STIMULATED RAMAN AND RAYLEIGH SPECTROSCOP Y OF ONE-DIMENSIONAL OPTICAL MOLASSES .1.

In this paper, we present a detailed theoretical investigation of the transmission spectra of a weak probe beam through one-dimensional opti cal molasses in the so-called lin perpendicular to lin and sigma(+) - sigma(-) laser configurations. We show that the resonant structures di splayed by the spectra in both situations can be interpreted in terms of stimulated Raman or Rayleigh scattering and that they provide impor tant information about the physical properties of the molasses. The pa per is divided into two main parts. In order to emphasize the specific ity of the stimulated scattering processes taking place in optical mol asses, we present in a first part the main characteristics of the stim ulated Raman and Rayleigh processes occurring in conventional atomic a nd molecular media. Section 2 is devoted to stimulated Raman scatterin g, which is associated with the presence of scattering particles havin g differently populated nondegenerate states. In the case of atomic va pours, which is traditionnally not discussed in textbooks, we demonstr ate the occurrence of stimulated Raman transitions between differently populated and light shifted ground state Zeeman sublevels, which mani fest themselves on pump-probe transmission spectra in the form of Lore ntzian resonances having a width of the order of the optical pumping r ate. Section 3 presents a more detailed study of stimulated Rayleigh s cattering, which is associated with the modulation of nonpropagating o bservables (i.e., of observables whose dynamics does not contain any e igen evolution frequency) by the interference pattern between a probe and a pump field, and with the existence of a physical mechanism respo nsible for a phase shift between the time and spatial modulation of th e observables and the pump-probe excitation. By considering the most g enerally encountered situation where the phase shift arises from a rel axation mechanism taking place in the material medium, and where stimu lated Rayleigh scattering manifests itself in the form of a dispersive resonance having a width equal to twice the associated relaxation rat e, we identify three classification criteria for the stimulated Raylei gh mechanisms, involving the characteristics of the scattering medium, of the relaxation process occurring in the medium, and of the excitat ion mechanism of the medium by the probe field, respectively. This cla ssification scheme is then employed on the one hand in the case of den se molecular media, where stimulated Rayleigh-wing scattering (associa ted with the laser-induced orientation of anisotropic molecules) is di scussed, together with the so-called electrostrictive and thermodiffus ive Rayleigh scattering mechanisms (related to a spatial modulation of the molecular density); and on the other hand in the case of dilute a tomic vapours, where one distinguishes between two-level atoms (for wh ich the Rayleigh resonance is interpreted in terms of quantum interfer ence between photon scattering processes), and multilevel atoms (where stimulated Rayleigh scattering involves optical pumping induced relax ation of internal observable modulations). The second part of the pape r is devoted to the investigation of the stimulated Raman and Rayleigh processes taking place in one-dimensional optical molasses. These pro cesses exhibit outstanding characteristics because of the entanglement between internal and external degrees of freedom of the atoms, which is an intrinsic feature of the cooling mechanisms. Section 4 discusses the case of lin perpendicular to lin molasses. We restrict ourselves to the situation of a J(g) = 1/2 --> J(e) = 3/2 atomic transition, and to the limit where the dissipative part of the atom-laser coupling is negligible compared to the Hamiltonian part (oscillating regime of Si syphus cooling). We first consider stimulated Raman processes between quantized vibrational states of the atoms at the bottom of the optical potential wells associated with the light shifts of the ground state Zeeman sublevels, and we demonstrate the occurrence of a lengthening o f the lifetime of the coherences between the vibrational levels due to the strong spatial atomic localization (Lamb-Dicke effect). Stimulate d Rayleigh resonances sensitive to the probe polarization are also pre dicted in the center of the spectra. These structures are interpreted in terms of diffraction of the cooling beams onto time-modulated densi ty or magnetization gratings induced by the probe beam, and we show th at these resonances provide information about the dynamical properties of the medium and the anti-ferromagnetic spatial order of the atoms i n the,molasses. indications about the treatment of atomic transition h aving larger angular moments are given by considering more particularl y the situation of the J(g) = 4 --> J(e) = 5 transition of cesium, for which an inversion of the stimulated Rayleigh resonance is predicted, which is related to the resonant variation of the populations of the vibrational levels with the otpical potential depth. Section 5 is devo ted to the case of the sigma(+) - sigma(-) molasses. We consider the c ase of a J(g) = 1 --> J(e) = 2 atomic transition, and me restrict ours elves to the Limit where the steady-state momentum distribution lies w ithin the linearity range of the cooling force. Under such conditions, it is possible to account for the external atomic dynamics through a Fokker-Planck equation derived by adiabatically eliminating the atomic internal degrees of freedom. One investigates on the one hand the sti mulated Raman processes taking place between the ground state Zeeman s ublevels, indicating the occurrence of differences in the populations and Light shifts in the ground state, and on the other hand the stimul ated Rayleigh processes providing information about the dynamics of th e external degrees of freedom. One considers two polarization configur ations for the probe beam; depending on the probe polarization's being identical or opposite to the circular polarization of the copropagati ng pump beam. In the former case, it is shown that the stimulated Rama n lines are homogeneously broadened, and that a stimulated Rayleigh st ructure appears on the spectra because of the probe-induced time modul ation of the cooling force, which induces a modulation of the atomic m omentum distribution. In the latter situation, the Raman structures ar e inhomogeneously broadened, and a recoil-induced resonance is predict ed in the center of the spectrum. Its shape corresponds to t