Superradiance has drawn increasing interest, motivated by the development of quantum technology. In general, a large number of atoms are favored for inducing a strong superradiance. However, our analytical and numerical calculations of light scattering from an atomic grating longitudinally pumped by a laser show that when the atom number is small, superradiant light scattering (SLS) is induced, that is, the reflected light intensity is proportional to the square of the atom number, whereas the SLS is saturated with the increase in the atom number. In our calculation, using the coupled-wave theory, we treat the atomic grating as a dynamical photonic crystal and find rich time-dependent optical properties due to collective atomic recoil motion, which is available within research under current experimental condition. Thus, our paper could also spark an investigation of the optical features of tunable photonic crystals in the time domain.
Superradiance has drawn increasing interest, motivated by the development of quantum technology. In general, a large number of atoms are favored for inducing a strong superradiance. However, our analytical and numerical calculations of light scattering from an atomic grating longitudinally pumped by a laser show that when the atom number is small, superradiant light scattering (SLS) is induced, that is, the reflected light intensity is proportional to the square of the atom number, whereas the SLS is saturated with the increase in the atom number. In our calculation, using the coupled-wave theory, we treat the atomic grating as a dynamical photonic crystal and find rich time-dependent optical properties due to collective atomic recoil motion, which is available within research under current experimental condition. Thus, our paper could also spark an investigation of the optical features of tunable photonic crystals in the time domain.
A semi-classical theory of coherent light scattering from an elongated sample of cold atoms exposed to an off-resonant laser beam is presented. The model, which is a direct extension of that of the collective atomic recoil laser (CARL), describes the emission of two superradiant pulses along the sample's major axis simultaneous with the formation of a bidimensional atomic grating inside the sample. It provides a simple physical picture of the recent observation of collective light scattering from a Bose-Einstein condensate [S. Inouye et al., Science N.285, p. 571 (1999)]. In addition, the model provides an analytical description of the temporal evolution of the scattered light intensity which shows good quantitative agreement with the experimental results of Inouye et al.
Cooperative scattering has been the subject of intense research in the last years. In this article, we discuss the concept of cooperative scattering from a broad perspective. We briefly review the various collective effects that occur when light interacts with an ensemble of atoms. We show that some effects that have been recently discussed in the context of ‘single-photon superradiance’, or cooperative scattering in the linear-optics regime, can also be explained by ‘standard optics’, i.e. using macroscopic quantities such as the susceptibility or the diffusion coefficient. We explain why some collective effects depend on the atomic density, and others on the optical depth. In particular, we show that, for a large and dilute atomic sample driven by a far-detuned laser, the decay of the fluorescence, which exhibits superradiant and subradiant dynamics, depends only on the on-resonance optical depth. We also discuss the link between concepts that are independently studied in the quantum-optics community and in the mesoscopic-physics community. We show that the coupled-dipole model predicts a departure from Ohm’s law for the diffuse light, that incoherent multiple scattering can induce a saturation of fluorescence and we also show the similarity between the weak-localization correction to the diffusion coefficient and the inaccuracy of Lorentz local field correction to the susceptibility.
Due to its coherence properties and high optical depth, a Bose–Einstein condensate [BEC] provides an ideal setting to investigate collective atom-light interactions. Superradiant light scattering [SLS] in a BEC is a fascinating example of such an interaction. It is an analogous process to Dicke superradiance, in which an electronically inverted sample decays collectively, leading to the emission of one or more light pulses in a well-defined direction. Through time-resolved measurements of the superradiant light pulses emitted by an end-pumped BEC, we study the close connection of SLS with Dicke superradiance. A 1D model of the system yields good agreement with the experimental data and shows that the dynamics result from the structures that build up in the light and matter-wave fields along the BEC. This paves the way for exploiting the atom–photon correlations generated by the superradiance.
We propose an alternative formulation for atomic side mode dynamics from superradiant light scattering of trapped atoms. A detailed analysis of the recently observed superradiant light scattering from trapped Bose gases [S. Inouye et al., Science 285, 571 (1999)] is presented. We find that scattered light intensity can exhibit both oscillatory and exponential growth behaviors depending on densities, pump pulse characteristics, temperatures, and geometric shapes of trapped gas samples. The total photon scattering rate as well as the accompanying matter wave amplification depend explicitly on atom number fluctuations in the condensate. Our formulation allows for natural and transparent interpretations of subtle features in the experimental data, and provides numerical simulations in good agreement with most important aspects of the experimental observations.
A theory of coherent light scattering from an elongated Bose-Einstein condensate exposed to an off-resonant laser beam is presented. The model describes the emission of two superradiant pulses along the sample's major axis simultaneous with the formation of a bidimensional atomic grating inside the sample, as was observed in a recent MIT experiment [Inouye, S. et al., 1999, Science, 285, 571]. We predictions of the semiclassical model, in which the atomic motion is treated classically, are compared with these of the quantum model, obtained including the quantum mechanical description of the atomic motion. In the quantum limit the superradiant regime becomes a sequential process, in which during each collective scattering atoms emit a it hyperbolic secant pulse and populate an adjacent momentum state.
The interaction of light with an atomic sample containing a large number of particles gives rise to many collective (or cooperative) effects, such as multiple scattering, superradiance, and subradiance, even if the atomic density is low and the incident optical intensity weak (linear optics regime). Tracing over the degrees of freedom of the light field, the system can be well described by an effective atomic Hamiltonian, which contains the light-mediated dipole-dipole interaction between atoms. This long-range interaction is at the origin of the various collective effects, or of collective excitation modes of the system. Even though an analysis of the eigenvalues and eigenfunctions of these collective modes does allow distinguishing superradiant modes, for instance, from other collective modes, this is not sufficient to understand the dynamics of a driven system, as not all collective modes are significantly populated. Here, we study how the excitation parameters, i.e., the driving field, determines the population of the collective modes. We investigate in particular the role of the laser detuning from the atomic transition, and demonstrate a simple relation between the detuning and the steady-state population of the modes. This relation allows understanding several properties of cooperative scattering, such as why superradiance and subradiance become independent of the detuning at large enough detuning without vanishing, and why superradiance, but not subradiance, is suppressed near resonance. We also show that the spatial properties of the collective modes allow distinguishing diffusive modes, responsible for radiation trapping, from subradiant modes.