniature linear radio-frequency (rf) Paul trap was designed and built. Trap frequencies above 1 MHz in all directions are obtained with 50 V on the trap end-caps and less than 1 W of rf power. We encode a quantum bit (qubit) in the two spin states of the $S_{1/2}$ electronic ground-state of the ion. We constructed all the necessary laser sources for laser cooling and full coherent manipulation of the ions' external and internal states. Oscillating magnetic fields are used for coherent spin rotations. High-fidelity readout as well as a coherence time of 2.5 ms are demonstrated. Following resolved sideband cooling the average axial vibrational quanta of a single trapped ion is $\bar n=0.05$ and a heating rate of $\dot{\bar n}=0.016$ ms$^{-1}$ is measured.Comment: 8 pages,9 figure

The theory of heating of the quantum ground state of trapped ions

Using a displacement operator formalism, I analyse the depopulation of the vibrational ground state of trapped ions. Two heating times, one characterizing short time behaviour, the other long time behaviour are found. The short time behaviour is analyzed both for single and multiple ions, and a formula for the relative heating rates of different modes is derived. The possibility of correction of heating via the quantum Zeno effect, and the exploitation of the suppression of heating of higher modes to reduce errors in quantum computation is considered.Comment: 9 pages, 2 figure

An efficient scheme for the deterministic maximal entanglement of N trapped ions

We propose a method for generating maximally entangled states of N two-level trapped ions. The method is deterministic and independent of the number of ions in the trap. It involves a controlled-NOT acting simultaneously on all the ions through a dispersive interaction. We explore the potential application of our scheme for high precision frequency standards.Comment: 4 pages, no figures, submitted to PRL, under review, Revised Version: Incorporated referee comment

Destabilization of dark states and optical spectroscopy in Zeeman-degenerate atomic systems

We present a general discussion of the techniques of destabilizing dark states in laser-driven atoms with either a magnetic field or modulated laser polarization. We show that the photon scattering rate is maximized at a particular evolution rate of the dark state. We also find that the atomic resonance curve is significantly broadened when the evolution rate is far from this optimum value. These results are illustrated with detailed examples of destabilizing dark states in some commonly-trapped ions and supported by insights derived from numerical calculations and simple theoretical models.Comment: 14 pages, 10 figure

Motional sidebands and direct measurement of the cooling rate in the resonance fluorescence of a single trapped ion

Resonance fluorescence of a single trapped ion is spectrally analyzed using a heterodyne technique. Motional sidebands due to the oscillation of the ion in the harmonic trap potential are observed in the fluorescence spectrum. From the width of the sidebands the cooling rate is obtained and found to be in agreement with the theoretical prediction.Comment: 4 pages, 4 figures. Final version after minor changes, 1 figure replaced; to be published in PRL, July 10, 200

Sub-dekahertz ultraviolet spectroscopy of 199Hg+

Using a laser that is frequency-locked to a Fabry-Perot etalon of high finesse and stability, we probe the 5d10 6s 2S_1/2 (F=0) - 5d9 6s 2D_5/2 (F=2) Delta-m_F = 0 electric-quadrupole transition of a single laser-cooled 199Hg+ ion stored in a cryogenic radio-frequency ion trap. We observe Fourier-transform limited linewidths as narrow as 6.7 Hz at 282 nm (1.06 X 10^15 Hz), yielding a line Q = 1.6 X 10^14. We perform a preliminary measurement of the 5d9 6s2 2D_5/2 electric-quadrupole shift due to interaction with the static fields of the trap, and discuss the implications for future trapped-ion optical frequency standards.Comment: 4 pages, 4 figures, submitted for publicatio