Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

AIP conference proceedings

Reflexion Laws In Atoms Optics

S. Ghezali, A. Taleb, El-Hachemi Amara, Saïd Boudjemai, Djamila Doumaz

Published Jan 1, 2008• 0 citations
Publisher

Abstract

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).

DOI
10.1063/1.2999922

Related papers

Evanescent Wave Atomic Mirror

S. Ghezali, A. Taleb, El-Hachemi Amara +2 more

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.

AIP conference proceedings•Jan 1, 2008•0 citations

New Physics with Evanescent Wave Atomic Mirrors: The van der Waals Force and Atomic Diffraction

Nathalie Westbrook, Christoph Ira Westbrook, Arnaud Landragin +11 more

After a brief introduction to the field of atom optics and to atomic mirrors, we present experimental results obtained in our group during the last two years while studying the reflection of rubidium atoms by an evanescent wave. These involve the first measurement of the van der Waals force between an atom in its ground state and a dielectric wall, as well as the demonstration of a reflection grating for atoms at normal incidence. We also consider the influence of quantum reflection and tunnelling phenomena. Further studies using the atomic mirror as a probe of the van der Waals interaction, and of very small surface roughness are briefly discussed.

Physica Scripta•Jan 1, 1998•28 citations

Design of atomic mirror for silicon atoms

Shinichi Shimizu, T. Iwane, Akira Kunieda +3 more

Cook and Hill suggested that the gradient of an optical field can be used to reflect atoms. To reflect atoms, the repulsive dipole force is used, which comes from the interaction between the electric dipole moment of atoms and the evanescent field. The evanescent wave is generated when light is totally reflected internally at the interface of different refractive indices. Later, the way to enhance the evanescent wave with a thin dielectric waveguide has been reported. We designed the atomic mirror for silicon atoms, whose structure enhances the evanescent field that is used to repel silicon atoms. We also set up the equations of motion for silicon atoms and derive trajectories of the atoms reflected by the atomic mirror. Optical intensity, incident angle of the light, and effective detuning are described in terms of controlling the trajectory of the atom.

Science and Technology of Advanced Materials•Jan 1, 2004•15 citations

High-resolution roughness measurements using cold atom reflection

V. Savalli, P. D. Featonby, Vincent Josse +5 more

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.

Conference on Lasers and Electro-Optics•Jan 1, 2000•0 citations

Observation of radiation pressure exerted by evanescent waves

D. Voigt, B. T. Wolschrijn, R. Jansen +3 more

We report a direct observation of radiation pressure, exerted on cold rubidium atoms while bouncing on an evanescent-wave atom mirror. We analyze the radiation pressure by imaging the motion of the atoms after the bounce. The number of absorbed photons is measured for laser detunings ranging from 190 MHz to 1.4 GHz and for angles from 0.9 mrad to 24 mrad above the critical angle of total internal reflection. Depending on these settings, we find velocity changes parallel with the mirror surface, ranging from 1 to 18 cm/s. This corresponds to 2 to 31 photon recoils per atom. These results are independent of the evanescent-wave optical power.

arXiv:quant-ph/9912101•Physical Review A•May 16, 2000•15 citations

Double reflection of spin-orbit-coupled cold atoms

Huang Zhen, Zeng Wen, Gu Yi +3 more

Artificial spin-orbit coupling in neutral cold atom have been experimentally implemented in alkali-metal atoms. Nowadays people begin to explore its possible applications. One of the most interesting applications is the atomic mirror, which is a key element in atom optics. And spin-orbit coupling provides the atomic beam with the possibility that the atomic spin can flip during its propagation, thus can be used to prepare the quantum-state-selective atomic mirror. In 2008, Juzeliūnas, et al. [Juzeliūnas G, et al. 2008 Phys. Rev. Lett. 100 200405] studied a spin-orbit-coupled matter wave packet of cold atom gas impinging on an infinite step potential created by the optical light field. Results showed that there is not only ordinary specular reflection, but also non-specular one. The reflected atoms split into two beams and double reflection takes place. Based on the previous study, here we consider a matter wave packet of spin-orbit-coupled cold atom gas impinging on a finite step potential created by the optical light field. Due to the effect of the spin-orbit coupling, in addition to the propagating state, the eigenstates of cold atoms include evanescent state and oscillating evanescent state. Under suitable conditions double reflection will take place. If there are just evanescent waves in the step potential, total internal reflection will take place. In other words, when there is propagating wave in the step potential, partial reflection will take place. By taking into account both the total internal reflection and partial reflection, we study not only the polarization rate but also the reflectivity each as a function of incident energy, incident angle and spin-orbit coupling strength. The properties different from those of previous studies are found. In the case of total internal reflection, we find that the polarization rate of the reflected atoms is sensitive to incident angle instead of the spin-orbit coupling strength and incident energy. While in the case of partial reflection, all these factors strongly affect the polarization rate and reflectivity. We carefully study these properties and find that, on one hand, high efficiency atomic mirror can be acquired in the case of total internal reflection, and on the other hand, we can acquire the different polarization rates by adjusting the incident angle, the spin-orbit coupling strength and incident energy in the case of partial reflection.

Acta Physica Sinica•Jan 1, 2016•1 citation
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.
After a brief introduction to the field of atom optics and to atomic mirrors, we present experimental results obtained in our group during the last two years while studying the reflection of rubidium atoms by an evanescent wave. These involve the first measurement of the van der Waals force between an atom in its ground state and a dielectric wall, as well as the demonstration of a reflection grating for atoms at normal incidence. We also consider the influence of quantum reflection and tunnelling phenomena. Further studies using the atomic mirror as a probe of the van der Waals interaction, and of very small surface roughness are briefly discussed.
Cook and Hill suggested that the gradient of an optical field can be used to reflect atoms. To reflect atoms, the repulsive dipole force is used, which comes from the interaction between the electric dipole moment of atoms and the evanescent field. The evanescent wave is generated when light is totally reflected internally at the interface of different refractive indices. Later, the way to enhance the evanescent wave with a thin dielectric waveguide has been reported. We designed the atomic mirror for silicon atoms, whose structure enhances the evanescent field that is used to repel silicon atoms. We also set up the equations of motion for silicon atoms and derive trajectories of the atoms reflected by the atomic mirror. Optical intensity, incident angle of the light, and effective detuning are described in terms of controlling the trajectory of the atom.
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.
We report a direct observation of radiation pressure, exerted on cold rubidium atoms while bouncing on an evanescent-wave atom mirror. We analyze the radiation pressure by imaging the motion of the atoms after the bounce. The number of absorbed photons is measured for laser detunings ranging from 190 MHz to 1.4 GHz and for angles from 0.9 mrad to 24 mrad above the critical angle of total internal reflection. Depending on these settings, we find velocity changes parallel with the mirror surface, ranging from 1 to 18 cm/s. This corresponds to 2 to 31 photon recoils per atom. These results are independent of the evanescent-wave optical power.
Artificial spin-orbit coupling in neutral cold atom have been experimentally implemented in alkali-metal atoms. Nowadays people begin to explore its possible applications. One of the most interesting applications is the atomic mirror, which is a key element in atom optics. And spin-orbit coupling provides the atomic beam with the possibility that the atomic spin can flip during its propagation, thus can be used to prepare the quantum-state-selective atomic mirror. In 2008, Juzeliūnas, et al. [Juzeliūnas G, et al. 2008 Phys. Rev. Lett. 100 200405] studied a spin-orbit-coupled matter wave packet of cold atom gas impinging on an infinite step potential created by the optical light field. Results showed that there is not only ordinary specular reflection, but also non-specular one. The reflected atoms split into two beams and double reflection takes place. Based on the previous study, here we consider a matter wave packet of spin-orbit-coupled cold atom gas impinging on a finite step potential created by the optical light field. Due to the effect of the spin-orbit coupling, in addition to the propagating state, the eigenstates of cold atoms include evanescent state and oscillating evanescent state. Under suitable conditions double reflection will take place. If there are just evanescent waves in the step potential, total internal reflection will take place. In other words, when there is propagating wave in the step potential, partial reflection will take place. By taking into account both the total internal reflection and partial reflection, we study not only the polarization rate but also the reflectivity each as a function of incident energy, incident angle and spin-orbit coupling strength. The properties different from those of previous studies are found. In the case of total internal reflection, we find that the polarization rate of the reflected atoms is sensitive to incident angle instead of the spin-orbit coupling strength and incident energy. While in the case of partial reflection, all these factors strongly affect the polarization rate and reflectivity. We carefully study these properties and find that, on one hand, high efficiency atomic mirror can be acquired in the case of total internal reflection, and on the other hand, we can acquire the different polarization rates by adjusting the incident angle, the spin-orbit coupling strength and incident energy in the case of partial reflection.