Hyperfine-changing collisions in an optically trapped gas of ultracold cesium and lithium

We present measurements of the rate of hyperfine-state-changing collisions of unpolarized cesium $\left({}^{133}\mathrm{Cs}\right)$ and lithium $\left({}^7\mathrm{Li}\right)$ atoms confined in an optical dipole trap in the temperature range between 30 and $130\mu \mathrm{K}$. To infer rate coefficients from trap-loss data, we derive a simple thermodynamic model describing relaxation heating as a consequence of atom loss in a conservative potential. For hyperfine-changing $\mathrm{Cs}\text{−}\mathrm{Cs}$ collisions, the experimental results are compared with theoretical predictions and excellent agreement is found. Hyperfine-state-changing collisions in a mixture of lithium and cesium atoms are observed and rate coefficients are inferred for all combinations of hyperfine ground-state asymptotes.

Figure 1

(Color online) Schematic setup of the experiment. Cesium and lithium atoms are trapped either separately or simultaneously in the focus of a ${\mathrm{CO}}_2$ laser beam. The number of trapped atoms and the density distribution are measured by fluorescence and absorption imaging, respectively.

Figure 2

(Color online) Trap loss and relaxation heating resulting from hyperfine-changing collisions in a sample of cold $\mathrm{Cs}$ atoms. The graphs show the evolution of (a) the mean density, (b) the temperature, and (c) the number of trapped atoms. At time $t=0$ the atoms are prepared in the ground state $\mid 6s_{1∕2},F=4⟩$ (filled symbols). For comparison, the open symbols show the dynamics for atoms prepared in the energetically lowest ground state $\mid 6s_{1∕2},F=3⟩$. The solid lines are least-squares fits of Eqs. (5, 7) to the data.

Figure 3

(Color online) Double-logarithmic representation of the temperature as a function of the number of trapped $\mathrm{Cs}$ atoms for the same data as in Figs. 2b, 2c. The data follow a power-law dependence [see Eq. (4), solid line] from which a reduction factor $q=0.5$ is inferred.

Figure 4

(Color online) (a) Temporal evolution of the density of $\mathrm{Cs}$ atoms prepared in a mixture of upper and lower hyperfine ground states ($\mid 6s_{1∕2},F=4⟩$ and $\mid 6s_{1∕2},F=3⟩$, respectively). The closed symbols display the evolution of the total density when 0%, 64%, 86%, and 100% of the population is pumped into $\mid F=4⟩$ (from bottom to top). Open symbols represent the density evolution of the $\mid F=4⟩$ state. The solid lines are best fits of Eq. (9) to the data. (b) Temperature evolution of the total atom sample. The solid lines are calculated according to Eq. (11) using the fit parameters of the corresponding density fit.

Figure 5

Comparison between experimental and theoretical results for the two-body rate coefficients $G_{(4,4)}$ and $G_{(3,4)}$ as a function of temperature. The shaded areas represent the total experimental uncertainty.

Figure 6

(Color online) Trap loss of (a) lithium and (b) cesium as a result of single-species and interspecies hyperfine-changing collisions involving $\mathrm{Cs}$ in the upper hyperfine ground state $\mid 6s_{1∕2},F=4⟩$. At time $t=0$, the $\mathrm{Cs}$ atoms are optically pumped into the upper hyperfine ground state $\mid F=4⟩$. The three different filled symbols reflect different values of the initial number and temperature of the $\mathrm{Cs}$ atoms. The initial values for $\mathrm{Cs}$ atom number and temperature are $N_{\mathrm{Cs},0}=7.2\times {10}^5$ and $T_{\mathrm{Cs},0}=38\mu \mathrm{K}$ (diamonds), $N_{\mathrm{Cs},0}=2.3\times {10}^5$ and $T_{\mathrm{Cs},0}=28\mu \mathrm{K}$ (triangles), and $N_{\mathrm{Cs},0}=7.2\times {10}^4$ and $T_{\mathrm{Cs},0}=26\mu \mathrm{K}$ (circles). The open symbols depict the evolution of the number of trapped particles for both $\mathrm{Cs}$ and $\mathrm{Li}$ prepared in their lowest ground states $\mid 6s_{1∕2},F=3⟩$ and $\mid 2s_{1∕2},F=1⟩$, respectively. Solid lines represent the result of fitting simultaneously rate equations (12) to the data.

Figure 7

(Color online) Trap loss of (a) lithium and (b) cesium as a result of single-species and interspecies hyperfine-changing collisions involving $\mathrm{Li}$ in the upper hyperfine ground state $\mid 2s_{1∕2},F=2⟩$. At time $t=0$, the $\mathrm{Li}$ atoms are optically pumped into the upper hyperfine ground state $\mid F=2⟩$. The initial values for $\mathrm{Cs}$ atom number and temperature are the same as in the measurements shown in Fig. 6. The open symbols depict the evolution of the number of trapped particles for both $\mathrm{Cs}$ and $\mathrm{Li}$ prepared in their lowest ground states $\mid 6s_{1∕2},F=3⟩$ and $\mid 2s_{1∕2},F=1⟩$, respectively. Solid lines represent the best fits of rate equations (13) to the data.