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

Non-Adiabatic Contributions to Bragg Regime Dynamics in the Atomic Kapitza-Dirac Effect

Dylan Manna

Published Sep 15, 2017• 0 citations
OpenAlex

Abstract

The primary mechanism of the atomic Kapitza-Dirac effect is a multi-photon process in which the electronic state is virtually excited while the direct product state is altered as the velocity of the atom undergoes spatial quantization. The Bragg resonance is a virtual multi-photon stimulated Raman scattering in which couterpropagating photons act as pump and probe imparting transverse velocity to the atom through recoil while the energy in the field is lowered such that the energy of the system is conserved. The bulk of the literature for the past three decades has presumed that the energy-nonconserving intermediate states which are described by non-adiabatic contributions could be neglected once the perturbative effects of next-order off-resonant states were included. This paper demonstrates the necessity of including higher-order non-adiabatic contributions of energy-nonconserving momentum states in calculating the final populations of Bragg resonances as a function of field strength. As the field strength is increased, the Pendell\{o}sung frequency varies while generally decreasing dramatically, requiring a greater number of intermediate states to calculate. This paper demonstrates that $n\propto\sqrt{\beta/\delta}$ states must be included to precisely calculate the populations of diffracted atoms as a function of field strength in better agreement with experiment.

Related papers

Nonadiabatic contributions to Bragg-regime dynamics in atomic Kapitza-Dirac scattering

Dylan Manna

Atomic Kapitza-Dirac Bragg regime scattering is a multiphoton process in which a neutral atom undergoes a change of momentum through an interaction with a coherent light source. When the Bragg conditions are met, the outgoing atom beams are spatially quantized. Counterpropagating lasers act as pump and probe scattering from far-off-resonant excited intermediate electronic states, leaving the atoms in the electronic ground state with quantized transverse momentum. Each nontrivial scattering event imparts transverse velocity and therefore kinetic energy to the deflected atoms through recoil. In the Bragg regime, the loss of energy in the light fields is equal to the gain of kinetic energy in the atom. Energy nonconserving intermediate states, which are described by nonadiabatic contributions, are not accounted for by first-order off-resonant states. By comparing the solutions of increasing orders of off-resonant intermediate states, it becomes clear that calculating the correct Pendell\"osung frequencies and phases requires including an ever increasing number of off-resonant states in proportion to the square root of the field strength.

arXiv:1709.05431•Physical Review A•Jun 15, 2020•1 citation

Doppleron-catalyzed Bragg resonances in atom optics

S. Glasgow, P. Meystre, N. Wilkens

Effective atomic beam splitters providing large scattering angles are central to atom optics and atom interferometry. Their most common optical realization relies on first-order Bragg scattering, which generates a splitting of the atomic wave function in momentum space. For typical atomic beam velocities of the order of 100 m/s, 2ħk produces very small scattering angles. Higher-order Bragg scattering is of questionable practicality, because of the need for atom–field interaction times that scale exponentially with the scattering order. Attempts at solving this problem include the introduction of multiple laser beams, the use of three-level transition schemes, and the application of velocity-tuned, or Doppleron, resonances. We present a novel scheme that uses a Doppleron resonance as a catalyst to speed up a high-order Bragg resonance by orders of magnitude. This effect occurs when the atom–field frequency detuning is such that the Bragg resonance and the Doppleron resonance become degenerate. Alternatively, in the band-theoretical description of the near-resonant Kapitza–Dirac effect, the Doppleron resonance is required to occur either at the center or at the boundary of the first Brillouin zone.

Annual Meeting Optical Society of America•Jan 1, 1992•0 citations

Kapitza-Dirac effect in the relativistic regime

Sven Ahrens, Heiko Bauke, Christoph H. Keitel +1 more

A relativistic description of the Kapitza-Dirac effect in the so-called Bragg regime with two and three interacting photons is presented by investigating both numerical and perturbative solutions of the Dirac equation in momentum space. We demonstrate that spin flips can be observed in the two-photon and the three-photon Kapitza-Dirac effects for certain parameters. During the interaction with the laser field the electron's spin is rotated, and we give explicit expressions for the rotation axis and the rotation angle. The off-resonant Kapitza-Dirac effect, that is, when the Bragg condition is not exactly fulfilled, is described by a generalized Rabi theory. We also analyze the in-field quantum dynamics as obtained from the numerical solution of the Dirac equation.

arXiv:1305.5507•Physical Review A•Jul 15, 2013•42 citations

Diffraction of atoms by light: The near-resonant Kapitza-Dirac effect

P. L. Gould, George A. Ruff, David E. Pritchard

We have observed the Kapitza-Dirac effect in the scattering of sodium atoms by a nearly resonant standing-wave laser field. The data clearly show diffraction peaks of the atomic momentum transfer at even multiples of the photon momentum. Theoretical predictions for an off-resonant, adiabatic interaction with a two-state system are in reasonable agreement with the data.

Physical Review Letters•Feb 24, 1986•408 citations

Optimizing the incident electron momentum for resonant few-photon Kapitza-Dirac scattering in bichromatic laser fields

Ingo Elsner, Carsten Müller

Nonrelativistic Kapitza-Dirac scattering of electrons from counterpropagating bichromatic laser waves is studied in the resonant Bragg regime, taking the electron spin into account. We show that the intrinsic field-induced detuning, which arises in the Rabi oscillation dynamics between initial and scattering state of the electron, can be compensated by a suitable adjustment of its incident momentum. Analytical formulas of the optimized electron momentum for spin-dependent three-photon and spin-independent four-photon Kapitza-Dirac scattering are obtained from simplified model systems in reduced dimensionality, which preserve the characteristic properties of the process.

arXiv:2507.06703•Physical Review A•Aug 21, 2025•0 citations

Quasiclassical approximation for the resonant Kapitza–Dirac scattering

G. A. Muradyan, A. Zh. Muradyan

In a momentum space, the resonant Kapitza–Dirac effect is described by the difference Schrödinger equation the step of which is the two-photon recoil momentum. For the interferometry of a multipath atom, the case of intense counter-propagating waves is of interest, when the number of generated momenta can reach to some tens. After that, in an intermediate stage of calculations, the discrete momentum distribution is regarded as a continuous one, and the Taylor expansion is applicable to it. This approximation preserves the spectrum of a diffraction well, in particular, the formation of a pair of almost monopulse states from the initial Gaussian distribution.

Journal of Contemporary Physics (Armenian Academy of Sciences)•Jul 1, 2017•1 citation
The primary mechanism of the atomic Kapitza-Dirac effect is a multi-photon process in which the electronic state is virtually excited while the direct product state is altered as the velocity of the atom undergoes spatial quantization. The Bragg resonance is a virtual multi-photon stimulated Raman scattering in which couterpropagating photons act as pump and probe imparting transverse velocity to the atom through recoil while the energy in the field is lowered such that the energy of the system is conserved. The bulk of the literature for the past three decades has presumed that the energy-nonconserving intermediate states which are described by non-adiabatic contributions could be neglected once the perturbative effects of next-order off-resonant states were included. This paper demonstrates the necessity of including higher-order non-adiabatic contributions of energy-nonconserving momentum states in calculating the final populations of Bragg resonances as a function of field strength. As the field strength is increased, the Pendell{o}sung frequency varies while generally decreasing dramatically, requiring a greater number of intermediate states to calculate. This paper demonstrates that n∝β/δn\propto\sqrt{\beta/\delta}n∝β/δ​ states must be included to precisely calculate the populations of diffracted atoms as a function of field strength in better agreement with experiment.
Atomic Kapitza-Dirac Bragg regime scattering is a multiphoton process in which a neutral atom undergoes a change of momentum through an interaction with a coherent light source. When the Bragg conditions are met, the outgoing atom beams are spatially quantized. Counterpropagating lasers act as pump and probe scattering from far-off-resonant excited intermediate electronic states, leaving the atoms in the electronic ground state with quantized transverse momentum. Each nontrivial scattering event imparts transverse velocity and therefore kinetic energy to the deflected atoms through recoil. In the Bragg regime, the loss of energy in the light fields is equal to the gain of kinetic energy in the atom. Energy nonconserving intermediate states, which are described by nonadiabatic contributions, are not accounted for by first-order off-resonant states. By comparing the solutions of increasing orders of off-resonant intermediate states, it becomes clear that calculating the correct Pendell\"osung frequencies and phases requires including an ever increasing number of off-resonant states in proportion to the square root of the field strength.
Effective atomic beam splitters providing large scattering angles are central to atom optics and atom interferometry. Their most common optical realization relies on first-order Bragg scattering, which generates a splitting of the atomic wave function in momentum space. For typical atomic beam velocities of the order of 100 m/s, 2ħk produces very small scattering angles. Higher-order Bragg scattering is of questionable practicality, because of the need for atom–field interaction times that scale exponentially with the scattering order. Attempts at solving this problem include the introduction of multiple laser beams, the use of three-level transition schemes, and the application of velocity-tuned, or Doppleron, resonances. We present a novel scheme that uses a Doppleron resonance as a catalyst to speed up a high-order Bragg resonance by orders of magnitude. This effect occurs when the atom–field frequency detuning is such that the Bragg resonance and the Doppleron resonance become degenerate. Alternatively, in the band-theoretical description of the near-resonant Kapitza–Dirac effect, the Doppleron resonance is required to occur either at the center or at the boundary of the first Brillouin zone.
A relativistic description of the Kapitza-Dirac effect in the so-called Bragg regime with two and three interacting photons is presented by investigating both numerical and perturbative solutions of the Dirac equation in momentum space. We demonstrate that spin flips can be observed in the two-photon and the three-photon Kapitza-Dirac effects for certain parameters. During the interaction with the laser field the electron's spin is rotated, and we give explicit expressions for the rotation axis and the rotation angle. The off-resonant Kapitza-Dirac effect, that is, when the Bragg condition is not exactly fulfilled, is described by a generalized Rabi theory. We also analyze the in-field quantum dynamics as obtained from the numerical solution of the Dirac equation.
Nonrelativistic Kapitza-Dirac scattering of electrons from counterpropagating bichromatic laser waves is studied in the resonant Bragg regime, taking the electron spin into account. We show that the intrinsic field-induced detuning, which arises in the Rabi oscillation dynamics between initial and scattering state of the electron, can be compensated by a suitable adjustment of its incident momentum. Analytical formulas of the optimized electron momentum for spin-dependent three-photon and spin-independent four-photon Kapitza-Dirac scattering are obtained from simplified model systems in reduced dimensionality, which preserve the characteristic properties of the process.
In a momentum space, the resonant Kapitza–Dirac effect is described by the difference Schrödinger equation the step of which is the two-photon recoil momentum. For the interferometry of a multipath atom, the case of intense counter-propagating waves is of interest, when the number of generated momenta can reach to some tens. After that, in an intermediate stage of calculations, the discrete momentum distribution is regarded as a continuous one, and the Taylor expansion is applicable to it. This approximation preserves the spectrum of a diffraction well, in particular, the formation of a pair of almost monopulse states from the initial Gaussian distribution.