Atomic motion in a pulsed evanescent wave, with a pulse duration on the order of the lifetime of the excited state, is calculated using the semiclassical Bloch-equation approach. The equations for the internal atomic motion are solved using two approximations based on high laser intensity and on slow atomic velocity. The center-of-mass motion in the field under the effect of the dipole force is subsequently determined by numerical integration. As an example, the calculations show that the maximum normally incident velocity allowing a sodium atom to be reflected is approximately 35 m/s when using a 10 MW/cm 2 laser pulse of 7 ns duration. Our results also demonstrate that the velocity distribution of the reflected atoms may considerably differ from the distribution of the incident atoms due to different deceleration and acceleration times in a short laser pulse. This effect may lead to an average slowing-down of the reflected part of a thermal particle beam.
Atomic motion in a pulsed evanescent wave, with a pulse duration on the order of the lifetime of the excited state, is calculated using the semiclassical Bloch-equation approach. The equations for the internal atomic motion are solved using two approximations based on high laser intensity and on slow atomic velocity. The center-of-mass motion in the field under the effect of the dipole force is subsequently determined by numerical integration. As an example, the calculations show that the maximum normally incident velocity allowing a sodium atom to be reflected is approximately 35 m/s when using a 10 MW/cm 2 laser pulse of 7 ns duration. Our results also demonstrate that the velocity distribution of the reflected atoms may considerably differ from the distribution of the incident atoms due to different deceleration and acceleration times in a short laser pulse. This effect may lead to an average slowing-down of the reflected part of a thermal particle beam.
In this thesis, the use of pulsed laser fields to control the center-of-mass motion of neutral atoms and molecules is studied both numerically and experimentally. In particular, we consider the use of a pulsed standing wave for the deflection of atomic beams, and develop novel types of mirrors for applications in atom and molecule optics. The research work shows that pulsed laser fields can be applied to form efficient mirrors for neutral particles regardless of the details of their internal energy-level structure. Moreover, it is shown that pulsed standing waves can also be utilized to efficiently deflect atomic beams. In the first part of the thesis, we study the effects of phase fluctuations of the laser field on the momentum distribution of atoms after interaction with a standing wave. Our numerical simulations show that the coherence properties of the laser field play a major role in diffraction of atoms, especially when using pulsed lasers. It turns out that the effects caused by the limited coherence time of the optical field are clearly observable as a transfer of atoms in momentum space to the region around zero momentum rather than to high momentum states. The numerical analysis of the pulsed standing-wave diffraction was complemented by experimental measurements of the deflection profiles of a beam of thermal sodium atoms. The experimental distributions were measured for a value of the coherence time intermediate between the Rabi period and the interaction time. A comparison of the results with an expected distribution calculated for a fully coherent interaction shows that the phase fluctuations of the light field drastically affect the achievable transverse momentum values. Based on our theoretical and experimental analysis of the diffraction profiles, we conclude that large deflection angles can be reached only when laser pulses with a Fourier-limited bandwidth are applied. The second part of the thesis concentrates on the development of pulsed mirrors for neutral atoms and molecules. In particular, we consider the use of an evanescent wave, formed in total internal reflection of light on a vacuum-dielectric interface, and of a standing wave as possible mirror configurations. Our numerical simulations of the pulsed evanescent-wave mirror show that atoms with initial velocities up to several tens of meters per second can be reflected already at the moderate field intensities of a few tens of MW/cm2. This allows pulsed evanescent waves to be applied in a compact setup to control the motion of thermal atomic beams, for which the traditional atom mirrors are suited only at grazing incidence. However, since the effective interaction volume of the atomic beam and the laser field is limited by the short decay length of the evanescent wave, only a relatively small number of atoms can be reflected with a single laser pulse. Furthermore, the reflection is always inelastic, since the force exerted on the atoms varies as a function of the initial position of the particles. To solve the above problem we consider the use of a standing wave as a pulsed mirror for atoms. Our numerical simulations show that with a proper choice of the pulse duration and field intensity, each period of the standing-wave pattern functions as an elastic mirror for particles with an initial kinetic energy below the depth of the standing-wave potential. Hence, the standing-wave pattern acts as a long row of independent atom mirrors, which provides a novel route to controlling large volumes of fast atoms even with a single laser pulse. As a second application for the pulsed standing-wave mirror we consider the reflection of slow molecules, for which no efficient mirror configuration previously has been available. It is shown that pulsed standing waves of nonresonant frequencies can be used to efficiently manipulate large volumes of rotationally cold molecules. With a suitable choice of the parameter values, the molecules can be reflected nearly elastically, or with a tailored momentum distribution. This opens up a possibility to use the pulsed standing-wave mirror to control the motion of particles in various applications of atomic and molecular physics. Such a mirror could be applied, for example, to steer and image molecular beams, separate molecular species, and to form pulsed molecular beams.
In the reflection of atoms by evanescent wave the amplitude of the light field can be changed not necessarily adiabatically slow in comparison with relaxation of internal atomic motion. An approach to describe the reflection of atoms by evanescent wave is the dressed state picture. An atomic mirror can be formed also by a focused elliptical laser beam, in which atoms intersect near the waist of the laser beam. A simple evanescent wave allows one to create a high homogeneous field along the surface of an atomic mirror, without a limitation on the intensity of the field in an evanescent wave. The size of an atomic mirror is usually restricted by the laser intensity required by the reflection. There are several processes at the reflection of atom by light which could lead to non ideal properties of the mirror. One of the remarkable properties of an atomic mirror is its ability to reflect atoms in a certain quantum state.
This poster presents a first analysis of the laws of reflection of cold atoms by an evanescent wave atomic mirror. We demonstrate that when the laser beam is tuned to the blue of the atomic transition, i.e, for a positive frequency detuning compared to the frequency resonance Δ = ωL−ωa, there is a reflection without a contact with the surface of the prism (no adsorption). The condition for an internal total reflection is θ>θc = arcsin (1/n) where θ is the incidence angle of the laser wave on the internal face of the prism and n is its refraction index. The evanescent wave is parallel to the surface and propagates over few wavelengths only for θ = θc. The atomic trajectory is such as the incidence angle φi is different from the reflection angle φr (non respect of the first law of reflection in photonic optics). We’ll have to demonstrate the reflection law in atom optics and give numerical examples as an illustration [1]. At its interaction with the evanescent wave, the atom is submitted to a pressure radiation force Fx parallel to the surface of separation which communicates a quantity of motion in the direction of the x axis. It is also submitted to a dipolar force Fy perpendicular to the separation surface responsible of the repulsion of cold atoms in the case where we neglect the Van der Waals forces. We define R as the ratio of two forces Fx and Fy. Their expressions, function of the detuning, are given by the Ehrenfest theorem and the Bloch equations [2]. When the ratio R tends towards zero (spontaneous emission negligible for a detuning important compared to natural linewidth of the excited state), the first law of Descartes reflection is thus satisfied idem φi = φr Thus, it is simple to demonstrate that the atomic trajectories obey to the general reflection law: tg φr = tg φi−2R where R is independent of the spatial component. Its expression is given by the ratio of the velocity transfers Δvx to Δvy. The case of retro‐reflection seen in quasi normal incidence and for values of the ratio R different from zero (φi = −φr) is also examined. In the case where the value of the ratio R is non null, we may demonstrate that the incidence plan is different from the reflection plan (second law of Descartes reflection).
This work discusses the effect of a high-intensity standing wave laser field on the motion of neutral atoms moving with a relatively high velocity. The analysis involves a detailed calculation of the force acting on the atoms and the calculation of the diffusion tensor associated with the fluctuations of the quantum force operator. The high-intensity laser field limit corresponds to a Rabi frequency much greater than the natural rate of the atom. The general results are valid for any atomic velocity. Results are then specialized to the case of slow and fast atoms where the Doppler shift of the laser frequency due to the atomic motion is either smaller or larger than the natural decay rate of the atom. The results obtained for the force and diffusion tensor are applied to a particular ideal experiment that studies the evolution of a fast atomic beam crossing a high-intensity laser beam. The theories developed previously, for a similar laser configuration, discuss only the low atomic velocities case and not the more realistic case of fast atoms. Here, an approximate solution of the equation for the distribution is obtained. Starting from the approximate distribution function, the deflection angle and dispersion angle for themore » atomic beam with respect to the free motion are calculated.« less
The propagation of a two-level atomic wave packet across a laser beam is considered. For small incident kinetic energies of the atom, the wave nature of the center-of-mass motion becomes apparent, giving reflections and refractions in the case of a square profile of the laser beam. When the incident momentum is low enough, we show that one of the dressed states cannot propagate inside the laser beam, giving rise to an evanescent atomic wave packet. Also a stopped excited component is found when the incident momentum equals in modulus---not in direction---the one-photon recoil. \textcopyright{} 1996 The American Physical Society.
This thesis reports an investigation of the interaction of a thermal sodium beam with a variety of near-resonant evanescent field configurations which was performed between March 1990 and September 1993.The evanescent fields were tuned above the sodium D2 transition, in order to repel atoms at glancing incident angles through the gradient force.Three evanescent field configurations, corresponding to various optic elements, were employed.The first configuration was a travelling evanescent field, from which reflection of the beam was observed at glancing angles up to 4.5mrad.This configuration corresponds to a mirror for atoms.The second configuration was a standing evanescent wave generated by retroreflecting the travelling evanescent wave.The resulting evanescent wave consisted of closely spaced reflective regions separated by non-reflecting nodes of the standing wave.This configuration corresponds to a mirror grating with periodicity 7J2.The atomic beam was reflected from the evanescent field.No diffraction was observed, however.The final configuration was a moving standing evanescent grating, generated by interference between two counterpropagating laser beams.The relative velocity between the atoms and the grating could be continuously varied by adjusting the frequency of one laser.Coherent exchange of photons between the two fields in the moving evanescent grating was observed.This exchange exhibited velocity dependent resonant behaviour corresponding to doppleron resonances.The results are explained in terms of a dressed-state model for diffraction of atoms from such a grating.A parameter search was performed in an attempt to observe the diffraction of the thermal sodium beam, with null results.However, deflections which were dependent on grating velocity are reported.