Experimental demonstration of entanglement-enhanced rotation angle estimation using trapped ions

We experimentally investigate three methods, utilizing different atomic observables and entangled states, to increase the sensitivity of rotation angle measurements beyond the "standard quantum limit" for nonentangled states. All methods use a form of quantum mechanical "squeezing." In a system of two entangled trapped (9)Be(+) ions we observe a reduction in uncertainty of rotation angle below the standard quantum limit for all three methods including all sources of noise. As an application, we demonstrate an increase in precision of frequency measurement in a Ramsey spectroscopy experiment.

Absolute frequency measurements of the Hg+ and Ca optical clock transitions with a femtosecond laser

The frequency comb created by a femtosecond mode-locked laser and a microstructured fiber is used to phase coherently measure the frequencies of both the Hg+ and Ca optical standards with respect to the SI second. We find the transition frequencies to be f(Hg) = 1 064 721 609 899 143(10) Hz and f(Ca) = 455 986 240 494 158(26) Hz, respectively. In addition to the unprecedented precision demonstrated here, this work is the precursor to all-optical atomic clocks based on the Hg+ and Ca standards. Furthermore, when combined with previous measurements, we find no time variations of these atomic frequencies within the uncertainties of the absolute value of( partial differential f(Ca)/ partial differential t)/f(Ca) < or =8 x 10(-14) yr(-1) and the absolute value of(partial differential f(Hg)/ partial differential t)/f(Hg) < or =30 x 10(-14) yr(-1).

Experimental violation of a Bell's inequality with efficient detection

Local realism is the idea that objects have definite properties whether or not they are measured, and that measurements of these properties are not affected by events taking place sufficiently far away. Einstein, Podolsky and Rosen used these reasonable assumptions to conclude that quantum mechanics is incomplete. Starting in 1965, Bell and others constructed mathematical inequalities whereby experimental tests could distinguish between quantum mechanics and local realistic theories. Many experiments have since been done that are consistent with quantum mechanics and inconsistent with local realism. But these conclusions remain the subject of considerable interest and debate, and experiments are still being refined to overcome 'loopholes' that might allow a local realistic interpretation. Here we have measured correlations in the classical properties of massive entangled particles (9Be+ ions): these correlations violate a form of Bell's inequality. Our measured value of the appropriate Bell's 'signal' is 2.25 +/- 0.03, whereas a value of 2 is the maximum allowed by local realistic theories of nature. In contrast to previous measurements with massive particles, this violation of Bell's inequality was obtained by use of a complete set of measurements. Moreover, the high detection efficiency of our apparatus eliminates the so-called 'detection' loophole.

A decoherence-free quantum memory using trapped ions

We demonstrate a decoherence-free quantum memory of one qubit. By encoding the qubit into the decoherence-free subspace (DFS) of a pair of trapped 9Be+ ions, we protect the qubit from environment-induced dephasing that limits the storage time of a qubit composed of a single ion. We measured the storage time under ambient conditions and under interaction with an engineered noisy environment and observed that encoding into the DFS increases the storage time by up to an order of magnitude. The encoding reversibly transfers an arbitrary qubit stored in a single ion to the DFS of two ions.

Direct comparison of two cold-atom-based optical frequency standards by using a femtosecond-laser comb

With a fiber-broadened, femtosecond-laser frequency comb, the 76-THz interval between two laser-cooled optical frequency standards was measured with a statistical uncertainty of 2x10(-13) in 5 s , to our knowledge the best short-term instability thus far reported for an optical frequency measurement. One standard is based on the calcium intercombination line at 657 nm, and the other, on the mercury ion electric-quadrupole transition at 282 nm. By linking this measurement to the known Ca frequency, we report a new frequency value for the Hg(+) clock transition with an improvement in accuracy of ~10(5) compared with its best previous measurement.

Primary Atomic Frequency Standards at NIST

The development of atomic frequency standards at NIST is discussed and three of the key frequency-standard technologies of the current era are described. For each of these technologies, the most recent NIST implementation of the particular type of standard is described in greater detail. The best relative standard uncertainty achieved to date for a NIST frequency standard is 1.5×10(-15). The uncertainties of the most recent NIST standards are displayed relative to the uncertainties of atomic frequency standards of several other countries.

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 5d(10)6s (2)S(1/2)(F = 0)<-->5d(9)6s(2) (2)D(5/2)(F = 2) Deltam(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 ( 1.06x10(15) Hz), yielding a line Q approximately 1.6x10(14). We perform a preliminary measurement of the 5d(9)6s(2) (2)D(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.

Direct observations of structural phase transitions in planar crystallized ion plasmas

Laser-cooled 9Be+ ions confined in two-dimensionally extended lattice planes were directly observed, and the images were used to characterize the structural phases of the ions. Five different stable crystalline phases were observed, and the energetically favored structure could be sensitively tuned by changing the areal density of the confined ions. The experimental results are in good agreement with theoretical predictions for the planar (infinite in two dimensions) one-component plasma. Qualitatively similar structural phase transitions occur, or are predicted to occur, in other experimentally realizable planar systems.

Experimental Issues in Coherent Quantum-State Manipulation of Trapped Atomic Ions

Methods for, and limitations to, the generation of entangled states of trapped atomic ions are examined. As much as possible, state manipulations are described in terms of quantum logic operations since the conditional dynamics implicit in quantum logic is central to the creation of entanglement. Keeping with current interest, some experimental issues in the proposal for trappedion quantum computation by J. I. Cirac and P. Zoller (University of Innsbruck) are discussed. Several possible decoherence mechanisms are examined and what may be the more important of these are identified. Some potential applications for entangled states of trapped-ions which lie outside the immediate realm of quantum computation are also discussed.

Bragg diffraction from crystallized ion plasmas

Single crystals of a one-component plasma were observed by optical Bragg diffraction. The plasmas contained 10(5) to 10(6) single-positive beryllium-9 ions (9Be+) at particle densities of 10(8) to 10(9) per cubic centimeter. In approximately spherical plasmas, single body-centered cubic (bcc) crystals or, in some cases, two or more bcc crystals having fixed orientations with respect to each other were observed. In some oblate plasmas, a mixture of bcc and face-centered cubic ordering was seen. Knowledge of the properties of one-component plasma crystals is required for models of white dwarfs and neutron stars, which are believed to contain matter in that form.