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

Physical Review A

Dynamical effects in atom optics

P. A. Ruprecht, Murray Holland, Keith R. Burnett

Published Jun 1, 1994• 7 citations
Publisher

Abstract

We present numerical calculations of the evolution of an atomic wave packet in the optical potential created by a laser standing wave. These calculations do not rely on the Raman-Nath approximation, and fully account for transverse atomic motion within the standing wave. Our results show that atomic dynamics is important even for very brief interactions, and that the wave packet can become well localized during and shortly after the interaction. We propose several atomic beam splitters and deflectors which make use of this effect. This effect may also have repercussions for recent proposals to measure the position of an atom in a standing wave by monitoring the phase shift of the optical field; these schemes require that the field does not act back on the atom to alter its position wave function. A standing wave can also localize the wave packet in momentum space, which we show can be used to cool an atomic beam in one transverse dimension.

DOI
10.1103/physreva.49.4726

Related papers

Atom optics with standing wave fields.

Jayson Leonard Cohen

This dissertation explores the spatial patterns that evolve dynamically in atomic clouds and beams after they interact with one or more standing wave fields, typically formed by laser beams. The main systems under study are ensembles of free atoms, but a model Bose-Einstein condensate and the harmonic oscillator are considered as well. Focused atomic patterns with features much smaller than the wave length of the light fields are possible owing to the nonlinear atom-field interaction and are emphasized. The quantitative results combine numerical simulations and analytical expressions. Computer algorithms were developed from known methods in partial differential equations to perform the numerical simulations. The analytical results relied on standard and newly contrived techniques in quantum physics. The analytical expressions were evaluated by computer in order to extract valuable quantitative information and to compare different analytical methods with one another and with the numerical simulations. The thesis is written as a self-contained piece, and as such, develops specific examples of atom-field configurations and atomic patterns of interest from a general theory of the atoms interacting with a spatially varying light field that influences the subsequent center-of-mass motion. Beyond those already published by our group and expanded upon in the thesis, significant advances are made in: the link between transient interactions in the time- and spatial-domains; an understanding of the Raman-Nath approximation, its range of validity, and its corrections; atomic focusing by pulsed adiabatic interactions between an atom and a single standing wave light field; the differences between classical and quantum free motion after periodic interactions; the distinctions between free motion after amplitude and phase gratings; harmonic oscillator ground states kicked by spatially varying pulses; and quasiperiodic echo effects. The general theoretical structure that was detailed can be applied effectively, as intended from the outset, to other problems in atom optics.

•Aug 1, 2000•0 citations

Atomic beam deflection in a quantum field

Pierre Meystre, E. Schumacher, Stig Stenholm +1 more

We investigate to which extent the quantum nature of light modifies laser-induced atomic beam deflection in a plane standing wave. Our model considers a single two-level atom interacting with a single quantized standing wave mode of the electromagnetic field. We neglect spontaneous emission into other field modes, an approximation valid for short enough times. We find that there is an essential qualitative difference between the cases of a coherent field and a thermal field. For a coherent field, the atomic momentum distribution after interaction has two symmetric peaks on the wings and resembles the semiclassical result of Arimondo et al. [Phys. Rev. A 24, 898 (1981)]. For a thermal field, this distribution has its maximum at p = 0. It is characterized by a constant contribution at p = 0, some sharp interference features, and near-Gaussian wings. The only feature common to both cases is that in the Raman-Nath regime of scattering, the range on transverse momenta grows linearly with time at a rate proportional to 〈 n 〉 , where 〈 n 〉 is the mean number of photons in the field.

Annual Meeting Optical Society of America•Jan 1, 1989•3 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

Topics in atom optics

Byron B. Taylor

This dissertation covers the field of atom optics and is divided into four main chapters: In Chapter 2 we investigate the effects of light forces on the center-of-mass motion of two-level atoms. This will lead to the discussion of two regimes: the "ray optic" and the "wave optic" regime. In the first case, an atom is well localized in the field which allows a comparison to be made with classical ray optics. In the second case, the atom is strongly delocalized which leads to a wave treatment and allows a comparison with diffractive optics. We finish this chapter with an example in each regime: Doppler cooling for ray optics and an atomic Fabry-Perot for wave optics. In Chapter 3 we extend the results of the previous chapter to the diffraction of atoms by a standing light field. We cover three regimes in the near resonant Kapitza-Dirac effect: the Raman-Nath, the Bragg and the optical Stern-Gerlach regime. In the Raman-Nath and Bragg regimes, the wave-packet is strongly delocalized compared to the period of the standing wave. In contrast, the Stern-Gerlach regime has a small spatial extent. The Raman-Nath and Bragg regimes are differentiated in their treatment of the kinetic energy. Initially we only discuss coherent interactions. In the later half of this chapter we introduce spontaneous emission and show how its presence affects the diffraction pattern in each of these regimes. In Chapter 4 we cover various atomic cooling schemes: strong field Sisyphus cooling, adiabatic cooling, evaporative cooling, polarization gradient cooling and velocity selective coherent population trapping. We begin with a brief discussion of atomic temperature. We then cover two cooling schemes for two-level atoms. We eventually move to multi-level atoms and end this chapter with a two-atom multi-level system. In Chapter 5 we conclude with a brief discussion of practical uses and devices that may arise from atom optics such as lenses, mirrors, gravitational interferometry, lithography and atomic clocks.

•Jan 1, 1997•0 citations

Dynamics of an atomic wave packet in a standing-wave cavity field: A cavity-assisted single-atom detection

Young-Tak Chough, Sun-Hyun Youn, Hyunchul Nha +2 more

We investigate the single-atom detection system using an optical standing-wave cavity, from the viewpoint of the quantized center-of-mass motion of the atomic wave packet. We show that since the atom-field coupling strength depends upon the overlap integral of the atomic wave packet and the field mode function, the effect of the wave-packet spreading via the momentum exchange process brings about a significant effect in the detection efficiency. We find that, as a result, the detection efficiency is not sensitive to the individual atomic trajectory for reasonably slow atoms. We also address an interesting phenomenon of the atomic wave-packet splitting occurring when an atom passes through a node of the cavity field.

Physical Review A•Jan 11, 2002•5 citations

Atomic de Broglie waves in multiple optical standing waves

Chang Jae Lee

In this work the dynamical behavior of the center of mass of a two-level atom in sequences of multiple optical standing waves is explored. In a standing wave the atomic momentum distribution fans out. But with a suitably designed sequence of standing waves it is possible to refocus the momentum-space wave packet and bring the momentum distribution to the initial value, which may be regarded as an atom optical analog to spin or photon echo. If the total interaction time is fixed, the refocusing performance gets better as the number of standing waves in a sequence increases. Also the atomic wave packet in position space evolves as if in free space. \textcopyright{} 1996 The American Physical Society.

Physical Review A•Jun 1, 1996•2 citations
We present numerical calculations of the evolution of an atomic wave packet in the optical potential created by a laser standing wave. These calculations do not rely on the Raman-Nath approximation, and fully account for transverse atomic motion within the standing wave. Our results show that atomic dynamics is important even for very brief interactions, and that the wave packet can become well localized during and shortly after the interaction. We propose several atomic beam splitters and deflectors which make use of this effect. This effect may also have repercussions for recent proposals to measure the position of an atom in a standing wave by monitoring the phase shift of the optical field; these schemes require that the field does not act back on the atom to alter its position wave function. A standing wave can also localize the wave packet in momentum space, which we show can be used to cool an atomic beam in one transverse dimension.
This dissertation explores the spatial patterns that evolve dynamically in atomic clouds and beams after they interact with one or more standing wave fields, typically formed by laser beams. The main systems under study are ensembles of free atoms, but a model Bose-Einstein condensate and the harmonic oscillator are considered as well. Focused atomic patterns with features much smaller than the wave length of the light fields are possible owing to the nonlinear atom-field interaction and are emphasized. The quantitative results combine numerical simulations and analytical expressions. Computer algorithms were developed from known methods in partial differential equations to perform the numerical simulations. The analytical results relied on standard and newly contrived techniques in quantum physics. The analytical expressions were evaluated by computer in order to extract valuable quantitative information and to compare different analytical methods with one another and with the numerical simulations. The thesis is written as a self-contained piece, and as such, develops specific examples of atom-field configurations and atomic patterns of interest from a general theory of the atoms interacting with a spatially varying light field that influences the subsequent center-of-mass motion. Beyond those already published by our group and expanded upon in the thesis, significant advances are made in: the link between transient interactions in the time- and spatial-domains; an understanding of the Raman-Nath approximation, its range of validity, and its corrections; atomic focusing by pulsed adiabatic interactions between an atom and a single standing wave light field; the differences between classical and quantum free motion after periodic interactions; the distinctions between free motion after amplitude and phase gratings; harmonic oscillator ground states kicked by spatially varying pulses; and quasiperiodic echo effects. The general theoretical structure that was detailed can be applied effectively, as intended from the outset, to other problems in atom optics.
We investigate to which extent the quantum nature of light modifies laser-induced atomic beam deflection in a plane standing wave. Our model considers a single two-level atom interacting with a single quantized standing wave mode of the electromagnetic field. We neglect spontaneous emission into other field modes, an approximation valid for short enough times. We find that there is an essential qualitative difference between the cases of a coherent field and a thermal field. For a coherent field, the atomic momentum distribution after interaction has two symmetric peaks on the wings and resembles the semiclassical result of Arimondo et al. [Phys. Rev. A 24, 898 (1981)]. For a thermal field, this distribution has its maximum at p = 0. It is characterized by a constant contribution at p = 0, some sharp interference features, and near-Gaussian wings. The only feature common to both cases is that in the Raman-Nath regime of scattering, the range on transverse momenta grows linearly with time at a rate proportional to 〈 n 〉 , where 〈 n 〉 is the mean number of photons in the field.
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
This dissertation covers the field of atom optics and is divided into four main chapters: In Chapter 2 we investigate the effects of light forces on the center-of-mass motion of two-level atoms. This will lead to the discussion of two regimes: the "ray optic" and the "wave optic" regime. In the first case, an atom is well localized in the field which allows a comparison to be made with classical ray optics. In the second case, the atom is strongly delocalized which leads to a wave treatment and allows a comparison with diffractive optics. We finish this chapter with an example in each regime: Doppler cooling for ray optics and an atomic Fabry-Perot for wave optics. In Chapter 3 we extend the results of the previous chapter to the diffraction of atoms by a standing light field. We cover three regimes in the near resonant Kapitza-Dirac effect: the Raman-Nath, the Bragg and the optical Stern-Gerlach regime. In the Raman-Nath and Bragg regimes, the wave-packet is strongly delocalized compared to the period of the standing wave. In contrast, the Stern-Gerlach regime has a small spatial extent. The Raman-Nath and Bragg regimes are differentiated in their treatment of the kinetic energy. Initially we only discuss coherent interactions. In the later half of this chapter we introduce spontaneous emission and show how its presence affects the diffraction pattern in each of these regimes. In Chapter 4 we cover various atomic cooling schemes: strong field Sisyphus cooling, adiabatic cooling, evaporative cooling, polarization gradient cooling and velocity selective coherent population trapping. We begin with a brief discussion of atomic temperature. We then cover two cooling schemes for two-level atoms. We eventually move to multi-level atoms and end this chapter with a two-atom multi-level system. In Chapter 5 we conclude with a brief discussion of practical uses and devices that may arise from atom optics such as lenses, mirrors, gravitational interferometry, lithography and atomic clocks.
We investigate the single-atom detection system using an optical standing-wave cavity, from the viewpoint of the quantized center-of-mass motion of the atomic wave packet. We show that since the atom-field coupling strength depends upon the overlap integral of the atomic wave packet and the field mode function, the effect of the wave-packet spreading via the momentum exchange process brings about a significant effect in the detection efficiency. We find that, as a result, the detection efficiency is not sensitive to the individual atomic trajectory for reasonably slow atoms. We also address an interesting phenomenon of the atomic wave-packet splitting occurring when an atom passes through a node of the cavity field.
In this work the dynamical behavior of the center of mass of a two-level atom in sequences of multiple optical standing waves is explored. In a standing wave the atomic momentum distribution fans out. But with a suitably designed sequence of standing waves it is possible to refocus the momentum-space wave packet and bring the momentum distribution to the initial value, which may be regarded as an atom optical analog to spin or photon echo. If the total interaction time is fixed, the refocusing performance gets better as the number of standing waves in a sequence increases. Also the atomic wave packet in position space evolves as if in free space. \textcopyright{} 1996 The American Physical Society.