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Chinese Physics

Diffracted field distribution from a knife-edge truncated semi-Gaussian beam as an atomic (molecular) mirror

Zheng Ping, Gao Wei-Jian, Yin Jianping

Published Jan 1, 2006• 3 citations
Publisher

Abstract

We investigate the diffraction characteristics of an incident Gaussian beam cut by a straight edge bounding a semi-infinite opaque plane using Kirchhoff scalar wave theory in the Fresnel limit and propose a new and simple mirror scheme to reflect atoms by using the intensity gradient induced by a blue-detuned semi-Gaussian laser beam. The optical potential of the diffracted light of the knife-cut semi-Gaussian beam for 85 Rb atom and its spontaneous emission probability are calculated and compared with the performance of the evanescent-wave mirror. Our study shows that the optical potential of the diffracted light of the semi-Gaussian beam is far higher than that of the evanescent light wave and the maximum normal velocity of the incident atoms can be far greater than that of the evanescent light wave under the same parameters, so the blue-detuned semi-Gaussian beam, as a novel atomic mirror, can be used to efficiently reflect cold atoms with a normal velocity of greater than 1 m/s. However, the intensity gradient (force) of the diffracted light of the semi-Gaussian-beam is much smaller than that of the evanescent light wave, so its spontaneous emission probability is greater than that from the evanescent-wave when the normal velocity of incident atoms is greater.

DOI
10.1088/1009-1963/15/1/019

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We investigate the diffraction characteristics of an incident Gaussian beam cut by a straight edge bounding a semi-infinite opaque plane using Kirchhoff scalar wave theory in the Fresnel limit and propose a new and simple mirror scheme to reflect atoms by using the intensity gradient induced by a blue-detuned semi-Gaussian laser beam. The optical potential of the diffracted light of the knife-cut semi-Gaussian beam for 85 Rb atom and its spontaneous emission probability are calculated and compared with the performance of the evanescent-wave mirror. Our study shows that the optical potential of the diffracted light of the semi-Gaussian beam is far higher than that of the evanescent light wave and the maximum normal velocity of the incident atoms can be far greater than that of the evanescent light wave under the same parameters, so the blue-detuned semi-Gaussian beam, as a novel atomic mirror, can be used to efficiently reflect cold atoms with a normal velocity of greater than 1 m/s. However, the intensity gradient (force) of the diffracted light of the semi-Gaussian-beam is much smaller than that of the evanescent light wave, so its spontaneous emission probability is greater than that from the evanescent-wave when the normal velocity of incident atoms is greater.
A novel and simple atomic mirror composed of a blue-detuned semi-Gaussian beam is proposed. From the Fresnel diffraction theory, the intensity distributions of a collimated Gaussian laser beam diffracted by the straight edge of a semi-infinite opaque plate are studied. The optical potential of the semi-Gaussian beam for 85 Rb atoms and its spontaneous emission probability are calculated and compared with the performance of the evanescent-wave mirror. Our study shows that the blue-detuned semi-Gaussian beam, as a novel atomic mirror, can be used to reflect atomic beam efficiently, and under the same beam parameters and lower normal atomic velocity, the performance of the semi-Gaussian-beam mirror is better than that of the evanescent-wave mirror.
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).
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 propose a new scheme to generate a focusing hollow beam (FHB) by use of an azimuthally distributed 2pi-phase plate and a convergent thin lens. From the Fresnel diffraction theory, we calculate the intensity distributions of the FHB in free propagation space and study the relationship between the waist w_0 of the incident Gaussian beam (or the focal length f of the lens) and the dark spot size (or the beam radius) at the focal point and the relationship between the maximum radial intensity of the FHB and the dark spot size (or the beam radius) at the focal point, respectively. Our study shows that the FHB can be used to cool and trap neutral atoms by intensity-gradient-induced Sisyphus cooling due to an extremely high intensity gradient of the FHB itself near the focal point, or to guide and focus a cold molecular beam. We also calculate the optical potential of the blue-detuned FHB for ^85Rb atoms and find that in the focal plane, the smaller the dark spot size of the FHB is, the higher the optical potential is, and the greater the corresponding optimal detuning delta is; these qualities are beneficial to an atomic lens not only because it is profitable to obtain an atomic lens with a higher resolution, but also because it is helpful to reduce the spontaneous photon-scattering effect of atoms in the FHB.
We calculate the reflection probability for ultracold atoms incident on an evanescent-wave atomic mirror, and analyze the optimum conditions to observe quantum reflection. We find that averaging over the Gaussian profile of the laser beam dramatically reduces the quantum signature, and consider the effects of an appropriate aperture that limits the variation of beam intensity. We show that quantum reflection is particularly sensitive to details of the atom-surface potential, and could be used to resolve retardation effects.