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Physical Review A

Quadratic collisional loss rate of a Li7 trap

Junji Kawanaka, Kazuko Shimizu, Hiroshi Takuma, Fujio Shimizu

Published Aug 1, 1993• 43 citations
Publisher

Abstract

We report a measurement of the quadratic collisional loss rate coefficient \ensuremath{\beta} of a $^{7}\mathrm{Li}$ trap as a function of the trap potential in a range covering the energy of the fine-structure splitting $^{2}$${\mathit{P}}_{3/2\mathrm{\ensuremath{-}}}^{2}$${\mathit{P}}_{1/2}$. The value of \ensuremath{\beta} decreases an order of magnitude when the trap potential is increased beyond 0.24 K, and reaches the minimum value of 3\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}13}$ ${\mathrm{cm}}^{3}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ at 0.45 K. At a higher trap potential the \ensuremath{\beta} increases proportionally to the trap potential.

DOI
10.1103/physreva.48.r883

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Near-threshold photodissociation of ${\mathrm{Br}}_{2}$ from a supersonic beam produces slow bromine atoms that are trapped in the magnetic-field minimum formed between two opposing permanent magnets. Here we quantify the dominant trap-loss rate due to collisions with two sources of residual gas: the background limited by the vacuum chamber base pressure and the carrier gas during the supersonic gas pulse. The loss rate due to collisions with residual Ar in the background follows pseudo-first-order kinetics and the bimolecular rate coefficient for collisional loss from the trap is determined by measurement of this rate as a function of the background Ar pressure. This rate coefficient is smaller than the total elastic collision rate coefficient, as it only samples those collisions that lead to trap loss, and is determined to be $\ensuremath{\langle}\ensuremath{\nu}\ensuremath{\sigma}\ensuremath{\rangle}=(1.12\ifmmode\pm\else\textpm\fi{}0.09)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{3}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$. The calculated differential cross section can be used with this value to estimate a trap depth of $293\ifmmode\pm\else\textpm\fi{}24\phantom{\rule{0.28em}{0ex}}\mathrm{mK}$. Carrier-gas collisions occur only during the tail of the supersonic beam pulse. Using the differential cross section verified by the background-gas collision measurements provides an estimate of the peak molecular-beam density of $(3.0\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{13}\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$, in good agreement with the prediction of a simple supersonic expansion model. Finally, we estimate the trap-loss rate due to Majorana transitions to be negligible, owing to the relatively large trapped-atom phase-space volume.

arXiv:1412.5790•Physical Review A•Dec 11, 2014•5 citations
We report a measurement of the quadratic collisional loss rate coefficient \ensuremath{\beta} of a 7Li^{7}\mathrm{Li}7Li trap as a function of the trap potential in a range covering the energy of the fine-structure splitting ^{2}$${\mathit{P}}_{3/2\mathrm{\ensuremath{-}}}^{2}$${\mathit{P}}_{1/2}. 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\ensuremath−13{10}^{\mathrm{\ensuremath{-}}13}10\ensuremath−13 cm3{\mathrm{cm}}^{3}cm3 s\ensuremath−1{\mathrm{s}}^{\mathrm{\ensuremath{-}}1}s\ensuremath−1 at 0.45 K. At a higher trap potential the \ensuremath{\beta} increases proportionally to the trap potential.
The origin of the collisional loss‐rate of a 7Li magneto‐optical trap is investigated by measuring the quadratic fluorescence decay rate coefficient β as a function of the trap potential in a range covering the energy of the fine structure splitting. The value of β shows one order of magnitude decrease with the increase of the trapping potential beyond 0.24 K down to the minimum value of 3×10−13 cm2 s−1 at 0.45 K, strongly supporting the prediction that the main cause is the fine‐structure changing collision. At a higher trap potential the value of β increases proportionally to the trap potential.
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.
Measurements of the trap loss rate in ultra-cold magneto-optically trapped sp6\\sp6sp6Li and sp7\\sp7sp7Li 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 sp6\\sp6sp6Li and sp7\\sp7sp7Li were found to be largest at smaller detunings and of comparable magnitude in sp6\\sp6sp6Li and sp7\\sp7sp7Li. The RE trap loss rate in sp6\\sp6sp6Li was seen to be roughly four times the RE trap loss rate in sp7\\sp7sp7Li. 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\\DeltaDelta - k v, where Delta\\DeltaDelta 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{\mathrm{D}}_{1}D1​ resonance line, with the trap lasers operating on the D2{\mathrm{D}}_{2}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.
Inelastic atomic collisions constitute loss mechanisms for neutral atom traps, and the study of trap-loss rates may provide detailed information on the long-range interaction between atoms and on the dynamics of very slow collisions. Gallagher and Pritchard (1989) have given a simple two-state model for such collisions which includes a radiative transition or a single curve crossing at short range representing, for example, fine-structure-changing collisions. In order to better describe the more complicated case found in alkali metals, we have extended this model to include several excited hyperfine structure levels with curve crossings at long range. We find that collisions in a laser field that are capable of expelling atoms from the trap can be suppressed in some laser frequency regions and enhanced in others, in comparison with the predictions of the simple two-state model. Using this model to represent radiative escape via the 2 u potential of alkali dimer molecules we are able to greatly improve agreement between theory and experiment, including new measurements on 85 Rb reported here.
Near-threshold photodissociation of Br2{\mathrm{Br}}_{2}Br2​ from a supersonic beam produces slow bromine atoms that are trapped in the magnetic-field minimum formed between two opposing permanent magnets. Here we quantify the dominant trap-loss rate due to collisions with two sources of residual gas: the background limited by the vacuum chamber base pressure and the carrier gas during the supersonic gas pulse. The loss rate due to collisions with residual Ar in the background follows pseudo-first-order kinetics and the bimolecular rate coefficient for collisional loss from the trap is determined by measurement of this rate as a function of the background Ar pressure. This rate coefficient is smaller than the total elastic collision rate coefficient, as it only samples those collisions that lead to trap loss, and is determined to be $\ensuremath{\langle}\ensuremath{\nu}\ensuremath{\sigma}\ensuremath{\rangle}=(1.12\ifmmode\pm\else\textpm\fi{}0.09)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{3}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$. The calculated differential cross section can be used with this value to estimate a trap depth of $293\ifmmode\pm\else\textpm\fi{}24\phantom{\rule{0.28em}{0ex}}\mathrm{mK}$. Carrier-gas collisions occur only during the tail of the supersonic beam pulse. Using the differential cross section verified by the background-gas collision measurements provides an estimate of the peak molecular-beam density of $(3.0\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{13}\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$, in good agreement with the prediction of a simple supersonic expansion model. Finally, we estimate the trap-loss rate due to Majorana transitions to be negligible, owing to the relatively large trapped-atom phase-space volume.