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Physical Review A

Multiple reflection of an extended atomic wave packet through a square-profile laser beam

Luis Pumares, Luis Plaja, L. Roso, Kazimierz Rza̧żewski

Published Jun 1, 1996• 1 citation
Publisher

Abstract

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.

DOI
10.1103/physreva.53.4260

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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.
The propagation of a two-level atomic wavepacket across a monochromatic laser beam is considered. For small incident kinetic energies of the atom, the wave nature of the centre-of-mass motion becomes apparent. For certain situations, we show that one of the dressed states cannot propagate inside the laser beam, giving rise to an evanescent atomic wavepacket. Their characteristic features close to the condition of evanescent (or non-propagating) wavepackets are analysed. In particular, we present two different situations where almost stopped wavepackets appear.
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 work the dynamical behavior of the center of mass of a two-level atom in sequences of multiple optical standing waves is explored. In a standing wave the atomic momentum distribution fans out. But with a suitably designed sequence of standing waves it is possible to refocus the momentum-space wave packet and bring the momentum distribution to the initial value, which may be regarded as an atom optical analog to spin or photon echo. If the total interaction time is fixed, the refocusing performance gets better as the number of standing waves in a sequence increases. Also the atomic wave packet in position space evolves as if in free space. \textcopyright{} 1996 The American Physical Society.
A research project at the “Laboratoire d’électronique quantique” consists in a theoretical study of the reflection and diffraction phenomena via an atomic mirror. This poster presents the principle of an atomic mirror. Many groups in the world have constructed this type of atom optics experiments such as in Paris‐Orsay‐Villetaneuse (France), Stanford‐Gaithersburg (USA), Munich‐Heidelberg (Germany), etc. A laser beam goes into a prism with an incidence bigger than the critical incidence. It undergoes a total reflection on the plane face of the prism and then exits. The transmitted resulting wave out of the prism is evanescent and repulsive as the frequency detuning of the laser beam compared to the atomic transition δ = ωL−ω0 is positive. The cold atomic sample interacts with this evanescent wave and undergoes one or more elastic bounces by passing into backward points in its trajectory because the atoms’ kinetic energy (of the order of the μeV) is less than the maximum of the dipolar potential barrier ℏΩ2/Δ where Ω is the Rabi frequency [1]. In fact, the atoms are cooled and captured in a magneto‐optical trap placed at a distance of the order of the cm above the prism surface. The dipolar potential with which interact the slow atoms is obtained for a two level atom in a case of a dipolar electric transition (D2 Rubidium transition at a wavelength of 780nm delivered by a Titane‐Saphir laser between a fundamental state Jf = l/2 and an excited state Je = 3/2). This potential is corrected by an attractive Van der Waals term which varies as 1/z3 in the Lennard‐Jones approximation (typical atomic distance of the order of λ0/2π where λ0 is the laser wavelength) and in 1/z4 if the distance between the atom and its image in the dielectric is big in front of λ0/2π. This last case is obtained in a quantum electrodynamic calculation by taking into account an orthornormal base [2]. We’ll examine the role of spontaneous emission for which the rate is inversely proportional to the detuning δ and is responsible of the non specular aspect of the atomic reflection (atomic diffusion). In the contrary, we note that the specularity of the reflection preserve the coherence of the atomic wave packet. The atoms will constitute a probe of the rugosity of the prism surface which can be imperfect or super‐polished.
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.
Evanescent matter-waves produced by an atom wave packet incident onto a repulsive barrier edge can be back-refracted and reconstructed by the application of negative-index "comoving" potential pulses. One shows that those collapses and revivals of evanescent matter waves give rise to surface matter waves and should be observable via atom reflection echoes issued from the barrier interface. This property, together with the property of inducing negative refraction, makes such potentials the matter-wave counterpart of negative-index materials in light optics.