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Physica Scripta

Bessel beams of laser-driven two-level atoms

Armen G. Hayrapetyan, S. Fritzsche

Published Sep 1, 2013• 5 citations
Publisher

Abstract

We study Bessel beams of two-level atoms that are coupled to a linearly polarized laser field. For such atom beams, we construct exact Bessel-type solutions of the Schrodinger equation beyond the paraxial approximation for beam propagation. In particular, we examine the probability density for Bessel beams of neutral two-level atoms driven by a laser field but without the level damping being taken into account. We show how the radial dependence of the probability density (from the beam axis) can be affected by tuning the parameters of the atom–laser system, such as the resonant frequency and amplitude of the laser field and/or the nuclear charge and velocity of the atomic beam.

DOI
10.1088/0031-8949/2013/t156/014067

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We study Bessel beams of two-level atoms that are coupled to a linearly polarized laser field. For such atom beams, we construct exact Bessel-type solutions of the Schrodinger equation beyond the paraxial approximation for beam propagation. In particular, we examine the probability density for Bessel beams of neutral two-level atoms driven by a laser field but without the level damping being taken into account. We show how the radial dependence of the probability density (from the beam axis) can be affected by tuning the parameters of the atom–laser system, such as the resonant frequency and amplitude of the laser field and/or the nuclear charge and velocity of the atomic beam.
Atomic beam focusing by a gradient (dipole) force of the near resonant first order Bessel beam is considered in the paraxial approximation. The first order Bessel beam (J1) is a nondivergent laser beam whose intensity profile is the square of the first-order Bessel function of the first kind. A co-propagating J1 beam, tuned above resonance, provides the minimum rate of spontaneous emission on axis where the intensity is minimum. It has a steeper intensity gradient and a longer interaction range than does TEM01*. Numerical results for the focal length and the atomic beam density distribution in the focal plane are presented. Focusing limitations due to aberrations are discussed. The results are compared with those of the TEM01* mode beam.
An effect of phase fluctuations of a driving laser field on dissipative and dipolar forces of two-level atom is considered. The phase fluctuations are treated by a phase diffusion model where phase fluctuations follow Wiener–Levy process. An exact master equation for the relevant density operator is obtained and solved in the steady state. Optical forces are calculated. The effect of phase fluctuations on angular momentum imparted by a Laguerre–Gaussian beam and an ideal Bessel beam to the atom is investigated.
We report a study on light force on a beam of neutral two-level atoms superimposed upon a few-cycle-pulse Gaussian laser field under both resonant and off-resonant conditions. The phenomena of focusing, defocusing, and steering of the neutral atoms in the laser field are analyzed by solving the optical Bloch equation beyond the rotating-wave approximation and the force equation self-consistently. We find that two-level atoms in an atomic beam can be focused and defocused for large, positively and negatively detuned interactions even in the regime of extreme nonlinear optics. The so-called optical potential may be used for stable trapping of the neutral two-level atoms for large positively detuned interaction. This work successfully reproduces some of the features reported in recent experimental and theoretical works.
In this paper we report on the study of two and multi-level atoms interacting with multiple laser beams. The semi-classical approach is used to describe the system in which the atoms are treated quantum mechanically via the density matrix operator, while the laser beams are treated classically using Maxwells equations. We present results of a two level atom interacting with single and multiple laser beams and demonstrate Rabi oscillations between the levels. The effects of laser modulation on the dynamics of the atom (atomic populations and coherences) are examined by solving the optical Bloch equations. Plots of the density matrix elements as a function of time are presented for various parameters such as laser intensity, detuning, modulation etc. In addition, phase-space plots and Fourier analysis of the density matrix elements are provided. The atomic polarization, estimated from the coherence terms of the density matrix elements, is used in the numerical solution of Maxwells equations to determine the behaviour of the laser beams as they propagate through the atomic ensemble. The effects of saturation and hole-burning are demonstrated in the case of two counter propagating beams with one being a strong beam and the other being very weak. The above work is extended to include four-wave mixing in four level atoms in a diamond configuration. Two co-propagating beams of different wavelengths drive the atoms from a ground state |1〉 to an excited state |3〉 via an intermediate state |2〉. The atoms then move back to the ground state via another intermediate state |4〉, resulting in the generation of two additional correlated photon beams. The characteristics of these additional photons are studied.
The motion of neutral, polarizable atoms (also called neutral particles in this work) in the field of the Bessel beam is considered. It is shown in the numerical way that the Bessel rings, i.e., the regions of high energy concentration, can trap particles of positive polarizability (atoms in red-detuned beams). This trapping occurs only in the plane perpendicular to the wave propagation, and the motion along the beam is unrestricted. When the beam is superposed with the plane wave of the same frequency propagating in the same direction, the particles are guided along helices, fixed in space. The shape of these helices depends on the parameters characterizing the electromagnetic fields but not on the initial state of guided particles. Depending on the vorticity of the Bessel beam, these helices can be made left- or right-handed. In the special case of zero vorticity, the helices are degenerated to the true, three-dimensional rings, which can serve as three-dimensional traps. The emerging structure of potential valleys can be applied to parallel guidance or capture several independent atoms, each in its own trap.