Polarization gradient cooling in a one-dimensional sigma⁺- sigma^-configuration for any atomic transition

Abstract

The authors discuss the radiation force in a one-dimensional sigma +- sigma - laser standing wave, for transitions J to J+ Delta J, for any J. and Delta J=+or-1.0. in the limit of low saturation of the atomic transition. The interaction between the radiation field and the atom produces a motion-induced orientation of the atomic ground state which grows rapidly with J. The radiative force on the atom is sensitive to this orientation. For J to J+1 the dissipative part of the total force is much larger than the reactive part, at low velocities, while for the other cases the two contributions are roughly equal and opposite. By using a simple method of calculation, the authors gain much physical insight into the mechanism of induced orientation, and give quantitative results for the size of the radiation force, including both the low-velocity friction coefficient and the velocity capture range.

Scaling laws in magneto-optical traps

“…At the same time, the trap images collected by CCD cameras and analyzed by a computer allowed us to calculate the MOT volume and the f -factor. For the data reported here the measured f-factors were between 0.3 and 0.4, indicating preferentially a Gaussian-like distribution instead of the flat top distribution reported in other conditions [7], [10].…”

“…with κ 0 a constant of proportionality, b = dB/dz the magnetic-field gradient, b 0 = 1 G/cm and c J a numerical coefficient that for Cs is 37.2, for 87 Rb 11.0 and for 85 Rb 22.1 [10]. Equation ( 4) did not reproduce the measured dependence of the density on the MOT parameters of ref.…”

Laser cooling and trapping of atoms

“…(Actually, some limited redistribution is possible in this type of standing wave, as explained by Dalibard and Cohen-Tannoudji, and this introduces a reactive component to the radiation force. However, Steane, Hillenbrand and Foot [79] show that this is always much smaller than the dissipative contribution, i.e. that part due to the population imbalance).…”

“…There have since appeared a number of other calculations for various transitions "and in differing numbers of dimensions, attempting to gain physical understanding of the nature of the force in general. Notably M01mer [63] has made numerical calculations in one, two and three dimensions for J = 1 > 2', and Steane, Hillenbrand and Foot [79] have presented both analytical and numerical one-dimensional calculations for J -> J + A J, for any J and AJ = 0,±1. Most of the treatments reported have been restricted to low saturation of the atomic transition and to small atomic velocities.…”

“…The factor A" 1 arises from the first order perturbation theory: the degree of mixing of the \MX } sublevels (and thus the size of the population imbalance) is inversely proportional to the energy splittings of the light shifted levels. Steane, Hillenbrand and Foot [79] showed that the form of Eq. (1.3) remains unchanged for higher J transitions, but significantly that the size of the force increases with J.…”