Observation of quantum diffractive collisions using shallow atomic traps

We present measurements and calculations of the trap loss rate for laser-cooled ${}^{87}\text{R}\text{b}$ atoms confined in either a magneto-optic trap (MOT) or a magnetic quadrupole trap when exposed to a room-temperature background gas of Ar. We study the loss rate as a function of trap depth and find that copious glancing elastic collisions, which occur in the so-called quantum diffractive regime and impart very little energy to the trapped atoms, result in significant differences in the loss rate for the MOT compared to a pure magnetic trap due solely to the difference in potential depth. This finding highlights the importance of knowing the trap depth when attempting to infer the total collision cross section from measurements of trap loss rates. Moreover, this variation in trap loss rate with trap depth can be used to extract information about the differential cross section.

Figure 1

(Color online) Schematic of the vacuum system. The variable leak valve allows Ar gas to be introduced and the residual gas analyzer (RGA) is used to measure the pressure and the composition of the background vapor. The laser cooled and trapped ${}^{87}\text{R}\text{b}$ atoms undergo collisions with the background gas which may or may not result in trap loss.

Figure 2

(Color online) MOT fluorescence as a function of time fit to the rate equation given in Eq. (13) with $\beta =0$.

Figure 3

(Color online) Fraction of atoms retained in a quadrupole magnetic trap as a function of time fit to the rate equation given in Eq. (13) with $R=0$ and $\beta =0$.

Figure 4

(Color online) Loss rate of trapped ${}^{87}\text{R}\text{b}$ versus room-temperature argon gas density. The results are fit to a line and the slope provides the value of the velocity averaged collision rate $⟨{\sigma }_{\text{Rb},\text{Ar}}{v}_{\text{Ar}}⟩$. The MOT (circles) exhibits the smallest cross section due to a much larger effective trap depth $\left(\sim 1\text{K}\right)$ than the magnetic trap (squares) where the $|F=1,m_F=-1⟩$ state was confined with $b^{\prime }=79\text{G}{\text{cm}}^{-1}$ resulting in a trap depth of 0.64 mK. The vertical error bars, most of which are smaller than the symbols, represent the statistical uncertainty in the loss rate based on fits similar to those shown in Figs. 2, 3.

Figure 5

(Color online) The theoretically computed total cross section for room-temperature ${}^{87}\text{R}\text{b-}{}^{40}\text{A}\text{r}$ collisions (averaged over a Maxwell-Boltzmann distribution at 295 K) given a Lennard-Jones interatomic potential as a function of the $C_6$ coefficient $\left(C_{12}=8.6\times {10}^7{E}_{\text{H}}{a}_{\text{B}}^{12}\right)$. The numerical results are fit to a power law, $\sigma =70{\text{Å}}^2\times {\left(C_6\right)}^{0.40}$, in agreement with the predicted dependence of 2/5.

Figure 6

(Color online) The theoretically computed total cross section for ${}^{87}\text{R}\text{b-}{}^{40}\text{A}\text{r}$ collisions averaged over a Maxwell-Boltzmann distribution at various temperatures given a Lennard-Jones interatomic potential with $C_6=280E_{\text{H}}{a}_{\text{B}}^6$ and $C_{12}=8.6\times {10}^7{E}_{\text{H}}{a}_{\text{B}}^{12}$. The results are fit to a power law, $\sigma =2100{\text{Å}}^2\times {\left(T\right)}^{-0.202}$, in agreement with the approximate expected power dependence of $-1/5$, corresponding to the power dependence of $-2/5$ on the collision velocity.

Figure 7

(Color online) The theoretically computed total cross section for room-temperature ${}^{87}\text{R}\text{b-}{}^{40}\text{A}\text{r}$ collisions (averaged over a Maxwell-Boltzmann distribution at 295 K) given a Lennard-Jones interatomic potential as a function of the $C_{12}$ coefficient with $C_6=280E_{\text{H}}{a}_{\text{B}}^6$. A value of $C_{12}=8.6\times {10}^7{E}_{\text{H}}{a}_{\text{B}}^{12}$ results in a potential with a minimum of $50{\text{cm}}^{-1}$ below threshold. As expected, for the collision energies characteristic of a room-temperature gas, the exact value of the $C_{12}$ coefficient (at or below ${10}^9{E}_{\text{H}}{a}_{\text{B}}^{12}$) plays little role in the resulting cross section.

Figure 8

(Color online) The theoretically computed loss cross section as a function of trap depth for ${}^{87}\text{R}\text{b-}{}^{40}\text{A}\text{r}$ collisions of different velocities. Loss cross sections for velocities corresponding to the average speed at 4 (open triangles), 295 (open diamonds), and 1000 K (open squares) are shown as well as the average loss cross section for a room-temperature thermal distribution (filled circles). The variation in the loss cross section with trap depth is most pronounced for the lowest velocity collisions. However, there still remains significant variation with trap depth for a thermal distribution at room temperature.

Figure 9

(Color online) The experimentally measured (squares) and theoretically computed (circles) loss rate slope, $⟨{\sigma }_{\text{Rb},\text{Ar}}{v}_{\text{Ar}}⟩$, as a function of trap depth for ${}^{87}\text{R}\text{b-}{}^{40}\text{A}\text{r}$ collisions. The line is only a guide to the eye. The data point at 800 mK was obtained using a MOT and the data below 10 mK were obtained with a quadrupole magnetic trap. These values were extracted from the data shown in Fig. 4. The horizontal error bar for the MOT data point represents an estimated trap-depth range based on the work of Hoffmann et al. [26]. The error bars for the data below 10 mK represent the radial and the axial magnetic trap depths. The horizontal dotted line indicates the zero trap-depth limit for $⟨{\sigma }_{\text{Rb},\text{Ar}}{v}_{\text{Ar}}⟩$, corresponding to the total collision cross section.