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Journal of Experimental and Theoretical Physics

Rectification of the dipole force in a monochromatic field created by elliptically polarized waves

Прудников Олег Николаевич, А. В. Тайченачев, Anatolii M Tumaikin, Valeriy I. Yudin

Published Jul 1, 2001• 3 citations
Publisher

Abstract

The rectification of the force of induced light pressure in laser fields formed by elliptically polarized running waves in zero magnetic field is considered. Explicit analytic expressions for the induced and spontaneous forces of light pressure exerted on a stationary atom are obtained for two classes of closed optical transitions: J g = J → J e = J +1 and J g = J → J e = J ( J is half-integral), where J g and J e are the total angular momenta of the ground and excited energy levels. It is shown that the ellipticity of waves is the necessary condition for the emergence of the rectification of the induced force in a monochromatic field. The optimal parameters of the field and the maximum rectification coefficient are calculated for a number of optical transitions. The dependence of the rectified force on the velocity is investigated analytically and numerically for the simplest 1/2→1/2 transition.

DOI
10.1134/1.1391520

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The rectification of the force of induced light pressure in laser fields formed by elliptically polarized running waves in zero magnetic field is considered. Explicit analytic expressions for the induced and spontaneous forces of light pressure exerted on a stationary atom are obtained for two classes of closed optical transitions: J g = J → J e = J +1 and J g = J → J e = J ( J is half-integral), where J g and J e are the total angular momenta of the ground and excited energy levels. It is shown that the ellipticity of waves is the necessary condition for the emergence of the rectification of the induced force in a monochromatic field. The optimal parameters of the field and the maximum rectification coefficient are calculated for a number of optical transitions. The dependence of the rectified force on the velocity is investigated analytically and numerically for the simplest 1/2→1/2 transition.
The dependence of the magnetooptical force on the ellipticity of the polarization of light beams is studied in terms of a one-dimensional model for closed J g → J e optical transitions. A linear velocity and magnetic-field approximation is used to find analytical expressions for the magnetooptical force for a number of transitions. In the light fields formed by waves with an elliptical polarization, qualitatively new contributions are shown to appear; they have an even dependence on the detuning of the light field and do not disappear even in the case of an exact resonance. An analysis of these results demonstrates that a magnetooptical trap can stably operate at the zero detuning of the field. Numerical methods are used to investigate the nonlinear dependence of the force on the atom velocity and the magnetic field and to estimate the characteristic atom trapping rate and the number of trapped atoms.
In a one-dimensional model we consider the dependence of the magneto-optical force on the elliptical polarization of laser beams for different types of closed atomic transitions ${J}_{g}\ensuremath{\rightarrow}{J}_{e}$. The linear dependencies on atomic velocity and magnetic field of the magneto-optical force are found analytically. These results establish the possibility (for Jg>0{J}_{g}>0Jg​>0) to capture atoms in a magneto-optical trap even at zero detuning (i.e., at the exact resonance of atoms with laser field) in certain $(ϵ\ensuremath{-}\ensuremath{\theta}\ensuremath{-}\overline{ϵ})$ field configurations as well as in an anomalous blue-detuned region. The nonlinear dependencies of the force on atomic velocity and magnetic field are studied numerically. The capture velocity and the number of trapped atoms are estimated.
The kinetics of atoms with degenerate energy levels in the field produced by elliptically polarized waves is considered in the semiclassical approximation. Analytic expressions for the force acting on an atom and for the diffusion coefficient in the momentum space are derived for the optical transition J g =1/2→J e = 1/2 in the slow atom approximation. These expressions are valid for an arbitrary one-dimensional configuration of the light field and for an arbitrary intensity. The peculiarities of the atomic kinetics are investigated in detail; these peculiarities are associated with ellipticity of light waves and are absent in particular configurations formed by circularly or linearly polarized waves, which were considered earlier.
The light force on slow atoms in a light field with arbitrary polarization distribution is explicitly evaluated in the case of an atomic transition J yields J with half-integer J values. The expression of the force is based on an exact analytical expression for the steady-state density matrix of the atoms. The force is naturally separated in contributions resulting from gradients of the field intensity, the polarization ellipticity, and the phase. In addition to a conservative part this force also contains a vortex component. In areas of spatial localization, where the total force vanishes, the atomic motion is governed by a potential, which in general is not harmonic for J greater than 1/2. Simple model of the formation of a one- or two-dimensional spatial atomic grating in a specific light field configuration illustrates the results.
A radiation-pressure force, changing only slightly within the wavelength of light (rectification effect), has been shown to arise in interfering fields. In a monochromatic field a rectified force (RF) has the scale of a spontaneous light-pressure force, and it is mainly a vortex one. In a bichromatic field the RF has the order of magnitude of the induced light-pressure force and does saturate in a strong field. The spatial RF structure can be either potential or rotational. The depth of the potential wells generated by the RF can exceed by several orders of magnitude the energy of the atom–field interaction, and it can reach 10 K and larger. A vortex periodic RF results either in regular rotating motion or in a random walk of atoms along the boundaries of elementary cells of the force field. Possible applications of the RF are discussed.
Abstract Electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA) resonances excited by a strong two-frequency field are considered for various values of the total angular momenta of the ground (F g) and excited (F e) states at a degenerated optical closed transition F g → F e. The light field is formed by two co-propagating waves with arbitrary elliptical polarisations. The process of spontaneous transfer of anisotropy from the excited state to the ground state is shown to determine the formation of the EIA resonance at the transition F g = F → F e = F + 1. The results obtained generalise the classification of transitions into ‘bright’ (F g = F → F e = F + 1) and ‘dark’ (F g = F → F e = F and F g = F → F e = F – 1) transitions with respect to the direction of a subnatural resonance.