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

Journal of Physics B Atomic and Molecular Physics

Interference of the states of translational motion of an atom in a light field

A. P. Kazantsev, Gregory I. Surdutovich, D. O. Chudesnikov, Valery P. Yakovlev

Published Jul 14, 1985• 2 citations
Publisher

Abstract

The quasiclassical theory of the Landau-Zener resonance arising because of the atomic motion in the field of a strong standing light wave is developed. A resonance atom in a spatially inhomogeneous field as two effective potentials and two trajectories of motion. The Landau-Zener (LZ) transitions from one trajectory to the other take place in the regions of quasi-intersection of the terms (standing-wave nodes). This effect leads to the appearance of strong quantum fluctuations which break the potential character of the atomic motion and result in the interference of the translational motion states. Therefore a number of the features of the atomic dispersion in the standing-wave field arise (anomalous widths of the forbidden gaps and allowed bands in the under-barrier energetic region and oscillations of the density of states in the over-barrier energetic region). The manifestation of LZ resonance in non-linear spectroscopy and for bipotential scattering of atoms by light is considered.

DOI
10.1088/0022-3700/18/13/014

Related papers

Kinetic phenomena of atomic motion in a light field

A. P. Kazantsev, Vladimir S. Smirnov, Gregory I. Surdutovich +2 more

Kinetic phenomena of resonant-particle motion in a standing-light-wave field are theoretically discussed. The light-pressure force and its fluctuations are found in a wide range of the parameters: the atomic velocity, the intensity, and the detuning of the field. There are two characteristic regions of the detunings in a strong field: the adiabatic region and the region of Landau–Zener resonances. The quantum fluctuations of the inner atomic state that are due to the Landau–Zener transitions result, specifically, in the interference effect in the mean light-pressure force. The effects of the spatial grating of the cooled atoms, the particle velocity bunching, and the recoil-effect dependence on the nonlinear absorption are considered for slow particles. The effect of optical pumping by linearly polarized light taking into account the recoil effect is fundamentally new. Because of this effect, the anisotropic resonance medium becomes gyrotropic.

Journal of the Optical Society of America B•Nov 1, 1985•43 citations

The effect of Landau-Zener tunnelings on the nonlinear dynamics of cold atoms in a modulated laser field

Victor Yu. Argonov

We study the motion of a cold atom in a frequency-modulated standing laser wave. If the detuning between the atomic electronic transition and the field is large, the atom moves in a modulated optical potential demonstrating known classical nonlinear effects such as chaos and nonlinear resonances. If the atom-field detuning is small, then two optical potentials emerge in the system, and the atom performs Landau-Zener (LZ) tunnelings between them. It is a radically non-classical behavior. However, we show that classical nonlinear structures in system's phase space (KAM-tori and chaotic layers) survive. Quantum effect of LZ tunnelings only induces small random jumps of trajectories between these structures (dynamical tunneling).

arXiv:1401.2156•Jan 9, 2014•0 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

Quantum deviation of an atom at coherent scattering

Andrew I. Trubilko

Effects of quantum deviation of a two-level atom at coherent scattering on an inhomogeneous optical potential created by crossed electromagnetic fields are considered. The region of interaction is formed by a lowfrequency quantized standing wave from a micromaser and a coherent traveling optical wave generated by an optical fiber located inside a cavity. The atom interacts with both fields under the conditions of two-photon two-wave resonance. It is shown that two effects of quantum deviation of translational motion of the atom can be observed. Interaction with the standing wave is caused under these conditions by a harmonic potential the character of scattering of the atom on which depends significantly on the initial conditions of preparation of the atom and quantized mode. The other effect—deviation of the atom by the classical traveling wave—is also completely quantum mechanical under these conditions and is produced by the noncommutative contribution of the kinetic energy operator of the atom and the interaction energy.

Journal of Experimental and Theoretical Physics Letters•May 1, 2017•5 citations

Proliferation of atomic wave packets at the nodes of a standing light wave

Sergey V. Prants

A quantum analysis is presented of the motion and internal state of a two-level atom in a strong standing-wave light field. Coherent evolution of the atomic wave-packet, atomic dipole moment, and population inversion strongly depends on the ratio between the detuning from atom-field resonance and a characteristic atomic frequency. In the basis of dressed states, atomic motion is represented as wave-packet motion in two effective optical potentials. At exact resonance, coherent population trapping is observed when an atom with zero momentum is centered at a standing-wave node. When the detuning is comparable to the characteristic atomic frequency, the atom crossing a node may or may not undergo a transition between the potentials with probabilities that are similar in order of magnitude. In this detuning range, atomic wave packets proliferate at the nodes of the standing wave. This phenomenon is interpreted as a quantum manifestation of chaotic transport of classical atoms observed in earlier studies. For a certain detuning range, there exists an interval of initial momentum values such that the atom simultaneously oscillates in an optical potential well and moves as a ballistic particle. This behavior of a wave packet is a quantum analog of a classical random walk of an atom, when it enters and leaves optical potential wells in a seemingly irregular manner and freely moves both ways in a periodic standing light wave. In a far-detuned field, the transition probability between the potentials is low, and adiabatic wave-packet evolution corresponding to regular classical motion of an atom is observed.

Journal of Experimental and Theoretical Physics•Nov 1, 2009•21 citations

Random walking of a two-level atom in a standing-wave field

V. Yu. Sirotkin, Sergey V. Prants

We study the coupled translational and internal dynamics of a two-level atom in a spatially periodic optical potential created by a single-mode field in a high-finesse Fabry-Perot cavity. The strongly-coupled atom-cavity system with atomic center-of-mass motion included in modeled by semiclassical nonlinear Heisenberg equations of motion with two degrees of freedom. At exact resonance between the internal atomic transition and the cavity eigen frequency, the internal and translational degrees of freedom are separated from each other resulting in periodically modulated Rabi oscillations and regular translational motion. Near the atom-field resonance, the coupled dynamics is found to be irregular and even chaotic in the sense of external sensitivity to initial conditions. It is manifested as a chaotic motion of an atom in an absolutely regular spatially periodic potential in the absence of any random fluctuations. This effect may be explained as a result of the interaction of nonlinear resonances in the atom-field nonlinear pendulum whose low- frequency translational motion is modulated by the high- frequency Rabi oscillations. The irregular motion is studied in detail in numerical experiments using the arsenal of methods of the dynamical systems theory. The results obtained are compared with recent experiments with ultra cold single atoms interacting with single photons in the strong-coupling regime. We estimate the ranges of the system's control parameters, the detuning, the recoil frequency, and the mean number of intracavity photons, in which the interaction of nonlinear resonances may lead, under realistic conditions, to local instability of the center-of-mass motion and some manifestations of dynamical chaos, the effect which is of interest in studying the quantum-classical correspondence and quantum chaos in atomic optics.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 3, 2002•1 citation
The quasiclassical theory of the Landau-Zener resonance arising because of the atomic motion in the field of a strong standing light wave is developed. A resonance atom in a spatially inhomogeneous field as two effective potentials and two trajectories of motion. The Landau-Zener (LZ) transitions from one trajectory to the other take place in the regions of quasi-intersection of the terms (standing-wave nodes). This effect leads to the appearance of strong quantum fluctuations which break the potential character of the atomic motion and result in the interference of the translational motion states. Therefore a number of the features of the atomic dispersion in the standing-wave field arise (anomalous widths of the forbidden gaps and allowed bands in the under-barrier energetic region and oscillations of the density of states in the over-barrier energetic region). The manifestation of LZ resonance in non-linear spectroscopy and for bipotential scattering of atoms by light is considered.
Kinetic phenomena of resonant-particle motion in a standing-light-wave field are theoretically discussed. The light-pressure force and its fluctuations are found in a wide range of the parameters: the atomic velocity, the intensity, and the detuning of the field. There are two characteristic regions of the detunings in a strong field: the adiabatic region and the region of Landau–Zener resonances. The quantum fluctuations of the inner atomic state that are due to the Landau–Zener transitions result, specifically, in the interference effect in the mean light-pressure force. The effects of the spatial grating of the cooled atoms, the particle velocity bunching, and the recoil-effect dependence on the nonlinear absorption are considered for slow particles. The effect of optical pumping by linearly polarized light taking into account the recoil effect is fundamentally new. Because of this effect, the anisotropic resonance medium becomes gyrotropic.
We study the motion of a cold atom in a frequency-modulated standing laser wave. If the detuning between the atomic electronic transition and the field is large, the atom moves in a modulated optical potential demonstrating known classical nonlinear effects such as chaos and nonlinear resonances. If the atom-field detuning is small, then two optical potentials emerge in the system, and the atom performs Landau-Zener (LZ) tunnelings between them. It is a radically non-classical behavior. However, we show that classical nonlinear structures in system's phase space (KAM-tori and chaotic layers) survive. Quantum effect of LZ tunnelings only induces small random jumps of trajectories between these structures (dynamical tunneling).
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.
Effects of quantum deviation of a two-level atom at coherent scattering on an inhomogeneous optical potential created by crossed electromagnetic fields are considered. The region of interaction is formed by a lowfrequency quantized standing wave from a micromaser and a coherent traveling optical wave generated by an optical fiber located inside a cavity. The atom interacts with both fields under the conditions of two-photon two-wave resonance. It is shown that two effects of quantum deviation of translational motion of the atom can be observed. Interaction with the standing wave is caused under these conditions by a harmonic potential the character of scattering of the atom on which depends significantly on the initial conditions of preparation of the atom and quantized mode. The other effect—deviation of the atom by the classical traveling wave—is also completely quantum mechanical under these conditions and is produced by the noncommutative contribution of the kinetic energy operator of the atom and the interaction energy.
A quantum analysis is presented of the motion and internal state of a two-level atom in a strong standing-wave light field. Coherent evolution of the atomic wave-packet, atomic dipole moment, and population inversion strongly depends on the ratio between the detuning from atom-field resonance and a characteristic atomic frequency. In the basis of dressed states, atomic motion is represented as wave-packet motion in two effective optical potentials. At exact resonance, coherent population trapping is observed when an atom with zero momentum is centered at a standing-wave node. When the detuning is comparable to the characteristic atomic frequency, the atom crossing a node may or may not undergo a transition between the potentials with probabilities that are similar in order of magnitude. In this detuning range, atomic wave packets proliferate at the nodes of the standing wave. This phenomenon is interpreted as a quantum manifestation of chaotic transport of classical atoms observed in earlier studies. For a certain detuning range, there exists an interval of initial momentum values such that the atom simultaneously oscillates in an optical potential well and moves as a ballistic particle. This behavior of a wave packet is a quantum analog of a classical random walk of an atom, when it enters and leaves optical potential wells in a seemingly irregular manner and freely moves both ways in a periodic standing light wave. In a far-detuned field, the transition probability between the potentials is low, and adiabatic wave-packet evolution corresponding to regular classical motion of an atom is observed.
We study the coupled translational and internal dynamics of a two-level atom in a spatially periodic optical potential created by a single-mode field in a high-finesse Fabry-Perot cavity. The strongly-coupled atom-cavity system with atomic center-of-mass motion included in modeled by semiclassical nonlinear Heisenberg equations of motion with two degrees of freedom. At exact resonance between the internal atomic transition and the cavity eigen frequency, the internal and translational degrees of freedom are separated from each other resulting in periodically modulated Rabi oscillations and regular translational motion. Near the atom-field resonance, the coupled dynamics is found to be irregular and even chaotic in the sense of external sensitivity to initial conditions. It is manifested as a chaotic motion of an atom in an absolutely regular spatially periodic potential in the absence of any random fluctuations. This effect may be explained as a result of the interaction of nonlinear resonances in the atom-field nonlinear pendulum whose low- frequency translational motion is modulated by the high- frequency Rabi oscillations. The irregular motion is studied in detail in numerical experiments using the arsenal of methods of the dynamical systems theory. The results obtained are compared with recent experiments with ultra cold single atoms interacting with single photons in the strong-coupling regime. We estimate the ranges of the system's control parameters, the detuning, the recoil frequency, and the mean number of intracavity photons, in which the interaction of nonlinear resonances may lead, under realistic conditions, to local instability of the center-of-mass motion and some manifestations of dynamical chaos, the effect which is of interest in studying the quantum-classical correspondence and quantum chaos in atomic optics.