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Journal of the Optical Society of America B

Excitation of atoms passing through a TEM_00 Gaussian laser beam at relativistic velocities

C. R. Quick, H. C. Bryant

Published May 1, 1990• 3 citations
Publisher

Abstract

The spectral distribution seen by an atom crossing a monochromatic Gaussian TEM00 beam with a relativistic speed normal to the direction of propagation of the beam is shown to be independent of the distance between the atom’s path and the position of the beam’s minimum waist. The dependence of the transition probability on the beam coordinates is also given. Finally, it is shown that the spectral width can be viewed as being due to the angular distribution of the plane waves of which the Gaussian TEM00 beam is composed.

DOI
10.1364/josab.7.000708

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The spectral distribution seen by an atom crossing a monochromatic Gaussian TEM00 beam with a relativistic speed normal to the direction of propagation of the beam is shown to be independent of the distance between the atom’s path and the position of the beam’s minimum waist. The dependence of the transition probability on the beam coordinates is also given. Finally, it is shown that the spectral width can be viewed as being due to the angular distribution of the plane waves of which the Gaussian TEM00 beam is composed.
There is extensive use of monochromatic lasers to select atoms with a narrow range of velocities in many atomic physics experiments. For the commonplace situation of the inhomogeneous Doppler-broadened (Gaussian) linewidth exceeding the homogeneous (Lorentzian) natural linewidth by typically two orders of magnitude, a substantial narrowing of the velocity class of atoms interacting with the light can be achieved. However, this is not always the case, and here we show that for a certain parameter regime there is essentially no selection – all of the atoms interact with the light in accordance with the velocity probability density. An explanation of this effect is provided, emphasizing the importance of the long tail of the constituent Lorentzian distribution in a Voigt profile.
The model description of the spectral line broadening for atoms crossing the laser beams is presented. The combined effect of the transit-time broadening, natural broadening, and transverse Doppler broadening is considered. This is done by introducing one-parametric adiabatic damping of atom-laser interaction where the particles interact with the laser during a finite time interval. The simplest rectangle distribution of the light intensity inside the laser beam is employed. The dependence of absorption probability on the transit time for different detunings is calculated and compared with earlier results. The limits for using the Lorentz line profile for describing the interaction of fast particles with laser beams are established.
We propose stochastic ray tracing for laser beam propagation in Fresnel diffraction to find the duality between wave and ray representations. We transform from the Maxwell equations to the Schrödinger equation for a monochromatic laser beam in the slowly varying envelope approximation. The stochastic ray tracing method interprets this Schrödinger equation as a stochastic process, of an analogy of Nelson's stochastic mechanics. It can illustrate the stochastic paths and the wavefront of an optical beam. This ray tracing method includes Fresnel diffraction effects naturally. We show its general theoretical construction and numerical tests for a Gaussian laser beam with diffraction, that stochasticity realizes the beam waist around the Rayleigh range.
Abstract A theoretical analysis is presented on the photoexcitation of a macroscopic atomic target by a Hermite–Gaussian (HG) beam within the framework of density matrix theory. Special emphasis is paid to the influence of the incoming HG mode on the population of an excited state and the emitted fluorescence radiation. In particular, a general expression for the alignment parameter of the excited state is derived, which depends on the beam parameters of the HG mode. Although the developed theory can be applied to any atomic system, here the electric dipole transition in neutral sodium atoms is investigated when driven by three , and modes. For this optical (valence‐shell) excitation, it is demonstrated that the population of the excited state is sensitive to the beam waist and the mode index of the HG beam. Furthermore, the influence of beam parameters on the angular distribution and linear polarization of the emitted fluorescence radiation is discussed.
Experimental and theoretical analyses show the effect of laser beam radial intensity distribution on line-shapes and line-widths of the electromagnetically induced transparency (EIT). We used Gaussian and Π (flat top) laser beam profiles, coupling the D1 transition of 87Rb atoms in the vacuum cell in the Hanle experimental configuration. We obtained non-Lorentzian EIT line-shapes for a Gaussian laser beam, while line-shapes for a Π laser beam profile are very well approximated with Lorentzian. EIT line-widths, lower for Gaussian than for Π, show nonlinear dependence on laser intensity for both laser beam profiles. EIT amplitudes have similar values and dependence on laser intensity for both laser beams, showing the maximum at around 0.8 mW cm−2. Differences between the EIT line-shapes for the two profiles are mainly due to distinct physical processes governing atomic evolution in the rim of the laser beam, as suggested from the EIT obtained from the various segments of the laser beam cross-section.
We propose an efficient method of cooling atoms in a strong Gaussian standing wave. The steep gradients of the atomic potential energy give rise to large dipole forces, which can be much stronger than the maximum radiation pressure force and can therefore stop atoms in a much shorter distance. We have simulated the cooling process using a semi-classical Monte- Carlo method, which includes the radial motion, in addition to the motion along the beams. Both motions are calculated directly without separation the dynamics into force and diffusion terms. To cool a large range of atomic velocities the frame in which the standing wave is at rest was swept by changing the frequencies of the counter-propagating beams, in a similar way to the well-known chirp cooling technique using the radiation pressure force. If the curvature of Gaussian beams far from beam waist is employed the radial motion and velocities can be reduced even for the blue detuning comparing to the near waist case. The simulations show that it is possible to stop caesium atoms in a distance of several centimeters (the exact value depends on the laser power, beam waist radius and acceptable chirping force) starting from the most probable velocity at room temperature. Narrower radial and wider axial velocity distribution was obtained for red detuning comparing with the blue one.