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/0008264 · Physical Review Letters

Atomic Four-Wave Mixing: Fermions versus Bosons

M. G. Moore, Pierre Meystre

Published May 7, 2001• 62 citations
arXivHTMLPDF

Abstract

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."

DOI
10.1103/physrevlett.86.4199

Related papers

Does Matter Wave Amplification Work for Fermions?

Wolfgang Ketterle, S. Inouye

We discuss the relationship between bosonic stimulation, density fluctuations, and matter wave gratings. It is shown that enhanced stimulated scattering, matter wave amplification, and atomic four-wave mixing do not require macroscopic occupation of a single quantum state. These processes are in principle possible for fermionic or nondegenerate samples, if they are prepared in a cooperative state. In practice, there are limitations due to short coherence times.

arXiv:cond-mat/0008232•Physical Review Letters•May 7, 2001•68 citations

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

quantum interference in bosonic and fermionic matter-wave amplification

Hui Deng, Y. Yamamoto

We investigate the quantum interference effects in two types of matter-wave mixing experiments: one with initial matter waves prepared in independent Fock states (type I) and the other with each individual particle prepared in a same coherent superposition of states (type II). In the type I experiment, a symmetric wavefunction of bosons leads to constructive quantum interference and shows final state stimulation, while an anti-symmetric wavefunction of fermions results in destructive quantum interference and inhibited matter wave mixing. In the type II experiment, a coherent superposition state leads to constructive quantum interference and enhanced matter wave mixing for both bosons and fermions, independent of their quantum statistics.

arXiv:quant-ph/0210178•Oct 25, 2002•0 citations

Four-wave mixing in degenerate atomic gases

Pierre Villain, Patrik Öhberg, Luis Santos +2 more

We study the process of four-wave mixing (FWM) in ultracold degenerate atomic gases. In particular, we address the problem of FWM in boson-fermion mixtures. We develop an approximate description of such processes using asymptotic analysis of high-order perturbation theory taking into account quantum statistics. We perform also numerical simulations of FWM in boson-fermion mixtures and obtain an analytic and numerical estimate of the efficiency of the process.

arXiv:cond-mat/0005417•Physical Review A•Jul 1, 2001•22 citations

Crossed-beam optically degenerate wave mixing with bosonic quantum gases

Chengjie Zhu, Yan Li, L. Deng

Highly efficient, optical-degenerate wave-mixing involving bosonic quantum gas is studied using a crossed-beam geometry. We show a very large enhancement due to nonlinear gain from a matter-optical wave-mixing process involving four photons and two matter-wave excitations. Under suitable conditions with a red-detuned pump field this optically degenerate, four-photon process can be stronger than the traditional two-photon inelastic light-scattering mechanism, leading to strong nonlinear growth of the observed matter-wave scattering. This optically degenerate four-wave mixing is independent of other enhancements arising from bosonic stimulations. More importantly, this highly efficient, backward degenerate wave generation and growth process does not have a correspondence in thermal gases in nonlinear optics.

Physical Review A•Mar 8, 2019•0 citations

Nonlinear atom optics: four-wave mixing

Y. B. Band, Marek Trippenbach, Paul S. Julienne

The advent of the laser as an intense, coherent light source gave birth to nonlinear optics, which now plays an important role in many areas of science and technology. One of the first applications of nonlinear optics was the production of coherent light of a new frequency by multi-wave mixing of several optical fields in a nonlinear medium. Until the experimental realization of Bose-Einstein Condensation (BEC) there had been no intense coherent source of matter-waves analogous to the optical laser. BEC has already been exploited to produce a matter-wave 'laser' atom optics was reported: the observation of coherent four wave mixing in which three sodium matter waves mix to produce a fourth. The experiment utilized light pulses to create two high-momentum wavepackets via Bragg diffraction from a stationary Bose- Einstein condensate. The high-momentum components and the remaining zero momentum condensate component interact to form a new momentum component due to the nonlinear self- interaction of the bosonic atoms. We develop a quantum mechanical description, based on the slowly-varying-envelope approximation to the time-dependent nonlinear Schroedinger equation, to describe four-wave mixing in Bose-Einstein condensates and apply this description to understand the experimental observations and to make new predictions. We examine the role of phase-modulation, momentum and energy conservation, and particle number conservation in four-wave mixing of matter waves.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Mar 23, 2000•0 citations
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."
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.
We investigate the quantum interference effects in two types of matter-wave mixing experiments: one with initial matter waves prepared in independent Fock states (type I) and the other with each individual particle prepared in a same coherent superposition of states (type II). In the type I experiment, a symmetric wavefunction of bosons leads to constructive quantum interference and shows final state stimulation, while an anti-symmetric wavefunction of fermions results in destructive quantum interference and inhibited matter wave mixing. In the type II experiment, a coherent superposition state leads to constructive quantum interference and enhanced matter wave mixing for both bosons and fermions, independent of their quantum statistics.
Highly efficient, optical-degenerate wave-mixing involving bosonic quantum gas is studied using a crossed-beam geometry. We show a very large enhancement due to nonlinear gain from a matter-optical wave-mixing process involving four photons and two matter-wave excitations. Under suitable conditions with a red-detuned pump field this optically degenerate, four-photon process can be stronger than the traditional two-photon inelastic light-scattering mechanism, leading to strong nonlinear growth of the observed matter-wave scattering. This optically degenerate four-wave mixing is independent of other enhancements arising from bosonic stimulations. More importantly, this highly efficient, backward degenerate wave generation and growth process does not have a correspondence in thermal gases in nonlinear optics.
The advent of the laser as an intense, coherent light source gave birth to nonlinear optics, which now plays an important role in many areas of science and technology. One of the first applications of nonlinear optics was the production of coherent light of a new frequency by multi-wave mixing of several optical fields in a nonlinear medium. Until the experimental realization of Bose-Einstein Condensation (BEC) there had been no intense coherent source of matter-waves analogous to the optical laser. BEC has already been exploited to produce a matter-wave 'laser' atom optics was reported: the observation of coherent four wave mixing in which three sodium matter waves mix to produce a fourth. The experiment utilized light pulses to create two high-momentum wavepackets via Bragg diffraction from a stationary Bose- Einstein condensate. The high-momentum components and the remaining zero momentum condensate component interact to form a new momentum component due to the nonlinear self- interaction of the bosonic atoms. We develop a quantum mechanical description, based on the slowly-varying-envelope approximation to the time-dependent nonlinear Schroedinger equation, to describe four-wave mixing in Bose-Einstein condensates and apply this description to understand the experimental observations and to make new predictions. We examine the role of phase-modulation, momentum and energy conservation, and particle number conservation in four-wave mixing of matter waves.