Optical atomic clocks represent the state of the art in the frontier of modern measurement science. In this article a detailed review on the development of optical atomic clocks that are based on trapped single ions and many neutral atoms is provided. Important technical ingredients for optical clocks are discussed and measurement precision and systematic uncertainty associated with some of the best clocks to date are presented. An outlook on the exciting prospect for clock applications is given in conclusion.

Ultracold cesium atoms are prepared in the ground energy band of the potential induced by an optical standing wave. We observe Bloch oscillations of the atoms driven by a constant inertial force. We measure the momentum distribution of Bloch states and effective masses different from the mass of the free atom. [S0031-9007 (96)00366-3] PACS numbers: 32.80.Pj, 03.75.-b 45080031-9007͞96͞76(24)͞4508(4)$10.00

We experimentally investigate an optical frequency standard based on the (2)S1/2(F=0)→(2)F7/2(F=3) electric octupole (E3) transition of a single trapped (171)Yb+ ion. For the spectroscopy of this strongly forbidden transition, we utilize a Ramsey-type excitation scheme that provides immunity to probe-induced frequency shifts. The cancellation of these shifts is controlled by interleaved single-pulse Rabi spectroscopy, which reduces the related relative frequency uncertainty to 1.1×10(-18). To determine the frequency shift due to thermal radiation emitted by the ion's environment, we measure the static scalar differential polarizability of the E3 transition as 0.888(16)×10(-40)  J m(2)/V(2) and a dynamic correction η(300  K)=-0.0015(7). This reduces the uncertainty due to thermal radiation to 1.8×10(-18). The residual motion of the ion yields the largest contribution (2.1×10(-18)) to the total systematic relative uncertainty of the clock of 3.2×10(-18).

PACS. 23.20.-g -Electromagnetic transitions. PACS. 42.62.Fi -Laser spectroscopy. PACS. 33.40.+f -Multiple resonances (including double and higher-order resonance processes, such as double nuclear magnetic resonance, electron double resonance, and microwave optical double resonance).Abstract. -We propose high-resolution laser spectroscopy of the 3.5 eV nuclear transition in Th-229 in isolated atoms. Laser excitation of the nucleus can be detected efficiently in a double-resonance method by probing the hyperfine structure of a transition in the electron shell. It is shown that for a suitably chosen electronic level, the frequency of the nuclear transition is independent of external magnetic fields to first order and of electric fields to second order. This makes Th-229 a possible reference for an optical clock of very high accuracy. The nuclearelectronic double-resonance method can be conveniently applied to a laser-cooled ion of 229 Th 3+ in a radiofrequency trap. Further applications of nuclear laser spectroscopy are discussed.

Accurate measurements of different transition frequencies between atomic levels of the electronic and hyperfine structure over time are used to investigate temporal variations of the fine structure constant α and the proton-to-electron mass ratio µ. We measure the frequency of the 2 S 1/2 → 2 F 7/2 electric octupole (E3) transition in 171 Yb + against two caesium fountain clocks as f (E3) = 642 121 496 772 645.36(25) Hz with an improved fractional uncertainty of 3.9×10 −16 . This transition frequency shows a strong sensitivity to changes of α. Together with a number of previous and recent measurements of the 2 S 1/2 → 2 D 3/2 electric quadrupole transition in 171 Yb + and with data from other elements, a least-squares analysis yields (1/α)(dα/dt) = −0.20(20) × 10 −16 /yr and (1/µ)(dµ/dt) = −0.5(1.6) × 10 −16 /yr, confirming a previous limit on dα/dt and providing the most stringent limit on dµ/dt from laboratory experiments. The search for variations of fundamental constants is motivated by theories unifying the fundamental interactions and is regarded as an opportunity to open a window to new physics with implications on cosmology as well as on particle physics [1][2][3][4]. While early proposals for such a search using atomic spectroscopy have been made shortly after the discovery of the expansion of the universe [5], sensitive observational and experimental tools became available only recently. Astrophysical observations of absorption spectra of interstellar matter have led to claims for [6][7][8] and against [9-13] variations of the fine structure constant α and the proton-to-electron mass ratio µ = m p /m e at relative uncertainties in the range 10 −5 to 10 −7 on a cosmological time scale of several billion years. In the laboratory, the high precision of atomic clocks that now reach relative uncertainties of 10 −16 and below in frequency ratios has been used to infer limits on variations of α and µ in the present epoch [14][15][16][17].In this Letter we present a high-accuracy absolute frequency measurement of the 2 S 1/2 → 2 F 7/2 electric octupole transition in 171 Yb + that possesses a strong sensitivity to changes of α. Together with recently reported frequency measurements of the 2 S 1/2 → 2 D 3/2 electric quadrupole transition in the same ion [18] this allows us to constrain possible temporal changes of both transition frequencies relative to caesium clocks. Besides confirming limits on dα/dt in the low 10 −17 /yr range these data provide the most stringent limit on dµ/dt from a laboratory experiment.171 Yb + is particularly attractive for a search for variations of fundamental constants because there are two transitions with low natural linewidth from the ground state to metastable states that have rather different electronic configurations [see Fig. 1(a)]. In case of the 2 S 1/2 (F = 0) → 2 D 3/2 (F = 2, m F = 0) electric quadrupole (E2) transition at 436 nm the 6s va- lence electron is promoted to the 5d level, while on the 2 S 1/2 (F = 0) → 2 F 7/2 (F = 3, m F = 0) electric octupole (E3) transitio...

The comparison of different atomic transition frequencies over time can be used to determine the present value of the temporal derivative of the fine structure constant alpha in a model-independent way without assumptions on constancy or variability of other parameters, allowing tests of the consequences of unification theories. We have measured an optical transition frequency at 688 THz in 171Yb+ with a cesium atomic clock at 2 times separated by 2.8 yr and find a value for the fractional variation of the frequency ratio f(Yb)/f(Cs) of (-1.2+/-4.4)x10(-15) yr(-1), consistent with zero. Combined with recently published values for the constancy of other transition frequencies this measurement sets an upper limit on the present variability of alpha at the level of 2.0x10(-15) yr(-1) (1sigma), corresponding so far to the most stringent limit from laboratory experiments.

We experimentally investigate an optical frequency standard based on the 467 nm (642 THz) electric-octupole reference transition 2 S 1/2 (F = 0) → 2 F 7/2 (F = 3) in a single trapped 171 Yb + ion. The extraordinary features of this transition result from the long natural lifetime and from the 4f 13 6s 2 configuration of the upper state. The electric-quadrupole moment of the 2 F 7/2 state is measured as −0.041(5) ea 2 0 , where e is the elementary charge and a0 the Bohr radius. We also obtain information on the differential scalar and tensorial components of the static polarizability and of the probe-light-induced ac Stark shift of the octupole transition. With a real-time extrapolation scheme that eliminates this shift, the unperturbed transition frequency is realized with a fractional uncertainty of 7.1 × 10 −17 . The frequency is measured as 642 121 496 772 The basis of all precise atomic clocks is a transition frequency that represents an unperturbed quantum property of the chosen atomic system. The most impressive progress in clocks of high accuracy has recently been made with optical transitions between states with vanishing electronic angular momentum (J = 0) in Al + and Sr [1,2]. The frequency of this type of transition is in general only weakly affected by external electric and magnetic fields. Here we present a precision study of a reference transition of a very different type, an electric-octupole transition (∆J = 3) connecting the 2 S 1/2 ground state with the 2 F 7/2 first excited state in 171 Yb + , and show that it has a very low sensitivity to field-induced frequency shifts, making it a promising basis for an optical clock of the highest accuracy.At variance with other ion frequency standards, 171 Yb + offers the advantage of two optical reference transitions with high quality factor which have rather different physical characteristics. A frequency standard based on the electric-quadrupole 2 S 1/2 → 2 D 3/2 transition [3,4] is established as one of the secondary representations of the SI second. The electric-octupole 2 S 1/2 → 2 F 7/2 transition investigated in this Letter was first studied at the National Physical Laboratory (UK) [5]. The extraordinary features of this transition result from the long natural lifetime of the 2 F 7/2 state in the range of several years [5,6] and from its electronic configuration (4f 13 6s 2 ) consisting of a hole in the 4f shell surrounded by a spherically symmetric 6s shell. Since the octupole transition can be resolved with a linewidth that is virtually unaffected by spontaneous decay and determined only by the available laser stability, a quantum projection noise limited single-ion frequency standard with very low instability can be realized. The electric-quadrupole moment of the 2 F 7/2 state is predicted to be much smaller than that of the 2 D 3/2 state [7] so that the transition frequency is only weakly affected by the quadrupole shift from electric field gradients. Furthermore, there are no strong dipole transitions from the 2 F 7/2 state with excitation en...

We study the dynamics of ultracold atoms in a periodic optical potential submitted to a constant external force. Bloch oscillations in the fundamental and first excited bands of the potential are observed. In addition to a solid-state analysis we give a quantum-optics interpretation of this effect in terms of photon exchanges between the atoms and the laser waves. The dynamics of Bloch oscillations are equivalent to a sequence of adiabatic rapid passages between momentum states and can be described using the dressed-atom approach. We demonstrate efficient and dissipation-free acceleration of atoms by coherent transfer of a large number of photon momenta (Ϸ100). This technique produces atomic beams with a very small longitudinal velocity spread that may find applications in atom optics and precision measurements. ͓S1050-2947͑97͒03504-X͔