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Journal of Physics B Atomic Molecular and Optical Physics

Nonlinear matter-wave optics of bosons and fermions

Pierre Meystre

Published Apr 25, 2005• 5 citations
Publisher

Abstract

We briefly review some recent developments in nonlinear atom optics. Basic principles, as well as some of the early effects predicted and observed in the nonlinear optics of bosonic atoms, are presented in general terms. Recent results on fermionic four-wave mixing and on the matter-wave analogue of optical second-harmonic generation are discussed in detail.

DOI
10.1088/0953-4075/38/9/012

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•Oct 21, 2004•0 citations
We briefly review some recent developments in nonlinear atom optics. Basic principles, as well as some of the early effects predicted and observed in the nonlinear optics of bosonic atoms, are presented in general terms. Recent results on fermionic four-wave mixing and on the matter-wave analogue of optical second-harmonic generation are discussed in detail.
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. FEC has already been exploited to produce a matter-wave `laser' leading to the threshold of a new field of physics: nonlinear atom optics. Recently the first experiment in nonlinear 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 Schrodinger equation (also called the Gross-Pitaevskii 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 (i.e., phase-matching), and particle number conservation in four-wave mixing of matter waves.
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.
The availability of coherent matter waves from Bose-Einstein condensates had led to the extension of atom optics from the linear to the nonlinear regime, in analogy with the developments in optics following the invention of the laser. We provide a tutorial introduction to this emerging field, emphasizing the role of collisions as a “nonlinear medium” in the focusing and defocusing of matter waves, the launching of atomic solitons, the generation of vortices, and the demonstration of four-wave mixing both among matter waves and between optical and matter waves.
This paper reviews some of our recent results in nonlinear atom optics. In addition to nonlinear wave-mixing between matter waves, we also discuss the dynamical interplay between optical and matter waves. This new paradigm, which is now within experimental reach, has the potential to impact a number of fields of physics, including the manipulation and applications of atomic coherence, and the preparation of quantum entanglement between microscopic and macroscopic systems. Possible applications include quantum information processing, matter-wave holography, and nanofabrication.
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."
The general goal of our research is the generation, manipulation, and characterization of coherent and nonclassical matter-wave sources. The research has both a theoretical and an experimental component. Theoretical achievements include the use of nonlinear atom optical techniques to generate beams of entangled atoms and squeezed atomic beams from Bose-Einstein condensates, as well as the generation of entangled atom-photon pairs, the extension of the ideas bosonic atom optics to the nonlinear atom optics to fermionic atoms and to boson-fermion mixtures. We have also started to analyze how the combination of these developments can be applied to the realization and manipulation of molecular fields of tailored quantum statistics. On the experimental side we have worked with Cs atoms in optical lattices to implement qubits, quantum gates and circuits. We have demonstrated trapping in deep 3D lattices initialization by sideband cooling and single-qubit control. In a second project we have used optical probes to implement continuous weak measurements of collective observables in an atomic ensemble. We have developed a detailed understanding of Faraday measurements of atomic spins, and a novel scheme to probe the pseudospin associated with the atomic clock transition.