Quantum teleportation is the faithful transfer of quantum states between systems, relying on the prior establishment of entanglement and using only classical communication during the transmission. We report teleportation of quantum information between atomic quantum memories separated by about 1 meter. A quantum bit stored in a single trapped ytterbium ion (Yb+) is teleported to a second Yb+ atom with an average fidelity of 90% over a replete set of states. The teleportation protocol is based on the heralded entanglement of the atoms through interference and detection of photons emitted from each atom and guided through optical fibers. This scheme may be used for scalable quantum computation and quantum communication.

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Quantum Teleportation Between Distant Matter Qubits

We demonstrate the use of trapped ytterbium ions as quantum bits for quantum information processing. We implement fast, efficient state preparation and state detection of the first-order magnetic field-insensitive hyperfine levels of $^{171}\mathrm{Yb}^{+}$, with a measured coherence time of $2.5\phantom{\rule{0.3em}{0ex}}\mathrm{s}$. The high efficiency and high fidelity of these operations is accomplished through the stabilization and frequency modulation of relevant laser sources.

Manipulation and detection of a trapped Yb+ hyperfine qubit

This work is on the Physics of the B Factories. Part A of this book contains a brief description of the SLAC and KEK B Factories as well as their detectors, BaBar and Belle, and data taking related issues. Part B discusses tools and methods used by the experiments in order to obtain results. The results themselves can be found in Part C.

The Physics of the B Factories

For many decades after the invention of the quark model in 1964 there was no evidence that hadrons are formed from anything other than the simplest pairings of quarks and antiquarks, mesons being formed of a quark-antiquark pair and baryons from three quarks. In the last decade, however, in an explosion of data from both $e^+e^-$ and hadron colliders, there are many recently observed states that do not fit into this picture. These new particles are called generically "exotics". They can be either mesons or baryons. Remarkably, they all decay into at least one meson formed of either a $c\overline{c}$ or $b\overline{b}$ pair. In this review, after the introduction, we explore each of these new discoveries in detail first from an experimental point of view, then subsequently give a theoretical discussion. These exotics can be explained if the new mesons contain two-quarks and two-antiquarks (tetraquarks), while the baryons contain four-quarks plus an antiquark (pentquarks). The theoretical explanations for these states take three divergent tracks: tightly bound objects, just as in the case of normal hadrons, but with more constituents, or loosely bound "molecules" similar to the deuteron, but formed from two mesons, or a meson or baryon, or more wistfully, they are not multiquark states but appear due to kinematic effects caused by different rescatterings of virtual particles; most of these models have all been post-dictions. Both the tightly and loosely bound models predict the masses and related quantum numbers of new, as yet undiscovered states. Thus, future experimental discoveries are needed along with theoretical advances to elucidate the structure of these new exotic states.

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Exotics: Heavy Pentaquarks and Tetraquarks

Nanostructure science and technology now forms a common thread that runs through all physical and materials sciences and is emerging in industrial applications as nanotechnology. The breadth of the subject material is demonstrated by the fact that it covers and intertwines many of the traditional areas of physics, chemistry, biology, and medicine. Within each main topic in this field there can be many subfields. For example, the electrical properties of nanostructured materials is a topic that can cover electron transport in semiconductor quantum dots, self-assembled molecular nanostructures, carbon nanotubes, chemically tailored hybrid magnetic-semiconductor nanostructures, colloidal quantum dots, nanostructured superconductors, nanocrystalline electronic junctions, etc. Obviously, no one book can cope with such a diversity of subject matter. The nanostructured material system is, however, of increasing significance in our technology-dominated economy and this suggests the need for a series of books to cover recent developments.    The scope of the series is designed to cover as much of the subject matter as possible – from physics and chemistry to biology and medicine, and from basic science to applications. At present, the most significant subject areas are concentrated in basic science and mainly within physics and chemistry, but as time goes by more importance will inevitably be given to subjects in applied science and will also include biology and medicine. The series will naturally accommodate this flow of developments in the sciences and technology of nanostructures and maintain its topicality by virtue of its broad emphasis. It is important that emerging areas in the biological and medical sciences, for example, not be ignored as, despite their diversity, developments in this field are often interlinked. The series will maintain the required cohesiveness from a judicious mix of edited volumes and monographs that while covering subfields in depth will also contain more general and interdisciplinary texts.    Thus the series is planned to cover in a coherent fashion the developments in basic research from the distinct viewpoints of physics, chemistry, biology, and materials science and also the engineering technologies emerging from this research. Each volume will also reflect this flow from science to technology. As time goes by, the earlier series volumes will then serve as reference texts to subsequent volumes.

Nanostructure Science and Technology

High-precision laser-resonance measurements accurate to \ifmmode\pm\else\textpm\fi{}0.5 MHz or better are reported for transitions among the 1s2s $^{3}$${\mathit{S}}_{1--}$1s2p $^{3}$${\mathit{P}}_{\mathit{J}}$ hyperfine manifolds for each of J=0, 1, and 2 in both $^{6}\mathrm{Li}^{+}$ and $^{7}\mathrm{Li}^{+}$. A detailed analysis of hyperfine structure is performed for both the S and P states, using newly calculated values for the magnetic dipole and electric quadrupole coupling constants, and the hyperfine shifts subtracted from the measurements. The resulting transition frequencies are then analyzed on three different levels. First, the isotope shifts in the fine-structure splittings are calculated from the relativistic reduced mass and recoil terms in the Breit interaction, and compared with experiment at the \ifmmode\pm\else\textpm\fi{}0.5-MHz level of accuracy. This comparison is particularly significant because J-independent theoretical uncertainties reduce through cancellation to the \ifmmode\pm\else\textpm\fi{}0.01-MHz level. Second, the isotope shifts in the full transition frequencies are used to deduce the difference in rms nuclear radii.The result is ${\mathit{R}}_{\mathrm{rms}}$${(}^{6}$Li)-${\mathit{R}}_{\mathrm{rms}}$${(}^{7}$Li)=0.15\ifmmode\pm\else\textpm\fi{}0.01 fm, in agreement with nuclear scattering data, but with substantially improved accuracy. Third, high-precision calculations of the low-order non-QED contributions to the transition frequencies are subtracted from the measurements to obtain the residual QED shifts. The isotope-averaged and spin-averaged effective shift for $^{7}\mathrm{Li}^{+}$ is 37 429.40\ifmmode\pm\else\textpm\fi{}0.39 MHz, with an additional uncertainty of \ifmmode\pm\else\textpm\fi{}1.5 MHz due to finite nuclear size corrections. The accuracy of 11 parts per million is the best two-electron Lamb shift measurement in the literature, and is comparable to the accuracies achieved in hydrogen. Theoretical contributions to the two-electron Lamb shift are discussed, including terms of order (\ensuremath{\alpha}Z${)}^{4}$ recently obtained by Chen, Cheng, and Johnson [Phys. Rev. A 47, 3692 (1993)], and the results used to extract a QED shift for the 2 $^{3}$${\mathit{S}}_{1}$ state. The result of 30 254\ifmmode\pm\else\textpm\fi{}12 MHz is shown to be in good accord with theory (30 250\ifmmode\pm\else\textpm\fi{}30 MHz) when two-electron corrections to the Bethe logarithm are taken into account by a 1/Z expansion method.

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Lamb shifts and hyperfine structure in 6Li+ and 7Li+: Theory and experiment.

We demonstrate laser cooling of $^{172}\mathrm{Yb}^{+}$ ions in a rf quadrupole trap using an alternative optical-excitation scheme. The metastable 4${\mathit{f}}^{14}$5${\mathit{d}}^{2}$${\mathit{D}}_{3/2}$ state of ${\mathrm{Yb}}^{+}$, to which ions decay if the resonance (cooling) transition is driven, is depleted by driving an optical transition at a wavelength of 935 nm, which is much more attractive than the 2.438 \ensuremath{\mu}m radiation used previously. This couples the metastable state to a fourth energy level from which the ions decay rapidly to the ground state. Fluorescence line shapes of the cooling transition indicate that small numbers of ${\mathrm{Yb}}^{+}$ ions were cooled in this way to kinetic temperatures below 1 K.

Laser cooling of trapped ytterbium ions using a four-level optical-excitation scheme

The 4f13 6s2 2F7/2–4f14 5d 2D5/2 3·43 μm infrared transition in 172Yb+ has been driven for the first time and measured to be 87 360 087(4) MHz The frequency was determined by probing a cloud of 172Yb+ ions held in a radiofrequency trap in the presence of helium buffer gas The infrared radiation was generated by difference frequency mixing in LiNbO3 The frequency measurement is part of a programme to locate the 4f14 6s 2S1/2–4f13 6s2 2F7/2 467 nm ultra-narrow transition in laser-cooled Yb+

Precision Measurement of the 2

The 4${\mathit{f}}^{14}$6s${\mathrm{}}^{2}$${\mathit{S}}_{1/2}$--4${\mathit{f}}^{14}$5d${\mathrm{}}^{2}$${\mathit{D}}_{5/2}$ 411-nm transition in $^{172}\mathrm{Yb}^{+}$ has been measured to be 729 476 868(11) MHz. The frequency was determined by probing a cold cloud of a few $^{172}\mathrm{Yb}^{+}$ ions held in a radio-frequency trap. The frequency measurement is part of a program to locate the 4${\mathit{f}}^{14}$6s${\mathrm{}}^{2}$${\mathit{S}}_{1/2}$--4${\mathit{f}}^{13}$6${\mathit{s}}^{2}$${\mathrm{}}^{2}$${\mathit{F}}_{7/2}$ 467-nm ultranarrow transition in laser-cooled ${\mathrm{Yb}}^{+}$. The 4${\mathit{f}}^{13}$6${\mathit{s}}^{2}$${\mathrm{}}^{2}$${\mathit{F}}_{7/2}$--4${\mathit{f}}^{13}$5d6s${\mathrm{}}^{1}$D[K= 5/2${]}_{\mathit{J}=5/2}$ transition at 638 nm has been driven in order to depopulate the 4${\mathit{f}}^{13}$6${\mathit{s}}^{2}$${\mathrm{}}^{2}$${\mathit{F}}_{7/2}$ state.

Measurement of the 2S1/2-2D5/2 411-nm interval in laser-cooled trapped 172Yb+ ions.

We report some laser-cooling effects in a few172Yb+ ions held in a Paul trap. Pronounced cloud-to-crystal phase transitions have been observed as discontinuities in the Yb+ fluorescence spectrum of the 369 nm cooling transition. The first reported two-dimensional images of Yb+ clouds with evidence of crystal structure have been recorded using a photon-counting position-sensitive detector. An ion temperature of 100 mK has been estimated from the size of a single ion image. Step-wise cooling of a re-heated, few-ion Yb+ cloud was also observed.

A. P. Levick

Papers

Lamb shifts and hyperfine structure in 6Li+ and 7Li+: Theory and experiment.

Laser cooling of trapped ytterbium ions using a four-level optical-excitation scheme

Precision Measurement of the 2

Measurement of the 2S1/2-2D5/2 411-nm interval in laser-cooled trapped 172Yb+ ions.

Laser-cooling effects in few-ion clouds of Yb+