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Journal of the Optical Society of America B

Rectification effect of a radiation force

A. P. Kazantsev, Lev Davidovič Landau, I. V. Krasnov

Published Nov 1, 1989• 67 citations
Publisher

Abstract

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.

DOI
10.1364/josab.6.002140

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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.
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.
Rectified dipole forces1 offer the possibility of providing deep potential wells for neutral atoms. In the intense standing wave, a two-level atom can experience a large dipole force due to the large intensity gradient. However, this force changes sign on the optical wavelength scale, preventing the formation of deep potential wells. If a second, nearly commensurate, standing wave is added, its ac Stark shift causes the effective detuning of the first field to vary on the optical wavelength scale. The resulting change in sign of the detuning can counteract the change in sign of the intensity gradient, causing the force to maintain its sign over many wavelengths (i.e., the force becomes rectified), thereby forming a deep potential well. This rectified force is periodic with the beat wavelength between the two laser fields. In a three-level atom the same basic mechanism applies, but with the advantage that the two frequencies of the bichromatic standing wave can now be tuned dose to resonance with the two transitions of the atom.
Explicit expressions are derived for the rectified radiative forces (RRFs) related to the action of a weak interfering optical field of an arbitrary three-dimensional (3D) configuration upon resonance particles featuring the J =0 → J =1 quantum transition. It is shown that, in contrast to the case of a monochromatic field, there are simple 3D biharmonic field configurations for which the ratio of the vortex and potential RRF components can be controlled by adjusting frequencies and polarizations of the interfering light waves. This modification of the RRF structure gives rise to qualitatively different types of both vortex and potential light-induced particle motions that may lead to a 3D spatial localization (confinement) of these particles within the cells of an effective optical lattice with a period significantly greater than the light wavelength. In particular, the particles may perform a stable rotational motion along closed trajectories inside the elementary cells.
A new three-dimensional scheme for rectifying a gradient force is proposed and analyzed. The scheme is based on the use of a strong, partially coherent optical field involving a component with a fluctuating phase. It is shown that the rectification of a gradient force acting on atoms with a nondegenerate ground state is a second-order effect with respect to field strength in this scheme, whereas an analogous effect is third-order in coherent bichromatic fields. Conditions for three-dimensional confinement of atoms are obtained by using the velocity dependence of the rectified radiative force. For a large class of atoms, such as even-even isotopes of ytterbium and alkaline-earth elements, these conditions can be implemented at a relatively high effective temperature (of the particle ensemble) of about 10 K. This finding can be used to widen substantially the range of energies of atoms amenable to effective three-dimensional optical manipulation.
The bichromatic force is a coherent optical force that has been demonstrated to exceed the saturated radiative force from a monochromatic cw laser by orders of magnitude in atomic systems. By stimulating photon emission between two states, the bichromatic force allows us to increase the photon scattering rate beyond the spontaneous emission rate while also suppressing decays into dark states. We present studies of the efficacy of the bichromatic force on molecular systems using the test cases of BBB-XXX (0,0), P11(1.5)/PQ12(0.5)P_{11}(1.5)/^PQ_{12}(0.5)P11​(1.5)/PQ12​(0.5) in CaF and A~\tilde{A}A~(000)−X~-\tilde{X}−X~(000), P11(1.5)/PQ12P_{11}(1.5)/^PQ_{12}P11​(1.5)/PQ12​(0.5) in the linear triatomic molecule SrOH. Computational results from detailed multilevel models indicate that both of these molecular systems are suitable for the use of the bichromatic force, with neither repumping nor magnetic destabilization of dark states interrupting the coherent cycling at the heart of the force. We comment on the applicability of the bichromatic force to arbitrary polyatomic molecules, and present our experimental progress in demonstrating the bichromatic force on CaF and possibly on SrOH.\footnote{Supported by the National Science Foundation.}