Atom Optics is a new branch of Atomic Physics, where one tries to act upon atoms, likewise one can act upon light (photons) in ordinary optics. The goal is therefore to reflect, focus, diffract, make interfere atoms1 .Afew years ago, this was considered as a fundamental goal, as had been the case decades ago for electron optics, or neutron optics. Indeed, it is always important to investigate the quantum behaviour of larger and larger objects, and studying the wave like behaviour of atoms has attracted a lot of attention. Moreover, atoms are objects that are coupled with the environment in a controlable way, in particular via quasi-resonant interaction with light. There is thus a hope to investigate how this coupling with the environment is relevant to the old problem of the division between the quantum world and the classical world2 ,and how it is related to the question of quantum decoherence. To keep in the domain of Atom Optics, the question of the preservation of coherence of the de Brogue waves describing the atomic motion is crucial. Another basic issue is the question of the collisions between atoms, or between an atom and a surface, when the atom is described as a matter-wave. From this point of view, the very interesting recent results in the domain of cold atoms collisions are only a part of what will probably come out, and new approaches may be fruitful. For instance, some collision effects may be considered as non-linear effects of atom optics... On the other hand, almost from the start, Atom Optics has been a domain where the question of applications has been raised. The experience of the many useful applications existing in the domain of electron and neutron optics has clearly shown the way. A first reason for expecting interesting applications to atom optics is the small value of the de Brogue wavelength, in the nanometer range or below, even at very low energies. This opens for instance the possibility of high resolution lithography, or of nanoprobes, at energies low enough to have a soft, non damaging interaction with a surface. Another important class of applications is in atomic interferometry. It can be shown that atomic interferometers (using atoms of mass Mat) are much more sensitive to inertial or gravitational effects3 than photonic interferometers (using photon of energy hw), by a ratio of the order of MatC2 / ho) . Note that this statement is true only under the condtion that the atomic and photonic interferometers under comparison have equivalent geometries, so that present day interferometers do not yet take full advantage of the 1011 factor of potential improvement. However, impressive results have already be demonstrated6. As a matter of fact, many of the papers presented in this symposium are linked to applications, either with atomic interferometers, or related to the possibility of deep focusing of an atomic beams. Most of these applications a Unite de recherche associée au CNRS can be easily understood by analogy with photon optics. However, there are also several features of atom optics that have no analogy in photon optics. The most important one is probably the possibility to increase the luminosity of an atomic beam (i.e. the flux of atoms per per unit time, surface, and solid angle) or —equivalently — to increase the atomic density in the phase space. This is possible by use of laser cooling, which is a dissipative process, and therefore is not constrained by the Liouville theorem. Another distinctive feature of atom optics —this one not particularly an advantage —is the lack of a sudden interface, that would be analogous to a glass-vacuum interface for light. By sudden interface, we mean that some characteristic parameter relevant to the propagation (the index of refraction in the case of light) changes on a scale small compared to the wavelength of the waves that propagate. In atom optics, the interfaces are usually soft, since the potentials acting on the atomic motion usually change on a scale large compared to the de Broglie wavelengths. In this overview, I intend to recall some basic principles of atom optics, and to point out some important analogies and differences with photon optics4 .Iexpect this discussion to be illustrated by the various presentations at this symposium, for which I hope to offer a framework. In addition, I will take the liberty to illustrate my presentation by some examples chosen among results obtained recently in my laboratory, on the subject of atomic mirrors. The comparison between atom optics and photon optics would of course be incomplete if I would not adress the question of the impact of Bose Einstein condensates onto Atom Optics. As many of us, I am convinced that we are assisting to a revolution as important for Atom Optics as the invention of the laser in the domain of Photon Optics, and we are lucky to have a full session on this hot subject.

Intense, highly collimated sources of atoms have many potential applications. Bright beams will be important for competitive high flux and high resolution direct-write techniques in lithography, with the added advantage of parallel writing through laser manipulation. Intense sources will also be useful in other atom optic devices e.g. for loading atoms into hollow fiber waveguides. In atomic physics, many collision processes can only be measured with the sensitivity offered by such high flux sources. We report progress on the development of an intense, collimated beam of metastable helium atoms which improves the brightness generated by conventional nozzle discharge sources by several orders of magnitude. The system uses diode lasers to transversely collimate and then to longitudinally slow the atoms, using Zeeman tuning to compensate for the changing Doppler shift. The slowed, collimated beam is then compressed in a 2D magneto-optic trap before a final collimation stage, to achieve the required increase in intensity. Initial experiments using the helium source for some of the applications above are described.

Since the first interferometers for atoms and molecules were demonstrated in 1991, they have already been applied to measure atomic and molecular properties, to investigate fundamental aspects of quantum mechanics, and to measure inertial motion. This tutorial is designed to introduce those with a vague understanding of optical interferometers to atom interferometry. We outline the basic theory needed to calculate the observed phase shift, indicate how this phase shift is experimentally determined, and then describe how the phase shift is found in two particular cases: phase shifts caused by application of a uniform electric field to atoms on one side of the interferometer, and phase shift arising from the presence of a gaseous medium through which the atom wave on one side of the interferometer must propagate. We illustrate this presentation with a description of our three grating interferometer, including data taken with it.

The method of Bragg scattering from a standing light wave for splitting atoms coherently into two beams is discussed. An interferometer for atoms is demonstrated by Bragg deflection of a beam of collimated metastable neon atoms from three standing light waves. Possibility of using the interferometer in nanolithography is discussed.

We laser-cool single beryllium ions in a Paul trap to the ground (n equals 0) quantum harmonic oscillator state with greater than 90% probability. From this starting point, we can put the atom into various quantum states of motion by application of optical and rf electric fields. Some of these states resemble classical states (the coherent states), while others are intrinsically quantum, such as number states or squeezed states. We have created entangled position and spin superposition states (Schrodinger cat states), where the atom's spatial wavefunction is split into two widely separated wave packets. We have developed methods to reconstruct the density matrices and Wigner functions of arbitrary motional quantum states. These methods should make it possible to study decoherence of quantum superposition states and the transition from quantum to classical behavior. Calculations of the decoherence of superpositions of coherent states are presented.

Atoms interacting with standing light waves are a model system for the propagation of waves in static and time varying periodic media. We present here experiments studying the coherent motion of atomic deBroglie waves in periodic potentials made from on and off resonant light. We observe anomalous transmission of atoms through resonant standing light waves and experimentally confirm that atoms fulfilling the Bragg condition form a standing matter wave pattern. We furthermore demonstrate how Bragg diffraction of atomic matter waves at a time-modulated thick standing light wave can be used to coherently shift the deBroglie frequency of the diffracted atoms. Our frequency shifter for atomic matter waves is similar to an acousto-optic frequency shifter for photons.

We have developed a rubidium atomic funnel for use as a matter-wave source in experiments in atom interferometry and atom optics. The funnel utilizes the techniques of laser cooling and trapping to produce a low-velocity beam of cold rubidium atoms. Atoms from a thermal beam are first slowed in a tapered magnetic field using 1D Zeeman slowing. The atoms are then loaded into a 2D magneto-optic trap or atomic funnel. The trap cools and compresses the atoms, which are then ejected from the trap by moving molasses formed with frequency-shifted laser beams. These slow atoms will be diffracted by microfabricated transmission gratings as part of a three-grating atom interferometer.

We describe two experiments that use neutral atomic beam techniques to write nanostructures. In the chromium experiment we have used neutral chromium atoms to write periodic nanometerscale structures in a direct way. In a second experiment we have used a self-assembling monolayer as a resist for metastable helium atoms.

Through the use of light forces exerted by near-resonant laser light, chromium atoms are focused as they deposit onto a substrate, forming nanometer-scale structures on the surface. The laser light is in the form of a standing wave, in which each node acts as an atom-optical `lens.'. The result is a highly accurate array of lines with a periodicity of (lambda) /2 equals 212.78 nm and full-width at half maximum as small as 38 nm. We discuss progress with this process, in particular the fabrication of a 2D array, the creation of an array with (lambda) /8 periodicity, the replication of the array in polymer material, the production of magnetic nanowires, and the reactive-ion etching of a chromium pattern on silicon to generate an array of distinct nanowires and/or nanotrenches.

We describe the fabrication of approximately 70-nm structures in silicon, silicon dioxide, and gold substrates by the exposure of the substrates to a beam of metastable argon atoms in the presence of dilute vapors of trimethylpentaphenyltrisiloxane, the dominant constituent of the diffusion pump oil used in these experiments. The atoms release their internal energy upon contacting the siloxanes physisorbed on the surface of the substrate, and this release causes the formation of a predominantly carbon-based resist. To demonstrate the resolution of the resist formation process, the atomic beam was patterned by a silicon nitride membrane, and the pattern formed in the resist material was transferred to the substrates by chemical etching. Simultaneous exposure of large areas (44 cm²) was also demonstrated. The sensitivity of the resist formation to the internal energy stored in the atom allows a new pattern formation technique based on spatially dependent optical de-excitation of the metastable atoms.

This paper describes the formation of nanometer-scale features in gold and silicon substrates. The features in gold were made by using a self-assembled monolayer (SAM) of nonanethiolate on gold as a resist damaged by neutral cesium atoms. A SAM resist of octyltrichlorosilane on silicon dioxide was used as a resist sensitive to cesium atoms in order to fabricate features in silicon. A silicon nitride membrane perforated with nm- and micrometers -scale holes was used to pattern the atomic beam. Etching transferred the pattern formed in the SAM layer into the underlying substrate. Features of < 100-nm size were etched into the gold and silicon substrates. Investigations of the reflectivity of samples of nonanethiolate on gold, exposed to the atomic beam without a mask and subsequently etched, revealed that the resist-etch system exhibited a minimum threshold dose of cesium for damage; at doses lower than approximately 3 monolayers, the damage was insufficient to allow penetration of the SAM by the etching solution. The threshold dose for damage of the octyltrichlorosilane SAM on silicon dioxide is under investigation.

Recent theoretical and experimental demonstrations have shown that blue-detuned laser light, propagating in the annular core-cladding region of a hollow-glass fiber, produces a repulsive, evanescent light-wave potential in the hollow, that can be used to guide near-resonant atoms down the fiber. In this work, I show that slight modifications to the hollow-fiber geometry can be used to turn this atom guide into an atom-bottle trap. The trap can be open and shut by varying the aperture angle at which light couples into the fiber, allowing the atoms to be easily loaded. This trap has an advantage over other optical atom traps in that the atoms move coherently in a field-free region with only brief specular reflections at the step-like potential walls.

We report the recent progress of the experiments on guiding atoms by evanescent waves in micron-sized hollow optical fibers. The lateral manipulation accuracy is enhanced up to 1 micron with a large increase of more than 50 times on the guided atom flux. Moreover, the frequency tuning enables the fine control of the guided flux with a numerical accuracy of 10 atom/s. The atom-guidance scheme is applied to in-line isotope separation on rubidium atoms and measurement of the cavity quantum electrodynamic effect in a cylindrical dielectric. In addition, the feasibility of fabricating micron-sized structures with nanometric depth is discussed including the manipulation of a small number of laser-cooled atoms.

Atoms, unlike photons, travel at velocities readily attainable in the laboratory, making possible novel atom optical devices based on optical elements which move relative to the atomic beam. We report design studies of a device to accelerate or decelerate and simultaneously monochromatize a helium atomic beam. A helium supersonic free-jet (v equals 950 m/s, (Delta) v equals 5 m/s, FWHM) is reflected from a moving surface to produce an output beam is continuously tunable in velocity from epithermal (2000 m/s) to ultra-slow (ca. 1 m/s, De Broglie wavelength 1000 angstroms). The decelerator is highly dispersive in the low velocity regime, making the collimated ultra-slow output beam nearly monochromatic, i.e. ultra-cold. Measured properties of an actual supersonic helium free-jet expansion were used in Monte Carlo simulations of the decelerator to predict the attainable decelerated beam properties. Ultra- slow beams of usable intensity at T < 100 nK appear attainable. Finite element stress calculations for a magnetically suspended rotor verify that the necessary reflector velocities (475 m/s) can be safely achieved. Possible applications of an ultra-cold helium beam might include gas-surface scattering experiments to probe `quantum reflection' of atoms from surfaces and to measure gas- surface bound states of exceptionally low binding energy, thereby testing the contributions of retardation to the gas- surface potential.

Using the stimulated force exerted by counterpropagating picosecond laser pulses from a mode-locked Ti:Sapphire laser we were able to focus a beam of laser-cooled cesium atoms along one dimension to about 57% of its original width in the detection zone. The force profile was measured outside and inside the overlap region of the pulses and found to be in agreement with an earlier theoretical prediction. A brief theoretical account of the interaction of atoms with pulsed laser light based on the optical Bloch equations is given.

A new method of studying and cooling trapped atoms is discussed, with particular attention to atoms in far detuned, 3D optical lattices. The technique, projection cooling, uses a combination of microwave and optical fields to cycle atoms between hyperfine sublevels. A single vibrational level will remain dark to both the light and the microwaves, so atoms will accumulate there. Cooling below the photon recoil limit is possible with this technique. As a diagnostic tool it promises to yield detailed information about atoms in the lattice, including vibrational spectra and the distribution of atoms among vibrational levels, even in the limit of relatively weak binding to lattice sites. Atoms cooled in this way and then allowed to adiabatically expand in their potentials could reach the Bose-Einstein condensation point in less than a second, or at least get close enough to reach it after only a modest amount of evaporative cooling in a larger volume trap. Atoms so cooled and trapped are also of interest for precision measurements.

We form a 1D optical lattices for Cs atoms using light tuned a few thousand linewidths below the 6S_1/2(F equals 4) yields 6P_3/2(F' equals 5) transition at 852 nm. In this far-off- resonance lattice the time scale for damping of motional coherences and kinetic energy can be orders of magnitude longer than the vibrational oscillation period for atoms trapped in the lattice potential wells. Atoms are loaded directly into deeply bound states, by adiabatic transfer from a superimposed, near-resonance optical lattice. This yields a mean vibrational excitation n approximately equals 0.3, and localization (Delta) z approximately (lambda) /20 deep in the Lamb-Dicke regime. Light scattering subsequently heats the atoms, but the initial rate is only of order 10^-3 vibrational quanta per oscillation period. Low vibrational excitation, localization in the Lamb-Dicke regime and low heating rates make these atoms good candidates for resolved- sideband Raman cooling, and for the generation and study of non-classical states of center-of-mass motion. We propose a scheme for resolved-sideband Raman cooling and quantum state preparation; the scheme employs Raman coupling between magnetic sublevels induced by the lattice light field itself.

We have designed a gravitational cavity for ultra-cold atoms using an atomic mirror made from an evanescent laser wave. By a temporal variation of the evanescent wave intensity, we have realized various atom optics components such as temporal slits and phase modulators. We have also designed an atom interferometer using this cavity which proves that the coherence of the de Broglie waves can be preserved during the bounce of the atoms on the mirror.

Multiple bounces of cold rubidium atoms have been observed for times up to one second in a trap formed by gravity and a 2 cm-diameter spherical mirror made from a sinusoidally magnetized floppy disk. We have studied the dynamics of the atoms bouncing in this trap from several different heights up to 40.5 mm and we conclude that the atoms are reflected specularly and with reflectivity 1.01(3). Slight roughness of the mirror is caused by harmonics in the magnetization of the surface and by discontinuities at the boundaries between recorded tracks. As the next step in this atom optics program we propose using a magnetic mirror to create a 2D atomic gas. We discuss how cold atoms can be loaded into the ground state of a static magnetic potential well that exists above the surface of the mirror as a consequence of the intermediate-field Zeeman effect.

We have fabricated and investigated efficient magnetic lenses, waveguides, and mirrors from rare earth permanent materials. They are affordable and maintenance free. In contrast to corresponding light force components they do not need any supplies, they have large apertures, high reflectivity, and there is no spontaneous emission. The cylindrical shape of magnetic components is furthermore well suited to steer atomic beams.

Although there are many kinds of different techniques developed to manipulate atomic matter waves, a laser beam is still considered as the most effective `optical element' to manipulate atomic waves in atom optics. In the laser-based atom optic devices, the spatial profiles of a laser beam play a central role in controlling the motion of atoms. By choosing different spatial profiles of laser beams, one can construct atom optic devices for different purposes. Recently experimental demonstrations of manipulation of center of mass motion of atoms by time-dependent light field were reported. In this paper we theoretically study the transient effects in atom optics by using a laser pulse train. The reflection and transmission of atoms through the laser pulse train are studied in detail. We find that the laser pulse train acts as both a spatial beam splitter and a `temporal grating' which can both reflect or transmit atoms in spatial domain and `diffract' atoms in the time domain.

We discuss the prospects for a class of laser-like sources of atoms where the stimulated accumulation of atoms in the fundamental mode of a matter wave resonator is achieved by optical pumping. Precooled atoms in an internal state a which is not affected by the resonator trapping potential are excited into a state e by means of laser light. Once the atom is in state e it decays into the electronic ground state g by means of spontaneous emission, thereby occupying one of the resonator modes v equals 0, 1, ... Neglecting reabsorption of the spontaneously emitted photon, the probability for a transition into mode v is proportional to 1 + n_v (`gain'), where n<sub>v</sub> is the number of atoms in mode v prior to the transition. Including linear losses this model shows threshold behavior in the fundamental mode v equals 0, mode competition and Poissonian atom statistics above threshold. We also analyze the `small-signal gain' including reabsorption of the spontaneously emitted photons. We demonstrate that the threshold for matter wave amplification can only be reached in small 3D resonators of linear size comparable to the wavelength of the spontaneous photon, or in resonators with effectively reduced dimensionality.

Bose-Einstein condensation of ⁷Li has been studied in a magnetically trapped gas. Because of the effectively attractive interactions between ⁷Li atoms, many-body quantum theory predicts that the occupation number of the condensate is limited to about 1400 atoms. We observe the condensate number to be limited to a maximum value between 650 and 1300 atoms. The measurements were made using a versatile phase-contrast imaging technique. We discuss our measurements, the current theoretical understanding of BEC in a gas with attractive interactions, and future experiments we hope to perform.

We consider the quantum dynamics of a neutral atom Bose- Einstein condensate in a double-well potential, including hard-sphere particle interactions. Using a mean-field factorization we show that the coherent oscillations due to tunnelling are suppressed when the number of atoms exceeds a critical value. An exact quantum solution, in a two-mode approximation, shows that the mean-field solution is modulated by a quantum collapse and revival sequence. Chaotic dynamics results when the potential is modulated.

In this paper the conventional electronic spin echo technique is proposed to detect the macroscopic quantum coherence of a Bose-Einstein condensate. In this technique, a (pi) /2 microwave pulse followed by a (pi) pulse with an appropriate delay is used to excite the Zeeman levels of a Bose condensed gas. After the two pulses, a spin echo pulse is generated due to the dephasing and rephasing processes in the gas. We show that the properties of the spin echo signal depends on the temperature of the gas. If a condensate exists in the gas, the echo signal can reflect the macroscopic quantum coherence of the Bose-Einstein condensate. The detection technique doesn't destroy the sample.

We study the cavity QED effects (modified decay rates and energy level shift) of an atom inside a cylindrical hollow fiber and outside a solid fiber using linear-response formalism. Next, we suggest the Sisyphus cooling process occurring inside the hollow fiber with blue-detuned evanescent wave and as a preliminary example, we show a Monte-Carlo simulation of the atoms in the conical hollow system. We also propose that the similar cooling process is expected in the dark hollow beam (doughnut beam) obtained from the hollow fiber of step index, which is more desirable than the case when atoms are inside the fiber since there is no attracting Van der Waals force.

Light-induced dipole-dipole interactions in a coherent atomic field result in an effective nonlinear interaction between atoms. This nonlinearity can induce self-focusing and self-trapping of a coherent atomic beam undergoing propagation through a travelling-wave laser beam; we show how such a scheme could be realized and evaluate the critical density required for atomic self-focusing and self- trapping. An analogy to optical self-focusing and self- trapping is discussed.

The study of physical properties of Bose condensed gases has recently become a very active topic due to the experimental realization of Bose-Einstein condensation in the magnetically trapped gases of alkali atoms. In this paper we theoretically study the Rabi oscillation of a weakly interacting Bose gas in the regime of microwave electronic spin resonance. For a Bose gas above the critical temperature for Bose-Einstein condensation, the microwave radiation induced by the driving microwave field exhibits the ordinary Rabi oscillation damped by the inhomogeneous Doppler dephasing. For a Bose gas with a condensate, the microwave radiation is composed of two components. One is the strong coherent Rabi oscillation from the condensate. The other is a modulated Rabi oscillation due to the noncondensed part of the gas. We show that the modulation of Rabi oscillation of the noncondensed gas is directly relative to the elementary collective excitation of atoms in the gas.

We present a novel and simple atom trap in a pyramidal and a conical hollow mirror cavity and its application to atom optics. Using a conical axicon mirror trap, we also have produced a pulsed cold atomic beam extracted from the trapped atoms. We point out several novel features of our cold atomic beams.

We present initial measurements of the dispersive index of refraction for sodium matter waves passing through argon. In addition, we describe a novel scheme for performing tomography on the longitudinal quantum state of particles in an atomic beam.

Recently, beams of metastable helium and argon atoms have been used to generate nanoscale patterns [1]. In this method, a thin layer of gold is coated with a self assembling monolayer of alcanethioles (SAM) and then exposed to the atomic beam which was spatially modulated by a mechanical mask. After exposure, etching with a wet gold etching solution transferred the structure of the mask into the gold layer. The achieved edge resolution of the transferred pattern at wazzu sub 100 rim scales suggested that this technique could provide a useful lithography method. Motivated by these results and discussions with colleagues [2], we have investigated the influence of a cesium atomic beam in a similar arrangement [3]. The use of alkali atoms would be desirable because light force methods have been extensively studied with alkali atomic beams, and because light sources are abundant.