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Physical Review A

Quantum field theory of atoms interacting with photons. II. Scattering of short laser pulses from trapped bosonic atoms

Li You, Maciej Lewenstein, J. Cooper

Published Jun 1, 1995• 49 citations
Publisher

Abstract

We discuss a method for probing a system of cold bosonic atoms in a trap using intense short laser pulses. Above the critical temperature for Bose-Einstein condensation, such a system scatters very weakly. Coherent scattering occurs primarily in the forward direction within a solid angle determined by phase matching conditions for the thermal atomic distribution. Below the critical temperature, the number of scattered photons increases dramatically and the scattered light is emitted into a solid angle determined by the size of the condensate. Quantum statistics of the atoms explicitly effect the spectrum as well as the squeezing properties of the scattered light. The theory accounts for the atom-atom interactions.

DOI
10.1103/physreva.51.4712

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We discuss a method for probing a system of cold bosonic atoms in a trap using intense short laser pulses. Above the critical temperature for Bose-Einstein condensation, such a system scatters very weakly. Coherent scattering occurs primarily in the forward direction within a solid angle determined by phase matching conditions for the thermal atomic distribution. Below the critical temperature, the number of scattered photons increases dramatically and the scattered light is emitted into a solid angle determined by the size of the condensate. Quantum statistics of the atoms explicitly effect the spectrum as well as the squeezing properties of the scattered light. The theory accounts for the atom-atom interactions.
We study the coherent scattering of weak light from a system of cooled bosonic atoms in a trap. We derive and discuss in detail the scattering equation for such a process that describes multiple scatterings from different atoms. Our theory accounts for atom-atom interactions and determines the density profile of the atomic fields from the self-consistent Bogoliubov-Hartree method. We present two kinds of analytic solutions to the scattering equation using the on-shell approximation and the generalized diffraction theory. We discuss the validity of those approaches, and demonstrate that they both lead to similar results. Our studies indicate that the scattering cross sections exhibit non-Lorentzian shapes with narrow features close to resonance. Coherent scattering occurs mainly in the forward direction, and the angular distribution is limited by the size of the atomic sample in the trap. We present results for various ranges of relevant parameters such as trap size, interaction strength, number of atoms, and temperature, etc. \textcopyright{} 1996 The American Physical Society.
We investigate the scattering of intense short laser pulses off trapped cold fermionic atoms. We discuss the sensitivity of the scattered light to the quantum statistics of the atoms. The temperature dependence of the scattered light spectrum is calculated. Comparisons are made with a system of classical atoms that obey Maxwell-Boltzmann statistics. We find the total scattering increases as the fermions become cooler but eventually tails off at very low temperatures (far below the Fermi temperature). At these low temperatures the fermionic degeneracy plays an important role in the scattering, as it inhibits spontaneous emission into occupied energy levels below the Fermi surface. We demonstrate that temperature dependent qualitative changes in the differential and total spectrum can be utilized to probe the quantum degeneracy of a trapped Fermi gas when the total number of atoms is sufficiently large (> 106).(>~{10}^{6}).(> 106). At smaller numbers of atoms, incoherent scattering dominates and it displays weak temperature dependence.
Summary form only given. Bose-Einstein condensed atomic gases are a new class of quantum fluids with many novel properties. We have studied collective modes and dissipation by perturbing the condensate with focused laser beams. The scattering of photons imparts momentum to the condensate and creates excitations. Consequently, the coherence and collective behavior of the condensate can strongly affect optical properties. We used light scattering to demonstrate that the coherence length of a condensate is equal to its physical size, and obtained dramatic evidence for the presence of correlated momentum excitations in the many-body condensate wavefunction. At higher laser intensity, a new form of superradiance was found which provided a gain mechanism for the generation of directed beams of atoms and light. This process amplified matter waves in a phase coherent way.