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Optical properties of degenerate atomic gases

Janne Ruostekoski

Published Jan 1, 1996• 0 citations
OpenAlex

Abstract

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. ^

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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 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 the interactions of a possibly dense and/or quantum degenerate gas with driving light. Both the atoms and the electromagnetic fields are represented by quantum fields throughout the analysis. We introduce a field-theory version of Markov and Born approximations for the interactions of light with matter, and devise a procedure whereby certain types of products of atom and light fields may be put to a desired, essentially normal, order. In the limit of low light intensity we find a hierarchy of equations of motion for correlation functions that contain one excited-atom field and one, three, five, etc., ground-state atom fields. It is conjectured that the entire linear hierarchy may be solved by solving numerically the classical equations for a 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 noncooperative 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.
Lasing [1, 2] and superradiance [3‐5] phenomena are currently enjoying a renaissance as research topics in atomic physics. Fundamentally based on the interaction of matter with an electromagnetic (light) field, the atomic dipoles in a “lasing medium” collectively emit into selected modes of the electromagnetic field and thereby create an amplified and coherent source of light. Present-day lasers use di erent types of gain media and cover a wide range of output frequencies for application in both, fundamental research and industry. A recent string of papers has reported on superradiance [6, 7] and lasing-type instabilities using Bose gases of various type (thermal atoms [8, 9], photon gases [10] and Bose-Einstein condensed atoms [11‐14]) in optical cavities. Buoyed by experimental control over essentially single excitation quanta of atoms and photons [15‐19] in cavity quantum electrodynamics, these works o er intriguing prospects for the next wave of experiments on strongly interacting light-mattter systems including a new regime where unexpected many-body and quantum fluctuation e ects of the lasing medium may become visible. Bohnet et al. [20] recently operated a superradiant “bad-cavity” laser in the few-photon regime based on coherent oscillations of the inter-atomic, collective dipole of the ultracold atoms in the cavity [21]. In this paper, we point out that a quantum degenerate Fermi gas has remarkable features as a lasing medium in a transversally driven cavity as sketched in Fig. 1. We show that the quantum statistics of the Fermi gas puts the coupled cavity+atoms system generically close to superradiance threshold as a consequence of the Pauli exclusion principle (“Pauli pressure”). Physically, this arises from enhanced scattering of fermions between di erent points on the Fermi surface with radiusjkFj by exchanging relatively large photon momenta Q from the cavity as illustrated in Fig. 1. By changing the power of the pump laser at a given density of the Fermi gas, the lasing transition is concomitant with the spontaneous formation of a charge density wave oscillating with 1=Q in real space. Tuning the ratiojkFj=jQj allows to generate a cavity spectrum with “broadband light” in certain spectral ranges or, for energies outside the particle-hole continuum of the fermions, light with relatively narrow linewidth. The normal mode splitting of the cavity by a single atom is completely replaced by many-body Ω |kF| Q
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 derive equations for the strongly coupled system of light and dense atomic ensembles. The formalism includes an arbitrary internal-level structure for the atoms and is not restricted to weak excitation of atoms by light. In the low-light-intensity limit for atoms with a single electronic ground state, the full quantum field-theoretical representation of the model can be solved exactly by means of classical stochastic electrodynamics simulations for stationary atoms that represent cold atomic ensembles. Simulations for the optical response of atoms in a quantum degenerate regime require one to synthesize a stochastic ensemble of atomic positions that generates the corresponding quantum statistical position correlations between the atoms. In the case of multiple ground levels or at light intensities where saturation becomes important, the classical simulations require approximations that neglect quantum fluctuations between the levels. We show how the model is extended to incorporate corrections due to quantum fluctuations that result from virtual scattering processes. In the low-light-intensity limit, we illustrate the simulations in a system of atoms in a Mott-insulator state in a two-dimensional optical lattice, where recurrent scattering of light induces strong interatomic correlations. These correlations result in collective many-atom subradiant and superradiant states and a strong dependence of the response on the spatial confinement within the lattice sites.