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

Quantum and Semiclassical Optics Journal of the European Optical Society Part B

Diffraction of atoms from a standing-wave Schrödinger field

Sabine Bödefeld, Martin Wilkens

Published Jun 1, 1996• 6 citations
Publisher

Abstract

The diffraction of cold atoms from the standing-wave Schrödinger field of a single atom in a microtrap is investigated. The diffraction patterns for both elastic and inelastic diffraction are derived, where inelastic diffraction is accompanied by transitions of the trapped atom between different trap states. The diffraction pattern corresponding to the elastic channel reveals the Fourier transform of the spatial distribution of the probability density associated with the Schrödinger wavefunction of the trapped atom. Diffraction patterns associated with inelastic channels reveal the convolution of the participating trap states in the momentum representation.

DOI
10.1088/1355-5111/8/3/014

Related papers

Diffraction of atoms by a standing wave at Gaussian initial momentum distribution of amplitudes

Artur Mikhailovich Ishkhanyan

The role of the initial-state preparation in the coherent diffraction of atoms in the field of a standing wave is considered. It is shown that the time evolution of the atomic wave packet with a Gaussian initial momentum distribution of amplitudes, due to the constructive quantum-mechanical interference, occurs practically without transformation of the initial Gaussian form. Depending on the phases of the initial momentum distribution components, the increment of the atomic momentum can vary from a maximum possible value (determined by the limiting speed of stimulated photon re-emission) to zero. Consequently, the standing wave presents an effective mirror for Gaussian atoms, the reflection angle being controllable.

Physical Review A•May 17, 2000•11 citations

Diffraction of atoms by a standing wave at Gaussian initial momentum distribution of amplitudes

Artur Mikhailovich Ishkhanyan

The role of the initial state preparation of the coherent diffraction of atoms in the field of a standing wave is considered. It is shown that the time evolution of the atomic wave packet with a Gaussian initial momentum distribution of amplitudes, due to the constructive quantum- mechanical interference, occurs practically without transformation of the initial Gaussian form. Depending on the phases of the initial momentum distribution components, the increment of the atomic momentum can vary from the maximum possible amount (determined by the limiting speed of stimulated photon re-emission acts) to zero. Consequently, for Gaussian atoms the standing wave presents an effective mirror with controllable reflection angle.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Dec 28, 1999•0 citations

Atom microtraps based on near-field Fresnel diffraction

Thejesh Bandi, Vladimir G. Minogin, Síle Nic Chormaic

We propose and present a quantitative analysis of neutral atom microtraps based on optical near fields produced by the diffraction of a laser wave on small apertures in a thin screen. We show that near-field atom microtraps are capable of storing atoms in micron-sized regions, with estimated trap lifetimes of about $1\phantom{\rule{0.3em}{0ex}}\mathrm{s}$, when using a moderate laser intensity of about $10\phantom{\rule{0.3em}{0ex}}\mathrm{W}∕{\mathrm{cm}}^{2}$. The depth of the proposed Fresnel atom microtraps is about $0.1\phantom{\rule{0.3em}{0ex}}\mathrm{mK}$. An array of such atom microtraps could have applications to site-selective manipulation of cold atoms.

Physical Review A•Jul 17, 2008•20 citations

Interference of atoms in separated optical fields

Veniamin P. Chebotayev, A. P. Kasantsev, Valery P. Yakovlev +1 more

We consider the interference of atoms caused by the wave nature of their motion. Coherently interfering beams of particles may be obtained by using the diffraction of atoms from separated standing waves resonant with the transition between the ground and excited states of the atoms. Interference arises with and without spatial separation of the diffracted atomic beams. A problem concerning two-quantum perturbation of the wave function of an atom in the ground state by a standing-wave field has been solved. Both amplitude and phase perturbation are taken into account. We show that in spite of the absence of coherence in the incident beam and a rapid decay of the coherence induced by the standing wave for scattered spatially overlapping beams, the interference can be observed for the conditions of an echo. We first consider the phenomenon of an echo under the quantum-mechanical action of light on the translational degrees of freedom. We show that owing to this phenomenon phase memory can be transferred through the ground state over unlimitedly large distances. Owing to the interference of the density harmonics, a periodic structure in the spatial distribution of the atomic density with a period of less than one wavelength of the light is localized at distances of the order of the distance between the fields. The harmonic amplitude is calculated for instantaneous excitation in the case in which the duration of the excitation is comparable with the backward Doppler linewidth in the beam and for scattering under Bragg conditions. In the latter case we show that the effective temperature of the atoms participating in the interference is less than one recoil energy.

Journal of the Optical Society of America B•Nov 1, 1985•100 citations

Diffraction of atoms moving through a standing light wave

Peter J. Martin, P. L. Gould, Bruce G. Oldaker +2 more

The diffraction of sodium atoms from a standing wave of near-resonant light is studied as a function of the atomic velocity component along the k vector of the wave. A simple theory is presented which quantitatively predicts the observed diffraction patterns and the decrease of the rms momentum transfer to the atoms with increasing velocity. This decrease results from the dephasing between the two counterpropagating traveling waves due to the first-order Doppler shift. In addition, these measurements have resolved the previous discrepancy between theory and experiment concerning the overall momentum transferred by a standing wave.

Physical Review A•Sep 1, 1987•106 citations

Diffraction of Atoms Using Standing Wave Light

Tim Byrnes, Ebubechukwu O. Ilo-Okeke

This chapter discusses the basic physics of atom diffraction. Starting with a short review on the diffraction of light, we describe the absorption of photons by an atom and its subsequent emission, where the atom to changes its momentum and internal state. Assuming a two-level atom, we describe the coherent interactions of atoms with light, showing its effect on the ground state of the atoms. We further illustrate how the light impacts forces on the atom that can be used for trapping it in the light field. Next, we discuss Bragg diffraction of atoms, where the internal state of an atom is unchanged after diffraction. Here the external motional state of the atom is put in a linear superposition of its movement. Finally, we describe the diffraction of atoms by Raman pulses, where the internal state of the atom is changed after diffraction, while achieving directed motion.

Cambridge University Press eBooks•Jul 23, 2021•0 citations
The diffraction of cold atoms from the standing-wave Schrödinger field of a single atom in a microtrap is investigated. The diffraction patterns for both elastic and inelastic diffraction are derived, where inelastic diffraction is accompanied by transitions of the trapped atom between different trap states. The diffraction pattern corresponding to the elastic channel reveals the Fourier transform of the spatial distribution of the probability density associated with the Schrödinger wavefunction of the trapped atom. Diffraction patterns associated with inelastic channels reveal the convolution of the participating trap states in the momentum representation.
The role of the initial-state preparation in the coherent diffraction of atoms in the field of a standing wave is considered. It is shown that the time evolution of the atomic wave packet with a Gaussian initial momentum distribution of amplitudes, due to the constructive quantum-mechanical interference, occurs practically without transformation of the initial Gaussian form. Depending on the phases of the initial momentum distribution components, the increment of the atomic momentum can vary from a maximum possible value (determined by the limiting speed of stimulated photon re-emission) to zero. Consequently, the standing wave presents an effective mirror for Gaussian atoms, the reflection angle being controllable.
The role of the initial state preparation of the coherent diffraction of atoms in the field of a standing wave is considered. It is shown that the time evolution of the atomic wave packet with a Gaussian initial momentum distribution of amplitudes, due to the constructive quantum- mechanical interference, occurs practically without transformation of the initial Gaussian form. Depending on the phases of the initial momentum distribution components, the increment of the atomic momentum can vary from the maximum possible amount (determined by the limiting speed of stimulated photon re-emission acts) to zero. Consequently, for Gaussian atoms the standing wave presents an effective mirror with controllable reflection angle.
We propose and present a quantitative analysis of neutral atom microtraps based on optical near fields produced by the diffraction of a laser wave on small apertures in a thin screen. We show that near-field atom microtraps are capable of storing atoms in micron-sized regions, with estimated trap lifetimes of about 1s1\phantom{\rule{0.3em}{0ex}}\mathrm{s}1s, when using a moderate laser intensity of about 10W∕cm210\phantom{\rule{0.3em}{0ex}}\mathrm{W}∕{\mathrm{cm}}^{2}10W∕cm2. The depth of the proposed Fresnel atom microtraps is about 0.1mK0.1\phantom{\rule{0.3em}{0ex}}\mathrm{mK}0.1mK. An array of such atom microtraps could have applications to site-selective manipulation of cold atoms.
We consider the interference of atoms caused by the wave nature of their motion. Coherently interfering beams of particles may be obtained by using the diffraction of atoms from separated standing waves resonant with the transition between the ground and excited states of the atoms. Interference arises with and without spatial separation of the diffracted atomic beams. A problem concerning two-quantum perturbation of the wave function of an atom in the ground state by a standing-wave field has been solved. Both amplitude and phase perturbation are taken into account. We show that in spite of the absence of coherence in the incident beam and a rapid decay of the coherence induced by the standing wave for scattered spatially overlapping beams, the interference can be observed for the conditions of an echo. We first consider the phenomenon of an echo under the quantum-mechanical action of light on the translational degrees of freedom. We show that owing to this phenomenon phase memory can be transferred through the ground state over unlimitedly large distances. Owing to the interference of the density harmonics, a periodic structure in the spatial distribution of the atomic density with a period of less than one wavelength of the light is localized at distances of the order of the distance between the fields. The harmonic amplitude is calculated for instantaneous excitation in the case in which the duration of the excitation is comparable with the backward Doppler linewidth in the beam and for scattering under Bragg conditions. In the latter case we show that the effective temperature of the atoms participating in the interference is less than one recoil energy.
The diffraction of sodium atoms from a standing wave of near-resonant light is studied as a function of the atomic velocity component along the k vector of the wave. A simple theory is presented which quantitatively predicts the observed diffraction patterns and the decrease of the rms momentum transfer to the atoms with increasing velocity. This decrease results from the dephasing between the two counterpropagating traveling waves due to the first-order Doppler shift. In addition, these measurements have resolved the previous discrepancy between theory and experiment concerning the overall momentum transferred by a standing wave.
This chapter discusses the basic physics of atom diffraction. Starting with a short review on the diffraction of light, we describe the absorption of photons by an atom and its subsequent emission, where the atom to changes its momentum and internal state. Assuming a two-level atom, we describe the coherent interactions of atoms with light, showing its effect on the ground state of the atoms. We further illustrate how the light impacts forces on the atom that can be used for trapping it in the light field. Next, we discuss Bragg diffraction of atoms, where the internal state of an atom is unchanged after diffraction. Here the external motional state of the atom is put in a linear superposition of its movement. Finally, we describe the diffraction of atoms by Raman pulses, where the internal state of the atom is changed after diffraction, while achieving directed motion.