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Physical Review A

Off-resonance light scattering from low-temperature Bose and Fermi gases

Juha Javanainen, Janne Ruostekoski

Published Oct 1, 1995• 115 citations
Publisher

Abstract

We study interactions of light with a sample of two-level atoms, with full inclusion of angular momentum degeneracy, at temperatures and densities such that the quantum statistics of the atoms may have an effect. Coupled propagation equations are given for light and matter fields, and plausible general simplifications are enumerated. In particular, the motion of the atoms during the excited-state lifetime may often be ignored. The propagation equations of light and matter fields are decoupled within the assumption that the detuning of the driving light from atomic resonance is large, and the spectrum of scattered light is studied for ideal Bose and Fermi gases. In addition to the expected image of the velocity distribution, the spectra contain qualitatively distinct features that depend on the statistics of the atoms. This is because for bosons (fermions), those scattering events in which an atom recoils to an already occupied state are enhanced (inhibited).

DOI
10.1103/physreva.52.3033

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We study interactions of light with a sample of two-level atoms, with full inclusion of angular momentum degeneracy, at temperatures and densities such that the quantum statistics of the atoms may have an effect. Coupled propagation equations are given for light and matter fields, and plausible general simplifications are enumerated. In particular, the motion of the atoms during the excited-state lifetime may often be ignored. The propagation equations of light and matter fields are decoupled within the assumption that the detuning of the driving light from atomic resonance is large, and the spectrum of scattered light is studied for ideal Bose and Fermi gases. In addition to the expected image of the velocity distribution, the spectra contain qualitatively distinct features that depend on the statistics of the atoms. This is because for bosons (fermions), those scattering events in which an atom recoils to an already occupied state are enhanced (inhibited).
We study interactions of light with a sample of two-level atoms. Quantum statistical effects of degenerate boson and fermion gases are described by using the quantum field theory of atom-photon interactions, fully including the angular momentum degeneracies. Coupled propagation equations are given for light and matter fields, and plausible general simplifications are enumerated.^ In the limit of large atom-field detuning, multiple scattering of light and QED linewidths and line shifts may be ignored, and the propagation equations of light and matter fields may be decoupled. A general expression for the spectrum of the scattered light is derived, complete with the dependence on atomic level scheme, on various light polarizations, and on the geometry of the experiment. With these simplifications we are able to find distinct qualitative features in the spectrum of the scattered light in the case of both fermions and bosons that depend on the statistics of atoms. This is because for bosons (fermions), those scattering events in which an atom recoils to an already occupied state are enhanced (inhibited).^ As the driving light gets closer to the atomic resonance, multiple scattering and vacuum fluctuations of the electromagnetic fields should also be taken into account. We write the equations of motion for the excited state field operators by eliminating the vacuum electromagnetic field. It is always assumed that the driving external laser field is in the coherent state. We find in the limit of low light intensity, a hierarchy of equations of motion for correlation functions that contain one excited-atom field and one, two, three, etc., ground state atom fields. It is conjectured that the entire linear hierarchy may be solved by solving numerically the classical equations for the coupled system of electromagnetic fields and charged harmonic oscillators. We discuss the emergence of resonant dipole-dipole interactions and collective linewidths, and delineate the limits of validity of the column density approach in terms of non-cooperative atoms by presenting a mathematical example in which this approach is exact. ^
We calculate the spectrum of the scattered light from quantum degenerate atomic gases obeying Bose-Einstein statistics. The atoms are assumed to occupy two ground states, which are optically coupled through a common excited state by two low-intensity off-resonant light beams. In the presence of a Bose condensate in both ground states, the atoms may exhibit light-induced oscillations between the two condensates analogous to the Josephson effect. The spectrum of the scattered light is calculated in the limit of a low oscillation frequency. In the spectrum we are able to observe qualitative features depending on the phase difference between the macroscopic wave functions of the two condensates. Thus, our optical scheme could possibly be used as an experimental realization of the spontaneous breakdown of the U(1) gauge symmetry in the Bose-Einstein condensation.
Abstract The tendency of identical bosons to bunch, seen in the Hanbury Brown–Twiss effect and Bose–Einstein condensation, is a hallmark of quantum statistics. This bunching can enhance the rates of fundamental processes such as atom–atom and atom–light scattering when atoms scatter into already occupied states. For non-interacting bosons, the enhancement of light scattering follows directly from the occupation of the atom’s final momentum state. Here we study scattering between off-resonant light and atoms in a quasi-homogeneous Bose gas with tunable interactions and show that even weak interactions, which essentially do not alter the momentum distribution, strongly affect atom–light scattering. Changes in local atomic correlations suppress the bosonic enhancement under weak repulsive interactions and increase the scattering rate under attractive ones. Moreover, if the interactions are rapidly tuned, light scattering reveals correlation dynamics that are orders of magnitude faster than the collisional dynamics of the momentum-space populations. Its extreme sensitivity to correlation effects makes off-resonant light scattering a powerful probe of many-body physics in ultracold atomic gases.
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.
We develop the idea of manipulating optically the scattering length aaa in low-temperature atomic gases. If the incident light is close to resonance with one of the bound ppp levels of electronically excited molecules, virtual radiative transitions of a pair of interacting atoms to this level can significantly change the value and even reverse the sign of aaa. The decay of the gas due to photon recoil and due to photoassociation can be minimized by selecting the frequency detuning and the Rabi frequency. Our calculations show the feasibility of optical manipulations of trapped Bose condensates through a light-induced change in the mean field interaction between atoms, which is illustrated for 7Li{}^{7}\mathrm{Li}7Li.