The process of collisional trap loss in magneto-optically trapped 7Li shows a rich dependence on the depth of the trapping potential, ET. When the trap is shallow enough to allow the escape of atoms with kinetic energy equal to one-half the fine-structure splitting, ΔEfs, fine-structure changing collisions [FS] dominate the collisional trap loss rate. However when the trap is deeper than 1 2 Δ E FS, only the radiative escape mechanism [RE] contributes to trap loss. In this regime, Julienne and Vigue predicted that the collisional loss rate will depend on ET as ~ET-17/6.1 We have measured the collisional loss rate, β, of 7Li from a beam-loaded magneto-optical trap.2 The circles in Fig. 1 show the data for four different trap laser detunings, Δ, and a range of trap laser intensities, 1. The solid line in Fig. 1 is the result of a semi-classical, optical Bloch equation calculation of the RE trap loss rate3 using as input ET, calculated from a truly three-dimensional model.4 The trap depth model predicts that ET is anisotropic. The dashed line in Fig. 1 shows the intensity at which the model predicts E T > 1 2 Δ E FS in all directions, for each detuning. The theory predicts the magnitude of the RE trap loss rate accurately near the point at which the fine structure mechanism turns off, where the trap depth is well known. However at larger detunings and intensities the calculations deviate from the measured values. This suggests that the trap depth model overestimates E, at higher intensities and detunings, or that the trap depth dependence of the RE loss rate deviates from ET-17/6.
We report a measurement of the quadratic collisional loss rate coefficient \ensuremath{\beta} of a
7Li trap as a function of the trap potential in a range covering the energy of the fine-structure splitting
2${\mathit{P}}_{3/2\mathrm{\ensuremath{-}}}^{2}$
P1/2. The value of \ensuremath{\beta} decreases an order of magnitude when the trap potential is increased beyond 0.24 K, and reaches the minimum value of 3\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}13}$
cm3 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ at 0.45 K. At a higher trap potential the \ensuremath{\beta} increases proportionally to the trap potential.
Measurements of the trap loss rate in ultra-cold magneto-optically trapped
sp6Li and
sp7Li are presented and compared. Clear evidence is presented for two different trap loss mechanisms involving inelastic collisions between one ground state atom and one excited state atom. The fine-structure changing (FSC) mechanism, in which the excited state atom changes fine-structure level during a collision, is seen to dominate the rate at low trap laser intensities. However, as the intensity is increased, the trap becomes sufficiently deep to be able to contain the products of FSC collisions and this mechanism no longer contributes to trap loss. It is a unique aspect of Li that the energy imparted to an atom in a FSC collision is in a range that may be recaptured with experimentally attainable trap parameters. When the products of all FSC collisions remain trapped, only the radiative escape (RE) trap loss mechanism, due to the emission of a less energetic photon than the initial excitation photon, contributes to the trap loss rate. At small detunings, the rate of the RE trap loss mechanism is seen to be over two orders-of-magnitude smaller than the FSC rate. The FSC trap loss rate for
sp6Li and
sp7Li were found to be largest at smaller detunings and of comparable magnitude in
sp6Li and
sp7Li. The RE trap loss rate in
sp6Li was seen to be roughly four times the RE trap loss rate in
sp7Li. To understand better the dynamics of trap loss and magneto-optical traps in general, a sophisticated model of magneto-optical trap kinetics has been developed. This model has demonstrated that most critical factor determining the maximum velocity an atom may have and yet remained trapped is the initial atom's frame detuning,
Delta - k v, where
Delta is the trap laser detuning, k is the propagation vector of the trap beam most nearly anti-parallel to v, the atom's velocity. All else being equal, minimizing the magnitude of this quantity maximizes the velocity that a trap will retain. More detailed results of this model are also presented.
Losses from a cesium magneto-optical trap induced by fine-structure changing collisions have been measured directly by counting of fluorescence photons emitted at the
D1 resonance line, with the trap lasers operating on the
D2 resonance line. The absolute value of the fine-structure loss rate coefficient has been measured and its dependence on the hyperfine state occupation has been explored. These results provide a fundamental test for the theoretical descriptions of excited-state trap losses.
Accurate measurements are presented of the rate of trap-loss-producing collisions between ultracold magneto-optically trapped
7Li atoms for a range of trap laser intensities and frequencies. Intensities from near the atomic saturation intensity to well above it are investigated. At low intensities, fine-structure-changing collisions cause trap loss with a rate constant of \ensuremath{\sim}${10}^{\mathrm{\ensuremath{-}}10}$
cm3/s. At sufficiently high intensity, the trap can be deep enough to effectively freeze out the dominant fine-structure-changing collisions as a loss mechanism, enabling an accurate comparison of the radiative escape loss rate with theory. At the lowest intensities of this radiative escape regime, the measured loss rates compare favorably with those calculated using an optical Bloch equation theory and a three-dimensional model of trap depth. However, the intensity dependence of the measured rates does not show the saturation predicted by the optical Bloch equation theory. It is shown that reliable knowledge of trap depth is necessary to accurately compare experiment with theory.