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

Japanese Journal of Applied Physics

Atomic-Beam Propagation in a Two-Dimensional Standing Wave of Light: A Numerical Analysis Based on a Particle-Optics

Kenji Okamoto, Yasushi Inouye, Satoshi Kawata

Published Feb 1, 2001• 4 citations
Publisher

Abstract

We study the propagation of an atomic beam flow in an optical potential generated by a two-dimensional (2D) standing wave produced by two interfering laser beams with a frequency that is close to the resonant frequency of the propagated atoms. We extended the equations of motion of an atom in a light field to three-dimensional (3D) coordinate system and calculated the 3D trajectories of chromium atoms that are thermally evaporated and deflected by the gradient force of the standing wave laser field. The polarization and polarity of detuning of the frequency of the interfering beams are varied to study the formation of chromium atoms on a substrate. Our results show that a combination of parallel polarization and positive detuning forms a 2D grid structure. The rest of the combination of polarization and polarity of detuning yields a 2D array of point structures. An optimum size of the point structure with a diameter of approximately 50 nm can be formed with an orthogonal polarization and positive detuning of the laser frequency.

DOI
10.1143/jjap.40.609

Related papers

Laser-diode-tuned chromium atom trapping and fabrication with atom optics technology

Kenji Okamoto, Hironobu Inouye, Yasushi Inouye +1 more

We developed a laser-beam-controlled atom-manipulation system to deposit nanometric structure of atoms on a substrate. Atom beam of chromium is thermally evaporated and collimated with Doppler cooling technique using frequency-tuned laser diode. The gradient force is exerted on atoms by a standing wave over the substrate, and atoms are trapped in a low potential region of the standing wave. Consequently, a series of lines are formed on the substrate with the same periodicity to the standing wave. We present the analysis of trajectories of atoms in the light force potential to find conditions of the laser power, the sign and the degree of the detuning of the laser frequency from the resonance frequency of the atom, to reduce the width of the structure.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 7, 1999•0 citations

Two-dimensional light force lithography with polarization gradient fields

B. Brezger, Piet O. Schmidt, Th. Schulze +3 more

Summary form only given.Using neutral atoms for lithography is a new method of generating nanostructures on a substrate. This method is based on light masks formed by interfering laser beams perpendicular to the atomic beam. One- and two-dimensional periodic structures have been fabricated by various groups using light masks with intensity gradients and uniform polarization. The resulting periods are half the laser wavelength or greater. Atoms with a magnetic substructure in the electronic ground state are strongly sensitive to light polarization and static magnetic fields. Our work presents a detailed investigation of possible two-dimensional light field configurations including polarization gradients and static magnetic fields. The resulting nanostructures obtained in an experimentally realistic situation are simulated.

Conference on Lasers and Electro-Optics•Nov 27, 2002•0 citations

Splitting of atomic beams by light for creation of high-resolution spatial structures in optical nanolithography

V. O. Vitkovsky, Sergei V Prants

Diffraction of atomic wave packets from a standing laser wave with a Gaussian profile is studied theoretically and numerically in pursuing the aim of creating high-resolution spatial structures in optical nanolithography. To this end, we propose to use nonadiabatic transitions between two optical potentials which take place when square of the value of detuning off the resonance is approximately equal to the Doppler shift. In this case, atomic wave packets experience splitting at nodes of the standing wave, which allows creating atomic structures on a substrate with a period substantially smaller than the standard nanofabrication limit equal to half the wavelength of light. We propose a scheme of the experiment for the observation of nonadiabatic transitions and splitting of the wave of matter caused by them. A number of computer simulations with parameters corresponding to real atoms have been performed, which exhibit this effect in both momentum and coordinate spaces.

Optics and Spectroscopy•Jan 1, 2013•6 citations

Chaotic Walking of Cold Atoms in a 2D Optical Lattice

Sergey V. Prants

Abstract Coherent dynamics of cold atoms in a 2D optical lattice with interfering laser beams is studied with account for internal and external degrees of freedom of an atom. A system of differential equations for coupled degrees of freedom obtained in the semiclassical approximation has regular and chaotic solutions depending on the atomic-field detuning from resonance. The Hamilton chaos is manifested in the form of chaotic Rabi oscillations and random walks of cold atoms in the lattice for relatively small resonance detunings. It is shown that the deterministic chaos appears as a result of jumps in the value of the electric dipole moment of an atom approaching the nodes of a 2D standing wave. This in turn causes a pseudorandom behavior of momenta of atoms and, as a consequence, their random walks in the absolutely rigid 2D optical lattice without any external modulation of its parameters. It is shown in numerical experiments with 106 atoms that their distributions over the lattice for different resonance detunings differ significantly. This fact can be used for detecting the effect of random walks of cold atoms in a real experiment by the absorption image method.

Journal of Experimental and Theoretical Physics•Sep 1, 2020•4 citations

Atomic motion in a high-intensity standing wave laser field

L.F. Saez Ramdohr

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

•Jan 1, 1987•0 citations

Atom-optical properties of a standing-wave light field

Jabez J. McClelland

The focusing of atoms to nanometer-scale dimensions by a near-resonant standing-wave light field is examined from a particle optics perspective. The classical equation of motion for atoms traveling through the lens formed by a node of the standing wave is derived and converted to a spatial trajectory equation. A paraxial solution is obtained, which results in simple expressions for the focal properties of the lens, useful for estimating its behavior. Aberrations are also discussed, and an exact numerical solution of the trajectory equation is presented. The effects on focal linewidth of angular collimation and velocity spread in the atomic beam are investigated, and it is shown that angular collimation has a much more significant effect than velocity spread, even when the velocity spread is thermal.

Journal of the Optical Society of America B•Oct 1, 1995•89 citations
We study the propagation of an atomic beam flow in an optical potential generated by a two-dimensional (2D) standing wave produced by two interfering laser beams with a frequency that is close to the resonant frequency of the propagated atoms. We extended the equations of motion of an atom in a light field to three-dimensional (3D) coordinate system and calculated the 3D trajectories of chromium atoms that are thermally evaporated and deflected by the gradient force of the standing wave laser field. The polarization and polarity of detuning of the frequency of the interfering beams are varied to study the formation of chromium atoms on a substrate. Our results show that a combination of parallel polarization and positive detuning forms a 2D grid structure. The rest of the combination of polarization and polarity of detuning yields a 2D array of point structures. An optimum size of the point structure with a diameter of approximately 50 nm can be formed with an orthogonal polarization and positive detuning of the laser frequency.
We developed a laser-beam-controlled atom-manipulation system to deposit nanometric structure of atoms on a substrate. Atom beam of chromium is thermally evaporated and collimated with Doppler cooling technique using frequency-tuned laser diode. The gradient force is exerted on atoms by a standing wave over the substrate, and atoms are trapped in a low potential region of the standing wave. Consequently, a series of lines are formed on the substrate with the same periodicity to the standing wave. We present the analysis of trajectories of atoms in the light force potential to find conditions of the laser power, the sign and the degree of the detuning of the laser frequency from the resonance frequency of the atom, to reduce the width of the structure.
Summary form only given.Using neutral atoms for lithography is a new method of generating nanostructures on a substrate. This method is based on light masks formed by interfering laser beams perpendicular to the atomic beam. One- and two-dimensional periodic structures have been fabricated by various groups using light masks with intensity gradients and uniform polarization. The resulting periods are half the laser wavelength or greater. Atoms with a magnetic substructure in the electronic ground state are strongly sensitive to light polarization and static magnetic fields. Our work presents a detailed investigation of possible two-dimensional light field configurations including polarization gradients and static magnetic fields. The resulting nanostructures obtained in an experimentally realistic situation are simulated.
Diffraction of atomic wave packets from a standing laser wave with a Gaussian profile is studied theoretically and numerically in pursuing the aim of creating high-resolution spatial structures in optical nanolithography. To this end, we propose to use nonadiabatic transitions between two optical potentials which take place when square of the value of detuning off the resonance is approximately equal to the Doppler shift. In this case, atomic wave packets experience splitting at nodes of the standing wave, which allows creating atomic structures on a substrate with a period substantially smaller than the standard nanofabrication limit equal to half the wavelength of light. We propose a scheme of the experiment for the observation of nonadiabatic transitions and splitting of the wave of matter caused by them. A number of computer simulations with parameters corresponding to real atoms have been performed, which exhibit this effect in both momentum and coordinate spaces.
Abstract Coherent dynamics of cold atoms in a 2D optical lattice with interfering laser beams is studied with account for internal and external degrees of freedom of an atom. A system of differential equations for coupled degrees of freedom obtained in the semiclassical approximation has regular and chaotic solutions depending on the atomic-field detuning from resonance. The Hamilton chaos is manifested in the form of chaotic Rabi oscillations and random walks of cold atoms in the lattice for relatively small resonance detunings. It is shown that the deterministic chaos appears as a result of jumps in the value of the electric dipole moment of an atom approaching the nodes of a 2D standing wave. This in turn causes a pseudorandom behavior of momenta of atoms and, as a consequence, their random walks in the absolutely rigid 2D optical lattice without any external modulation of its parameters. It is shown in numerical experiments with 106 atoms that their distributions over the lattice for different resonance detunings differ significantly. This fact can be used for detecting the effect of random walks of cold atoms in a real experiment by the absorption image method.
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 focusing of atoms to nanometer-scale dimensions by a near-resonant standing-wave light field is examined from a particle optics perspective. The classical equation of motion for atoms traveling through the lens formed by a node of the standing wave is derived and converted to a spatial trajectory equation. A paraxial solution is obtained, which results in simple expressions for the focal properties of the lens, useful for estimating its behavior. Aberrations are also discussed, and an exact numerical solution of the trajectory equation is presented. The effects on focal linewidth of angular collimation and velocity spread in the atomic beam are investigated, and it is shown that angular collimation has a much more significant effect than velocity spread, even when the velocity spread is thermal.