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arXiv:cond-mat/9707319

Thomas-Fermi Description of Incoherent Light Scattering from an Atomic-Trap BEC

Eddy Timmermans, Paolo Tommasini

Published Jul 30, 1997• 0 citations
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Abstract

We present a Thomas-Fermi treatment of resonant incoherent scattering of low-intensity light by a dilute spatially confined Bose-Einstein condensate. The description gives simple analytical results and allows scattering data from finite-size condensates to be interpreted in terms of the properties of the homogeneous BEC-system. As an example, we show how the energy dispersion of the elementary excitations can be measured from scattering by a finite-size atomic-trap condensate. As a second example, we point out that a near-resonant scattering experiment can observe quasi-particle creation caused by particle annihilation.

DOI
10.48550/arxiv.cond-mat/9707319

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We present a Thomas-Fermi treatment of resonant incoherent scattering of low-intensity light by a dilute spatially confined Bose-Einstein condensate. The description gives simple analytical results and allows scattering data from finite-size condensates to be interpreted in terms of the properties of the homogeneous BEC-system. As an example, we show how the energy dispersion of the elementary excitations can be measured from scattering by a finite-size atomic-trap condensate. As a second example, we point out that a near-resonant scattering experiment can observe quasi-particle creation caused by particle annihilation.
The essence of the Thomas-Fermi model is the assumption that the local behavior of a many-body system can be approximated by that of a homogeneous system. In this paper, we present the natural extension of the static Thomas-Fermi treatment of dilute Bose condensates, by describing the dynamical behavior of the condensate in the same quasi-homogeneous approximation. In particular, we calculate the dynamical structure factor S(q,ω)S(q, ω)S(q,ω) of a low-temperature condensate, confined in a harmonic oscillator trap. The result is a remarkably simple analytical function, which, with the proper interpretation, gives a powerful and insightful description of the scattering properties of the BEC-system.
We consider a quantum theory of elastic light scattering from a macroscopic atomic sample existing in the Bose-Einstein condensate (BEC) phase. Following the second quantized formalism we introduce a set of coupled and closed diagram equations for the polariton propagator contributing to the T -matrix and scattering amplitude. Our approach allows us to follow important density corrections to the quasi-energy structure caused by static interaction and radiation losses associated with incoherent scattering in the case of near resonance excitation.
We present a single-scattering formalism for incoherent resonant light scattering by dilute quantum gas systems such as the atomic-trap Bose-Einstein condensates. We show that resonant scattering gives access to more information than the dynamical structure factor, familiar from non-resonant scattering. In particular, we show that the detuning dependence of the incoherent scattering cross-section allows the direct determination of the BEC pairing density <ψψ>< ψψ><ψψ>, which is a broken symmetry and provides evidence that the condensate is not in a good number state.
We derive a description of the spatially inhomogeneous Bose-Einstein condensate, treating the system locally as a homogeneous Bose gas. This approach, similar to the Thomas-Fermi model for the inhomogeneous many-particle fermion system, is well suited to describe the atomic Bose-Einstein condensates that have recently been obtained experimentally through atomic trapping and cooling. In this paper, we confine our attention to the zero-temperature case, although the treatment can be generalized to finite temperatures, as we shall discuss elsewhere. Several features of this approach, which we shall call the Thomas-Fermi-Bogoliubov description, are very attractive. (i) It is simpler than the Hartree-Fock-Bogoliubov technique. We can obtain analytical results in the case of weakly interacting bosons for quantities such as the chemical potential, the local depletion, pairing, pressure, and density of states. (ii) The method provides an estimate for the error due to the inhomogeneity of the Bose-condensed system. This error is a local quantity so that the validity of the description for a given trap and a given number of trapped atoms can be tested as a function of position. We see, for example, that at the edge of the condensate the Thomas-Fermi-Bogoliubov theory always breaks down. (iii) The Thomas-Fermi-Bogoliubov description can be generalized to treat the statistical mechanics of the Bose gas at finite temperatures.
We have observed strong scattering of a probe light by dilute Bose–Einstein condensate (BEC) 87 Rb gas in a tight magnetic trap. The scattering light forms fringes at the image plane. It is found that we can infer the real size of the condensation and the number of the atoms by modelling the imaging system. We present a quantitative calculation of light scattering by the condensed atoms. The calculation shows that the experimental results agree well with the prediction of the generalized diffraction theory, and thus we can directly observe the phase transition of BEC in a tight trap.
We study a dilute Bose gas of atoms whose scattering length a is large compared to the range of their interaction. We calculate the energy density E of a homogeneous Bose-Einstein condensate (BEC) to second order in the low-density expansion, expressing it in terms of a and a second parameter Lambda* that determines the low-energy observables in the three-body sector. The second-order correction to E has a small imaginary part that reflects the instability due to three-body recombination. In the case of a trapped BEC with large negative a, we calculate the coefficient of the three-body mean-field term in E in terms of a and Lambda*. It can be very large if there is an Efimov state near threshold.