The thermal motion of atoms often imposes limitations on the precision and accuracy of measurements involving those atoms. Atomic beam cesium clocks are one outstanding example, where the typical thermal velocity of the cesium atoms, on the order of 200 m/s, limits the observation time to a few milliseconds in a typical apparatus. This finite observation time results in a linewidth for the microwave resonance whose frequency defines the unit of time. Other motional effects include first- and second-order Doppler effects whose presence limits the performance of such clocks. Because conventional refrigeration would result in the condensation of cesium or other atoms into a solid, researchers sought other means of reducing the thermal motion, a quest that led to laser cooling and electromagnetic manipulation of neutral atoms. Similar techniques have been developed for trapped ions and used in metrological applications, but these are not treated here.
The thermal motion of atoms often imposes limitations on the precision and accuracy of measurements involving those atoms. Atomic beam cesium clocks are one outstanding example, where the typical thermal velocity of the cesium atoms, on the order of 200 m/s, limits the observation time to a few milliseconds in a typical apparatus. This finite observation time results in a linewidth for the microwave resonance whose frequency defines the unit of time. Other motional effects include first- and second-order Doppler effects whose presence limits the performance of such clocks. Because conventional refrigeration would result in the condensation of cesium or other atoms into a solid, researchers sought other means of reducing the thermal motion, a quest that led to laser cooling and electromagnetic manipulation of neutral atoms. Similar techniques have been developed for trapped ions and used in metrological applications, but these are not treated here.
Experimental techniques of laser cooling and trapping, along with other cooling techniques, have produced gaseous samples of atoms so cold that they are, for many practical purposes, in the quantum ground state of their centre-of-mass motion. Such low velocities have virtually eliminated effects such as Doppler shifts, relativistic time dilation and observation-time broadening that previously limited the performance of atomic frequency standards. Today, the best laser-cooled, caesium atomic fountain, microwave frequency standards realize the International System of Units (SI) definition of the second to a relative accuracy of ≈3×10(-16). Optical frequency standards, which do not realize the SI second, have even better performance: cold neutral atoms trapped in optical lattices now yield relative systematic uncertainties of ≈1×10(-16), whereas cold-trapped ions have systematic uncertainties of 9×10(-18). We will discuss the current limitations in the performance of neutral atom atomic frequency standards and prospects for the future.
The advent of the laser opened the way to the development of powerful new methods for manipulating and cooling atoms which were exploited in the realization of Bose–Einstein condensation in alkali atom vapours. To set the stage we describe a typical experiment, which is shown schematically in Fig. 4.1. A beam of sodium atoms emerges from an oven at a temperature of about 600 K, corresponding to a speed of about 800 m s –1 , and is then passed through a so-called Zeeman slower, in which the velocity of the atoms is reduced to about 30 m s –1 , corresponding to a temperature of about 1 K. In the Zeeman slower, a laser beam propagates in the direction opposite that of the atomic beam, and the radiation force produced by absorption of photons retards the atoms. Due to the Doppler effect, the frequency of the atomic transition in the laboratory frame is not generally constant, since the atomic velocity varies. However, by applying an inhomogeneous magnetic field designed so that the Doppler and Zeeman effects cancel, the frequency of the transition in the rest frame of the atom may be held fixed. On emerging from the Zeeman slower the atoms are slow enough to be captured by a magneto-optical trap (MOT), where they are further cooled by interactions with laser light to temperatures of order 100 μK. Another way of compensating for the changing Doppler shift is to increase the laser frequency in time, which is referred to as ‘chirping’. In other experiments the MOT is filled by transferring atoms from a second MOT where atoms are captured directly from the vapour.
The accelerated development of laser methods for manipulating the internal state and motion of atoms, and the recent primary evaluation in France of a cesium frequency standard using cold atoms in an atomic fountain configuration, allow the frontiers of time metrology, accuracy, and stability to be pushed near parts in the 1016 level, a factor of 100 over the present primary laboratory clocks. These positive results revived the development of more accurate cesium atomic clocks, and the Institute of National Measurement Standards (INMS), of the National Research Council of Canada (NRC) is undertaking a cesium-fountain project aimed at reaching these new levels of accuracy and stability. This paper reviews its present status. To appreciate the considerable impact of cold atoms in time and frequency metrology, we begin by recalling the background principles of traditional cesium frequency standards, their typical performance and main limitations. After introducing the important theoretical results essential to understanding the techniques of laser cooling and magneto-optical trapping, we focus on describing the characterization and control of our magneto-optical trap (MOT) and report the parameters that allow us to fill the trap with a few million atoms in less than a second and cool them to a temperature lower than 5 muK using optical molasses. We will describe the specifics of our cesium-fountain prototype, which operates with a 2-dimensional moving molasses. This special configuration is applicable for multipulse operation of the fountain, which can greatly relax the local oscillator requirements for time keeping. Finally, progress toward our objective of launching cooled atoms, at a rate of one ensemble per second, at speeds of 7 m/s, for a fountain with an interrogation time of about 1 s, will be analysed.PACS Nos.: 06.20, 06.30, and 32.80P
Atom trapping on chip opens new perspectives for time and frequency metrology and integrated atom interferometry. The TACC experiment (Trapped Atomic Clock on a Chip) was built to study the potential of degenerate and non-degenerate quantum gases for metrology and to develop new tools for atom manipulation. One of the aims is the demonstration of a secondary frequency standard with a stability of a few 10-13 at one second. This is the context of this thesis. We report on several metrology experiments carried out with thermal clouds or Bose-Einstein condensates. Firstly, we demonstrate a stability of 5.8 x 10-13 at one second and characterize the limiting technical noise. We then present a study of the coherence of Bose- Einstein condensates and, in particular, the eect of interactions. The data is compared with a numerical model. Secondly, we introduce several tools for producing and manipulating atoms on a chip. We show the realization of an atomic microwave powermeter and assess the current limits of its performance. We then demonstrate that high-gradient microwave elds allow one to coherently manipulate the atoms' external motion. Finally, we present and characterize a new device for high-repetition rate atom loading involving fast modulation of the rubidium pressure.
The final chapter of this book considers some applications of ultracold atoms in addition to the study of Bose–Einstein condensates. These applications focus largely on the use of ultracold atoms for the purpose of constructing a highly accurate atomic clock. These clocks include atomic fountain clocks, which are presently used for the definition of the second. These clocks operate at microwave frequencies by observing the transitions between hyperfine split atomic ground states. More recent developments in atomic clocks utilize optical transitions between the ground state and an excited atomic state and typically utilize atoms trapped in an optical lattice.
Beams of atoms and molecules (N.F. Ramsey). Momentum exchange between matter and light (S. Stenholm). Quantum effects in atomic optics (D.F. Walls). New laser cooling mechanisms (C. Cohen-Tannoudji). Laser cooling configurations (G. Nienhuis). Velocity-selective coherent population trapping in one and two dimensions (E. Arimondo). Coupled-pendulum model of the forces on three-level atoms (M. Prentiss et al.). Laser cooling and manipulation of atoms and selected applications (S. Chu). Laser cooling and trapping of neutral atoms (W.D. Phillips). Search for montional quantization of laser-cooled atoms (R. Gupta, S. Padua, T. Bergeman, H. Metcalf). The low (temperature) road toward Bose-Einstein condensation in optically and magnetically trapped cesium atoms (Ch. Monroe, E. Comell, C. Wieman). Manipulation of atoms by laser light (W. Ertmer). Laser manipulation of helium: the limits of the semi-classical description (A. Aspect et al.). Light manipulation of atoms (V.1. Balykin). Atom traps and atom optics (D.E. Pritchard and W. Ketterle). Electromagnetic traps for, charged and neutral particles (W. Paul). Laser cooling of trapped ions (W.M. Itano et al.). High-resolution atomic spectroscopy of laser-cooled ions (D.J. Wineland et al.).