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ACTA PHOTONICA SINICA

Quantum Analysis of ~(23)Na Atoms Deposition in the Gaussian Laser Standing Wave Field

Tongbao Li

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

The effect of a Gaussian laser standing wave on 23Na atoms was simulated by CRANK-NICOLSON numerical algorithm based on quantum-mechanical method.It was found that atoms focus on wave nodes in standing wave light field with a period of λ/2 when the laser is positive-detuned.The focusing results are in accord with thin lens regime,thick lens regime and channeling regime,respectively,as the optical potential is deepened or the longitudinal velocity of atoms is increased.In thick lens regime,the focal plane shifts backward and the full width at half maximum(FWHM)increases,along the z direction,as the atomic longitudinal velocity increases.With increasing laser power or decreasing beam waist,the FWHM of atomic density peak at the focal plane decreases,both the peak value and the contrast increase.

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The effect of a Gaussian laser standing wave on 23Na atoms was simulated by CRANK-NICOLSON numerical algorithm based on quantum-mechanical method.It was found that atoms focus on wave nodes in standing wave light field with a period of λ/2 when the laser is positive-detuned.The focusing results are in accord with thin lens regime,thick lens regime and channeling regime,respectively,as the optical potential is deepened or the longitudinal velocity of atoms is increased.In thick lens regime,the focal plane shifts backward and the full width at half maximum(FWHM)increases,along the z direction,as the atomic longitudinal velocity increases.With increasing laser power or decreasing beam waist,the FWHM of atomic density peak at the focal plane decreases,both the peak value and the contrast increase.
A grating structure with period of half of the laser wavelength generated by focusing Cr atoms with nearly resonant laser standing wave atom lens was simulated using a quantum-mechanical model.The influence of thermal atomic source on atom focusing,including the statistical distribution of the longitudinal veloc- ity and the beam divergence,was discussed.The background and full-width at half-maximum （FWHM） of atomic density peaks with vz in Maxwell distribution and vx0 in Gaussian distribution increase sig- nificantly compared with ideal atoms.Collimating atoms with laser cooling is necessary to decrease the peak broadening.更多还原
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The focusing of atoms after interacting with both far-detuned and resonant standing wave fields in the thin-lens regime is considered. Exact quantum expressions for the Fourier components of the density (that include all spherical aberration) are used to study the focusing numerically. The following lens parameters and density profiles are calculated as functions of the pulsed field area $\ensuremath{\theta}:$ the position of the focal plane, peak atomic density, atomic density pattern at the focus, focal spot size, depth of focus, and background density. The lens parameters are compared to asymptotic, analytical results derived from a scalar diffraction theory for which spherical aberration is small but non-negligible $(\ensuremath{\theta}\ensuremath{\gg}1).$ Within the diffraction theory analytical expressions show that the focused atoms in the far-detuned case have an approximately constant background density $0.5(1\ensuremath{-}0.635{\ensuremath{\theta}}^{\ensuremath{-}1/2})$ while the peak density behaves as $3.83{\ensuremath{\theta}}^{1/2},$ the focal distance as ${\ensuremath{\theta}}^{\ensuremath{-}1}(1+1.27{\ensuremath{\theta}}^{\ensuremath{-}1/2})$ ${L}_{T}/2\ensuremath{\pi},$ the depth of focus as ${0.304L}_{T}{\ensuremath{\theta}}^{\ensuremath{-}3/2},$ and the focal spot size $0.0592\ensuremath{\lambda}{\ensuremath{\theta}}^{\ensuremath{-}3/4},$ where LT{L}_{T}LT​ is the Talbot distance and \ensuremath{\lambda} is the wavelength of the light. Focusing by the resonant standing wave field leads to a new effect, a Rabi-like oscillation of the atom density. For the far-detuned lens, chromatic aberration is studied quantitatively with the exact Fourier results. Similarly, the degradation of the focus that results from angular divergence in beams or thermal velocity distributions in traps is studied quantitatively with the exact Fourier method and understood analytically using the asymptotic results. Overall, we show that strong thin-lens focusing is possible with modest laser powers and with currently achievable atomic beam characteristics.
The two-level atom focusing in a Gaussian standing wave laser field was analyzed from the perspective of both classical mechanics and wave mechanics. The effects of source imperfection such as velocity spread and beam spread on atom focusing were analyzed by numerically integrating the classical equation of atomic motion. The ideal focal plane can be easily determined by the variation of atomic density at the minimal potential of the standing wave laser field as a function of traveling distance. In the absence of source imperfection, the contribution of diffractive aberration originating from the wave nature of the atom to broadening of feature width is larger than that of spherical aberration. Several methods for improving atom lithography experiments were presented.