Precision measurement of light shifts in a single trapped Ba+^+ ion

Using a single trapped barium ion we have developed an rf spectroscopy technique to measure the ratio of the off-resonant vector ac Stark effect (or light shift) in the 6S_{1/2} and 5D_{3/2} states to 0.1% precision. We find R = Delta_S / Delta_D = -11.494(13) at 514.531 nm where Delta_{S,D} are the light shifts of the m = +/- 1/2 splittings due to circularly polarized light. Comparison of this result with an ab initio calculation of R would yield a new test of atomic theory. By appropriately choosing an off-resonant light shift wavelength one can emphasize the contribution of one or a few dipole matrix elements and precisely determine their values.Comment: 4 pages, 5 figures, in submission to PR

Laser Phase and Frequency Stabilization Using Atomic Coherence

We present a novel and simple method of stabilizing the laser phase and frequency by polarization spectroscopy of an atomic vapor. In analogy to the Pound-Drever-Hall method, which uses a cavity as a memory of the laser phase, this method uses atomic coherence (dipole oscillations) as a phase memory of the transmitting laser field. A preliminary experiment using a distributed feedback laser diode and a rubidium vapor cell demonstrates a shot-noise-limited laser linewidth reduction (from 2 MHz to 20 kHz). This method would improve the performance of gas-cell-based optical atomic clocks and magnetometers and facilitate laser-cooling experiments using narrow transitions.Comment: 7 pages, 6 figures, appendix on the derivation of Eq.(3) (transfer function for a polarization-spectroscopy-based frequency discriminator) has been adde

Precision measurement of light shifts at two off-resonant wavelengths in a single trapped Ba+ ion and determination of atomic dipole matrix elements

We define and measure the ratio (R) of the vector ac-Stark effect (or light shift) in the 6S_1/2 and 5D_3/2 states of a single trapped barium ion to 0.2% accuracy at two different off-resonant wavelengths. We earlier found R = -11.494(13) at 514.531nm and now report the value at 1111.68nm, R = +0.4176(8). These observations together yield a value of the matrix element, previously unknown in the literature. Also, comparison of our results with an ab initio calculation of dynamic polarizability would yield a new test of atomic theory and improve the understanding of atomic structure needed to interpret a proposed atomic parity violation experiment.Comment: 12 pages, 11 figures, in submission to PR

Optical clocks based on ultra-narrow three-photon resonances in alkaline earth atoms

A sharp resonance line that appears in three-photon transitions between the $^{1}S_{0}$ and $^{3}P_{0}$ states of alkaline earth and Yb atoms is proposed as an optical frequency standard. This proposal permits the use of the even isotopes, in which the clock transition is narrower than in proposed clocks using the odd isotopes and the energy interval is not affected by external magnetic fields or the polarization of trapping light. The method has the unique feature that the width and rate of the clock transition can be continuously adjusted from the $MHz$ level to sub-$mHz$ without loss of signal amplitude by varying the intensities of the three optical beams. Doppler and recoil effects can be eliminated by proper alignment of the three optical beams or by point confinement in a lattice trap. The three beams can be mixed to produce the optical frequency corresponding to the $^{3}P_{0}$ - $^{1}S_{0}$ clock interval.Comment: 10 pages, 4 figures, submitted to PR

Codes for the Quantum Erasure Channel

The quantum erasure channel (QEC) is considered. Codes for the QEC have to correct for erasures, i. e., arbitrary errors at known positions. We show that four qubits are necessary and sufficient to encode one qubit and correct one erasure, in contrast to five qubits for unknown positions. Moreover, a family of quantum codes for the QEC, the quantum BCH codes, that can be efficiently decoded is introduced.Comment: 6 pages, RevTeX, no figures, submitted to Physical Review A, code extended to encode 2 qubits, references adde

A Search for Time Variation of the Fine Structure Constant

A method offering an order of magnitude sensitivity gain is described for using quasar spectra to investigate possible time or space variation in the fine structure constant, alpha. Applying the technique to a sample of 30 absorption systems, spanning redshifts 0.5 < z< 1.6, obtained with the Keck I telescope, we derive limits on variations in alpha over a wide range of epochs. For the whole sample Delta(alpha)/alpha = -1.1 +/- 0.4 x 10^{-5}. This deviation is dominated by measurements at z > 1, where Delta(alpha)/alpha = -1.9 +/- 0.5 x 10^{-5}. For z < 1, Delta(alpha)/alpha = -0.2 +/- 0.4 x 10^{-5}, consistent with other known constraints. Whilst these results are consistent with a time-varying alpha, further work is required to explore possible systematic errors in the data, although careful searches have so far not revealed any.Comment: 4 pages, 1 figure, accepted for publication in Physical Review Letter

Quantum state engineering on an optical transition and decoherence in a Paul trap

A single 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=0> we have demonstrated coherent quantum state manipulation on an optical transition. Up to 30 Rabi oscillations within 1.4 ms have been observed. We find a similar number of Rabi oscillations after preparation of the ion in the |n=1> Fock state. The coherence of optical state manipulation is only limited by laser and ambient magnetic field fluctuations. Motional heating has been measured to be as low as one vibrational quantum in 190 ms.Comment: 4 pages, 5 figure

Quantum jumps in hydrogen-like systems

In this paper it is shown that the Lyman-$\alpha$ transition of a single hydrogen-like system driven by a laser exhibits macroscopic dark periods, provided there exists an additional constant electric field. We describe the photon-counting process under the condition that the polarization of the laser coincides with the direction of the constant electric field. The theoretical results are given for the example of $^4{He}^+$. We show that the emission behavior depends sensitively on the Lamb shift (W.E. Lamb, R.C. Retherford, Phys. Rev. 72, 241 (1947)) between the $2s_{1/2}$ and $2p_{1/2}$ energy levels. A possibly realizable measurement of the mean duration of the dark periods should give quantitative information about the above energy difference by using the proposed photon-counting process.Comment: 7 pages RevTeX + 2 figures Phys. Rev A accepte

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