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Physical Review A

Elementary Sisyphus process close to a dielectric surface

Pierre Desbiolles, Markus Arndt, Pascal Szriftgiser, Jean Dalibard

Published Nov 1, 1996• 48 citations
Publisher

Abstract

We investigate both theoretically and experimentally an elementary Sisyphus process occurring during the reflection of an atom onto a laser evanescent wave propagating at the surface of a dielectric prism. Cesium atoms bouncing at normal incidence may undergo a spontaneous Raman transition between their two hyperfine levels; this leads to an efficient cooling since those levels are light shifted by a different amount by the laser-atom interaction thanks to the large hyperfine splitting. We compare the measured final energy distributions after the bounce with Monte Carlo simulations. A quantitative agreement is obtained when the van der Waals interaction between the cesium atoms and the dielectric prism is taken into account. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.54.4292

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We investigate both theoretically and experimentally an elementary Sisyphus process occurring during the reflection of an atom onto a laser evanescent wave propagating at the surface of a dielectric prism. Cesium atoms bouncing at normal incidence may undergo a spontaneous Raman transition between their two hyperfine levels; this leads to an efficient cooling since those levels are light shifted by a different amount by the laser-atom interaction thanks to the large hyperfine splitting. We compare the measured final energy distributions after the bounce with Monte Carlo simulations. A quantitative agreement is obtained when the van der Waals interaction between the cesium atoms and the dielectric prism is taken into account. \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.
We present an experiment where a cloud of cold caesium atoms is dropped onto an atomic mirror formed by a laser evanescent wave, and is cooled during the reflection. This cooling is due to a single Sisyphus process, transferring atoms from one ground-state hyperfine level to another, less coupled to the evanescent wave. We compare our results with a simple one-dimensional theoretical model. We also give the first experimental evidence for a large increase in the confinement lifetime of the atoms in this ‘gravitational cavity’ because of the cooling process.
We show that internal state transitions may induce energy transfer among different directions of motion and lead efficiently to large scattering angles in atomic reflection from evanescent-wave mirrors. The proposed scattering mechanism is reminiscent of the so-called Sisyphus effect of laser cooling. Perturbative calculations are presented and discussed for the diffraction of atomic beams at grazing incidence on evanescent fields with polarization gradients and for the reflection of atoms by a rough mirror.
Summary form only given. Evanescent wave atomic mirrors have been shown to be very sensitive to the surface roughness of the glass substrate on which the evanescent wave is formed. Non-specular reflection of slow atoms at normal incidence has been observed for surface roughness as low as 0.1 nm. We interpret this behaviour in terms of diffraction of the atomic De Broglie wave on the modulated potential created by the interference of the evanescent wave with light scattered by the rough surface. However these experiments could not separate the specular peak of reflected atoms from the diffuse part. We have developed a new method to measure the velocity distribution of the atoms after the bounce with a much better resolution, using Raman transitions. Two phase locked counterpropagating laser beams induce a Raman transition between the ground state hyperfine levels of the /sup 85/Rb atoms falling from a magneto-optical trap. The resonance condition is only fulfilled for atoms with a transverse velocity controlled by the interaction time between the atoms and the beams. These velocity selected atoms bounce on the mirror and their velocity distribution after reflection can be measured using the same Raman beams, by scanning their difference in frequency.
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).
We experimentally demonstrate hyperfine optical pumping of rubidium atoms probed by an evanescent electromagnetic field at a dielectric-vapor interface. This light-atom interaction at the nanoscale is investigated using a right angle prism integrated with a vapor cell and excited by evanescent wave under total internal reflection. An efficient hyperfine optical pumping, leading to almost complete suppression of absorption on the probed evanescent signal, is observed when a pump laser beam is sent at normal incidence to the interface. In contrast, when the pump and probe beams are co-propagating in the integrated prism-vapor cell, no clear evidence of optical pumping is observed. The experimental results are supported by a detailed model based on the optical Bloch equation of a four atomic-level structure, which also includes a treatment of transit relaxation and wall collision with relaxation rates that were obtained directly from the thermal velocities of the atoms and the penetration depth of the evanescent wave. The obtained highly efficient optical pumping at the nanoscale is regarded as an important step in the quest for applications such as optical switching, magnetometry, and quantum memory.