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

arXiv:cond-mat/0212384 · Physical Review A

Dynamics of fermionic four-wave mixing

H. Christ, Christopher P. Search, Pierre Meystre

Published Jun 30, 2003• 11 citations
arXivHTMLPDF

Abstract

We study the dynamics of a beam of fermions diffracted off a density grating formed by fermionic atoms in the limit of a large grating. An exact description of the system in terms of particle-hole operators is developed. We use a combination of analytical and numerical methods to quantitatively explore the Raman-Nath and the Bragg regimes of diffraction. We discuss the limits in diffraction efficiency resulting from the dephasing of the grating due to the distribution of energy states occupied by the fermions. We propose several methods to overcome these limits, including the technique of ``atom echoes.''

DOI
10.1103/physreva.67.063611

Related papers

Four-wave mixing in degenerate Fermi gases: Beyond the undepleted pump approximation

T. Miyakawa, H. Christ, Christopher P. Search +1 more

We analyze the full nonlinear dynamics of the four-wave mixing between an incident beam of fermions and a fermionic density grating. We find that when the number of atoms in the beam is comparable to the number of atoms forming the grating, the dephasing of that grating, which normally leads to the decay of its amplitude, is suppressed. Instead, the density grating and the beam density exhibit large nonlinear coupled amplitude oscillations. In this case, four-wave mixing can persist for much longer times compared to the case of negligible back action. We also evaluate the efficiency of the four-wave mixing and show that it can be enhanced by producing an initial density grating with an amplitude that is less than the maximum value. These results indicate that efficient four-wave mixing in fermionic alkali gases should be experimentally observable.

arXiv:cond-mat/0301278•Physical Review A•Jun 17, 2003•5 citations

The diraction of atoms by light

Duncan H J O’Dell, H. H. Wills

The diffraction of a coherent, stationary, beam of atoms from a standing wave of light is considered. Particular attention is paid to long interaction times for which the motion of the atoms inside the light field must be taken into account. This is the regime of dynamical diffraction, and is treated within the framework of a set of differential difference equations due to Raman and Nath. The popular Raman-Nath approximation, in which the kinetic energy imparted to the atoms by the light wave is ignored, is no longer valid and the full equations must be solved. When the interaction between the atoms and the light is very weak then few beams are produced. To describe spontaneous emission from the atom one can invoke a complex potential as a model for dissipation. If the atom beam is obliquely incident one finds anomalously high transmission close to the Bragg angles which is the physical manifestation of degeneracies in non-Hermitian matrices. The classical limit is approached when the atom-light interaction is strong, producing many beams. The classical dynamics (geometrical rays) reveal that the farfield intensity pattern is dominated by caustics. These proliferate with increasing interaction distance. Two methods are presented for analytically treating the semiclassical limit of the wave mechanics. The first begins with W.K.B. solutions to the continuised Raman-Nath equations. Mapping onto parabolic cylinder functions removes the spurious divergences of the W.K.B. solutions, giving eigenvectors which are uniformly valid for all scattering angles and may be summed to give the wavefunction. The second method transforms the original W.K.B. eigensum, using the Poisson summation formula, giving a new sum, each term of which has classical significance. This method shows that wave theory decorates the classical caustics with an Airy function intensity profile, as predicted by catastrophe theory.

•Jan 1, 1998•1 citation

Far Resonance Kapitza-Dirac Diffraction: from Raman-Nath to Bragg and Multiple Beam Atomic Interferometer

Atom Zh. Muradyan

Abstract Near-resonant Kapitza–Dirac diffraction theory is extended out of familiar Raman–Nath approximation. New solutions with initial superposition of equidistant momentum states, applied to one- and two-optical grating atom interferometer schemes, reveals certain output patterns, usable as large-area multiple beam atom interferometer.

Optical Memory and Neural Networks•Dec 1, 2023•0 citations

Atom-wave diffraction between the Raman-Nath and the Bragg regime: Effective Rabi frequency, losses, and phase shifts

Holger Müller, Sheng‐wey Chiow, Steven Chu

We present an analytic theory of the diffraction of (matter) waves by a lattice in the ``quasi-Bragg" regime, by which we mean the transition region between the long-interaction Bragg and ``channeling'' regimes and the short-interaction Raman-Nath regime. The Schr\"odinger equation is solved by adiabatic expansion, using the conventional adiabatic approximation as a starting point, and reinserting the result into the Schr\"odinger equation to yield a second-order correction. Closed expressions for arbitrary pulse shapes and diffraction orders are obtained and the losses of the population to output states otherwise forbidden by the Bragg condition are derived. We consider the phase shift due to couplings of the desired output to these states that depends on the interaction strength and duration and show how these can be kept negligible by a choice of smooth (e.g., Gaussian) envelope functions even in situations that substantially violate the adiabaticity condition. We also give an efficient method for calculating the effective Rabi frequency (which is related to the eigenvalues of Mathieu functions) in the quasi-Bragg regime.

arXiv:0704.2627•Physical Review A•Feb 6, 2008•136 citations

Regimes of atomic diffraction: Raman versus Bragg diffraction in retroreflective geometries

Sabrina Hartmann, Jens Jenewein, Enno Giese +4 more

We provide a comprehensive study of atomic Raman and Bragg diffraction when coupling to a pair of counterpropagating light gratings (double diffraction) or to a single one (single diffraction) and discuss the transition from one case to the other in a retroreflective geometry as the Doppler detuning changes. In contrast to single diffraction, double Raman loses its advantage of high diffraction efficiency for short pulses and has to be performed in a Bragg-type regime. Moreover, the structure of double diffraction leads to further limitations for broad momentum distributions on the efficiency of mirror pulses, making the use of (ultra)cold ensembles essential for high diffraction efficiency.

arXiv:1911.12169•Physical Review A•May 8, 2020•45 citations

Atomic Four-Wave Mixing: Fermions versus Bosons

M. G. Moore, Pierre Meystre

We compare four-wave mixing in quantum degenerate gases of bosonic and fermionic atoms. We find that matter-wave gratings formed from either bosonic or fermionic atoms can in principle exhibit nearly identical Bragg scattering and four-wave mixing properties. This implies that effects such as coherent matter-wave amplification and superradiance can occur in degenerate Fermi gases. This effect is due to constructive many-particle quantum interferences, which in the boson case are interpreted as "Bose enhancement."

arXiv:cond-mat/0008264•Physical Review Letters•May 7, 2001•62 citations
We study the dynamics of a beam of fermions diffracted off a density grating formed by fermionic atoms in the limit of a large grating. An exact description of the system in terms of particle-hole operators is developed. We use a combination of analytical and numerical methods to quantitatively explore the Raman-Nath and the Bragg regimes of diffraction. We discuss the limits in diffraction efficiency resulting from the dephasing of the grating due to the distribution of energy states occupied by the fermions. We propose several methods to overcome these limits, including the technique of ``atom echoes.''
We analyze the full nonlinear dynamics of the four-wave mixing between an incident beam of fermions and a fermionic density grating. We find that when the number of atoms in the beam is comparable to the number of atoms forming the grating, the dephasing of that grating, which normally leads to the decay of its amplitude, is suppressed. Instead, the density grating and the beam density exhibit large nonlinear coupled amplitude oscillations. In this case, four-wave mixing can persist for much longer times compared to the case of negligible back action. We also evaluate the efficiency of the four-wave mixing and show that it can be enhanced by producing an initial density grating with an amplitude that is less than the maximum value. These results indicate that efficient four-wave mixing in fermionic alkali gases should be experimentally observable.
The diffraction of a coherent, stationary, beam of atoms from a standing wave of light is considered. Particular attention is paid to long interaction times for which the motion of the atoms inside the light field must be taken into account. This is the regime of dynamical diffraction, and is treated within the framework of a set of differential difference equations due to Raman and Nath. The popular Raman-Nath approximation, in which the kinetic energy imparted to the atoms by the light wave is ignored, is no longer valid and the full equations must be solved. When the interaction between the atoms and the light is very weak then few beams are produced. To describe spontaneous emission from the atom one can invoke a complex potential as a model for dissipation. If the atom beam is obliquely incident one finds anomalously high transmission close to the Bragg angles which is the physical manifestation of degeneracies in non-Hermitian matrices. The classical limit is approached when the atom-light interaction is strong, producing many beams. The classical dynamics (geometrical rays) reveal that the farfield intensity pattern is dominated by caustics. These proliferate with increasing interaction distance. Two methods are presented for analytically treating the semiclassical limit of the wave mechanics. The first begins with W.K.B. solutions to the continuised Raman-Nath equations. Mapping onto parabolic cylinder functions removes the spurious divergences of the W.K.B. solutions, giving eigenvectors which are uniformly valid for all scattering angles and may be summed to give the wavefunction. The second method transforms the original W.K.B. eigensum, using the Poisson summation formula, giving a new sum, each term of which has classical significance. This method shows that wave theory decorates the classical caustics with an Airy function intensity profile, as predicted by catastrophe theory.
We present an analytic theory of the diffraction of (matter) waves by a lattice in the ``quasi-Bragg" regime, by which we mean the transition region between the long-interaction Bragg and ``channeling'' regimes and the short-interaction Raman-Nath regime. The Schr\"odinger equation is solved by adiabatic expansion, using the conventional adiabatic approximation as a starting point, and reinserting the result into the Schr\"odinger equation to yield a second-order correction. Closed expressions for arbitrary pulse shapes and diffraction orders are obtained and the losses of the population to output states otherwise forbidden by the Bragg condition are derived. We consider the phase shift due to couplings of the desired output to these states that depends on the interaction strength and duration and show how these can be kept negligible by a choice of smooth (e.g., Gaussian) envelope functions even in situations that substantially violate the adiabaticity condition. We also give an efficient method for calculating the effective Rabi frequency (which is related to the eigenvalues of Mathieu functions) in the quasi-Bragg regime.
We provide a comprehensive study of atomic Raman and Bragg diffraction when coupling to a pair of counterpropagating light gratings (double diffraction) or to a single one (single diffraction) and discuss the transition from one case to the other in a retroreflective geometry as the Doppler detuning changes. In contrast to single diffraction, double Raman loses its advantage of high diffraction efficiency for short pulses and has to be performed in a Bragg-type regime. Moreover, the structure of double diffraction leads to further limitations for broad momentum distributions on the efficiency of mirror pulses, making the use of (ultra)cold ensembles essential for high diffraction efficiency.
We compare four-wave mixing in quantum degenerate gases of bosonic and fermionic atoms. We find that matter-wave gratings formed from either bosonic or fermionic atoms can in principle exhibit nearly identical Bragg scattering and four-wave mixing properties. This implies that effects such as coherent matter-wave amplification and superradiance can occur in degenerate Fermi gases. This effect is due to constructive many-particle quantum interferences, which in the boson case are interpreted as "Bose enhancement."