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arXiv:2010.09792 · Journal of the Optical Society of America B

Hollow Bessel beams for guiding atoms between vacuum chambers: a proposal and efficiency study

D. Rivero, Vinicius Soares de Angelis, C. Beli, Michelle A. Moreno-Armijos, Leonardo A. Ambrósio, Ph. W. Courteille

Published Jul 15, 2020• 9 citations
arXivHTMLPDF

Abstract

We explore a scheme for guiding cold atoms through a hollow Bessel beam generated by a single axicon and a lens from a two-dimensional magneto-optical trap toward a science chamber. We compare the Bessel beam profiles measured along the optical axis to a numerical propagation of the beam’s wavefront, and we show how it is affected by diffraction during the passage through a long narrow funnel serving as a differential pumping tube between the chambers. We derive an approximate analytic expression for the intensity distribution of the Bessel beam and the dipolar optical force acting on the atoms. By a Monte-Carlo simulation based on a stochastic Runge–Kutta algorithm of the motion of atoms initially prepared at a given temperature, we show that a considerable enhancement of the transfer efficiency can be expected in the presence of a sufficiently intense Bessel beam.

DOI
10.1364/josab.395200

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We explore a scheme for guiding cold atoms through a hollow Bessel beam generated by a single axicon and a lens from a two-dimensional magneto-optical trap toward a science chamber. We compare the Bessel beam profiles measured along the optical axis to a numerical propagation of the beam’s wavefront, and we show how it is affected by diffraction during the passage through a long narrow funnel serving as a differential pumping tube between the chambers. We derive an approximate analytic expression for the intensity distribution of the Bessel beam and the dipolar optical force acting on the atoms. By a Monte-Carlo simulation based on a stochastic Runge–Kutta algorithm of the motion of atoms initially prepared at a given temperature, we show that a considerable enhancement of the transfer efficiency can be expected in the presence of a sufficiently intense Bessel beam.
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The theory of atom guiding in a far blue-detuned hollow laser beam (HLB) is developed for the dipole interaction scheme described by a three-level $\ensuremath{\Lambda}$ model. The complete kinetic description of atomic motion based on the Fokker-Planck equation for the atomic distribution function is presented. The dipole gradient force, radiation pressure force, and momentum diffusion tensor are then derived. It is found that even for a far-detuned laser beam, the optical potential for a three-level $\ensuremath{\Lambda}$ atom is not generally reduced to a sum of two independent potentials associated with the two two-level interactions in the $\ensuremath{\Lambda}$ scheme. The theory developed here is also compared with the experimental guiding of cold 85Rb{}^{85}\mathrm{Rb}85Rb atoms in the HLB. The experimental results are found to be in good agreement with the Monte Carlo simulations based on the three-level $\ensuremath{\Lambda}$ model. We observe that the guiding efficiency depends strongly on the intensity and the detuning of the HLB and the initial temperature of atoms. In particular, the experimental results show that, at small detunings, the guiding efficiency is deteriorated strongly by the radiation pressure force. The Monte Carlo simulations also indicate that the efficiency of guiding versus detuning depends strongly on the direction of the HLB propagation with respect to that of atomic motion. Under optimal conditions, the guiding efficiency was found to be about 20%.
We propose an atomic funnel consisting of a dark hollow, divergent laser beam and an evanescent light in a short micron-sized hollow optical fiber. The cold atoms extracted from a magneto-optical trap experience effective Sisyphus cooling in the dark hollow beam. We calculate the potential barriers for atomic guiding in the evanescent light and the dark hollow beam, and analyze the atomic losses during the guiding and funneling process. Our results show that the equilibrium three-dimensional root-mean-square momentum of about $4.5\ensuremath{\Elzxh}k$ (temperature $\ensuremath{\sim}2.5\ensuremath{\mu}\mathrm{K}$) and the funneling efficiency of about 95% could be obtained. A low-velocity, intense coherent atomic beam can be generated in this funnel scheme and its potential applications in atom optics are briefly discussed.
We present a general theory of atom guiding in a blue-detuned hollow laser beam. Using the dressed-atom approach, we obtain the mean dipole gradient force, the radiation pressure force, and the momentum diffusion coefficients for three-level Λ-type cold atoms. Using Monte Carlo simulation, we calculate the guiding efficiencies and the final velocity distributions of atoms for various conditions. We find that the guiding efficiency depends not only on the intensity and detuning of the guiding hollow beam but also on the atom-guiding direction with respect to the propagation direction of the hollow laser beam. Comparing our analyses with recent experimental results, we find that they are mutually consistent. The results that we present can also be applied to atom guiding by hollow optical fibers.
The main objectives of this thesis were to create and investigate properties and applications of all-optical atomic guides, which are potential building blocks for atom optics experiments. Specifically, we investigated experimentally and theoretically the evolution of the transverse and longitudinal atomic distributions in blue-detuned Bessel tunnels. These tunnels provide confining potentials that are comparable to or higher than the average kinetic energy of cold hundreds of microKelvin) ensembles. The new work highlighted in this thesis include investigations of the following: 1) the generation of Bessel beams using a 2D spatial light modulator (SLM) (both experimental measurement and numerical simulations were performed), 2) the efficiency of the SLM for converting light from a Gaussian beam to a Bessel beam, 3) the behavior of several propagating structures that might be useful for guiding atoms, 4) the atom-tunnel dynamics, 5) an atom switch and delay line (along with measurements of the switch efficiency), and 6) the single-mode propagation in an idealized tunnel. To the best of our knowledge, the work in this thesis constitutes the first time that (1) an atom switch and a delay line have been demonstrated using blue detuned unnels and (2) the atom-tunnel dynamics and thephase-space distribution of a non-interacting dilute gas in a non-equilibrium state has been tracked experimentally.
We propose a scheme for producing and magnifying a hollow beam, as might be desired for purposes of storing and guiding cold atoms, through the use of a simple spherically aberrating lens and a projection lens. The field is a superposition of J0 Bessel fields, so that simple (linear, circular) polarizations can be utilized. analyze some of the beam properties through analytical approximations. Some examples of field zeros along the optical axis are given, together with some of their characteristics. Numerical calculations largely confirm the validity of the analytical expressions. For the most important zero nearly all of the beam power is contained within the first two Bessel spacings, with a resulting highly efficient trapping. Isophotes are calculated and displayed for the region surrounding this null point. They have regular shapes, for which we give an approximate expression.