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Physical Review A

Calculating the diffusion coefficient for laser cooling of atoms with long-range collisions

Andrew M. Smith II, Keith R. Burnett, J. Cooper

Published Oct 1, 1992• 4 citations
Publisher

Abstract

A calculation of the collisional diffusion coefficient is made which estimates the effect of collisions in an optical trap. The theory is based on the method of Gordon and Ashkin [Phys. Rev. A 21, 1606 (1980)] and incorporates the equations derived by Smith and Burnett [J. Opt. Soc. Am. B 8, 1592 (1991)] to describe the interaction of two two-level atoms in a laser field. Results are obtained by using a nearest-neighbor model for the collisions and suggest a definite relationship between atomic density and collisional diffusion.

DOI
10.1103/physreva.46.4065

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This research aimed to study the friction and diffusion coefficients of neutral atoms that moving and interact with a laser field .The Mathcad 14 program used to calculate the results. The theoretical model was solved and shown the effect of different optical parameters on the diffusion and friction of neutral atoms .The different values of ellipticity (Ɛ) were used to find the friction and diffusion coefficients ,for each value of ellipticity we found that the relationship between the natural width of excited level( γ) and the difference(δ) between the frequency of laser field(ω) and the atomic resonance (ω0 ) has strong effect on the friction coefficient of atoms .The effect of Rabi frequency (Ω ) on the diffusion coefficient has been investigated .In this research the results showed that each of the parameters δ and Ω has effect on the diffusion of atom and the Rabi frequency has more influence. The dependence of the friction and diffusion coefficients on the natural width of the excited level was studied. The measuring of the friction and diffusion coefficients of atom very important to control the movement and then localize it, this have many applications in physics fields.

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Journal of the Optical Society of America B•Oct 1, 1985•13 citations
A calculation of the collisional diffusion coefficient is made which estimates the effect of collisions in an optical trap. The theory is based on the method of Gordon and Ashkin [Phys. Rev. A 21, 1606 (1980)] and incorporates the equations derived by Smith and Burnett [J. Opt. Soc. Am. B 8, 1592 (1991)] to describe the interaction of two two-level atoms in a laser field. Results are obtained by using a nearest-neighbor model for the collisions and suggest a definite relationship between atomic density and collisional diffusion.
An extension to a previous model [ J. Opt. Soc. Am. B8, 1594 ( 1991)], which described the collision between two atoms in a cooling laser field, is made, which allows diffusive effects to be analyzed. A method similar to that used in Monte Carlo studies is developed, except that the diffusion is now determined exactly at all times. This approach relies directly on making a local classical path approximation for the atoms’ trajectories. For the simple case of a single two-level atom in the cooling field, the energy of the atom reaches equilibrium at the Doppler limit, as one would expect. In the full collisional situation we make the assumption that each atom undergoes a series of binary collisions. For sufficiently high atomic densities these collisions provide a limit on the lowest temperature that may be achieved by the cooling process.
A theory to describe collisions between pairs of atoms that are being cooled by a laser field is presented. The derivation uses the Heisenberg picture and results in a set of coupled optical Bloch equations and associated equations for the translational motion. By defining a correlation variable between the two atoms, we obtain a system of linear equations that may be solved numerically. If the interaction is ignored, the usual cooling curve is obtained: In the full simulation it is found that long-range collisions (0.1ƛ → 10ƛ) can significantly alter the atomic velocities. Depending on how the atoms approach each other, there are various effects: jumps in velocity at the center of the collision, interruptions of the cooling cycle, and signs of collective effects for long-range collisions. If the atom density is sufficiently large and the atoms are moving slowly, these collisional mechanisms may prevent any further cooling.
An analytical description of long-range collisions between atoms in a laser cooling field is developed. We begin by considering an N-atom master equation. In the regime of low atomic densities (i.e., where the mean distance between two atoms is much larger than the laser wavelength) it is possible to treat the atom-atom interactions in perturbation theory. Furthermore we assume temperatures which allow a semiclassical treatment of the cooling process. The effect of the presence of other atoms can be separated analytically into two parts; an attenuation force due to the absorption of the laser beams in the atomic cloud similar to the results of Dalibard [Opt. Commun. 68, 203 (1988)], which tends to compress the atomic cloud, and a two-atom force due to photon emission and absorption cycles between different atoms. This force proves to be repulsive for the configurations studied and prevents the cloud from collapsing. The result for the first-order perturbation expansion in collision strength generalizes the model proposed by Walker, Sesko, and Wieman [J. Opt. Soc. B 8, 946 (1991)] by including additional terms, such as those associated with Raman couplings.
This research aimed to study the friction and diffusion coefficients of neutral atoms that moving and interact with a laser field .The Mathcad 14 program used to calculate the results. The theoretical model was solved and shown the effect of different optical parameters on the diffusion and friction of neutral atoms .The different values of ellipticity (Ɛ) were used to find the friction and diffusion coefficients ,for each value of ellipticity we found that the relationship between the natural width of excited level( γ) and the difference(δ) between the frequency of laser field(ω) and the atomic resonance (ω0 ) has strong effect on the friction coefficient of atoms .The effect of Rabi frequency (Ω ) on the diffusion coefficient has been investigated .In this research the results showed that each of the parameters δ and Ω has effect on the diffusion of atom and the Rabi frequency has more influence. The dependence of the friction and diffusion coefficients on the natural width of the excited level was studied. The measuring of the friction and diffusion coefficients of atom very important to control the movement and then localize it, this have many applications in physics fields.
An analytical description of the collisions between atoms in a laser cooling field is developed. The results confirm predictions made in our recent numerical simulations for the same model. The effect of the collision can be separated analytically, to first order in a perturbation expansion in collision strength, into two parts. The first of these parts comes from the interruption of the laser cooling cycle in each atom, and the second from the direct force resulting from a photon exchange between the atoms.
Cross correlation refers to the situation in which the fluctuations in the fields of two or more lasers are correlated in some way. Recently, Thomas et al. [ Opt. Lett.6, 298 ( 1981); Phys. Rev. Lett.48, 867 ( 1982)] proposed the generation of cross correlation between two laser fields interacting with a three-level system as a means of reducing noise and went on to exploit this property in the observation of narrow Ramsay fringes. Dalton and Knight [ J. Phy. B15, 3997 ( 1982)] discussed the theoretical aspects of cross correlation and showed that it produced interesting effects in population trapping for example. We have demonstrated that it has significant effects on the optical double-resonance (ODR) spectra [ J. Phys. B17, L389 ( 1984)]. On the other hand, the effects of non-Lorentzian laser line shapes have been shown by various workers to have significant effects on a wide range of phenomena, such as multiphoton ionization, resonance fluorescence, and ODR. In this paper we present a theory of the interactions of lasers whose fluctuations are governed by the phase-diffusion process with atomic systems that includes the effects of cross correlation and non-Lorentzian line shapes. We derive the basic equations (which in general have to be solved numerically) and obtain analytic results in the case in which the line shape is approximately Lorentzian near line center but falls off faster than a Lorentzian in the wings. We believe that this analytic model shows all the essential features of the interplay between cross correlation and non-Lorentzian line shapes. The theory is applied to the ODR experiment. In particular, we find that the asymmetry of the spectra is strongly affected by these two features, and so is the ODR spectral line shape when the saturating laser intensity is close to the threshold for producing two peaks.