Single-atom thermometer for ultracold gases

We use single or a few Cs atoms as a thermometer for an ultracold, thermal Rb cloud. Observing the thermometer atoms' thermalization with the cold gas using spatially resolved fluorescence detection, we find an interesting situation, where a fraction of thermometer atoms thermalizes with the cloud while the other fraction remains unaffected. We compare release-recapture measurements of the thermometer atoms to Monte Carlo simulations while correcting for the nonthermalized fraction, and recover the cold cloud's temperature. The temperatures obtained are verified by independent time-of-flight measurements of the cold cloud's temperature. We also check the reliability of our simulations first by numerically modeling the unperturbed in-trap motion of single atoms in the absence of the cold cloud, and second by performing release-recapture thermometry on the cold cloud itself. Our findings pave the way for local temperature probing of quantum systems in nonequilibrium situations.

Figure 1

Schematic drawing of the involved traps and the calculated dipole potential for Cs used for the measurement discussed in Sec. 4. The single-atom MOT (yellow, dashed) is located left of the dipole-trap-crossing region (red). A conveyor-belt lattice (blue) is used to freeze the axial motion of the single atoms during fluorescence imaging. The vertical dashed line indicates the potential minimum.

Figure 2

Dynamics of single Cs atoms in the crossed dipole trap. Many fluorescence images of single or few Cs atoms (a) are taken at a time $t$ after extinguishing the MOT. The accumulated signal for $t=5\mathrm{ms}$ is shown in (b). A quantitative analysis is given in the histograms (c)–(h), where the experimentally obtained atom positions (orange, borderless) are shown together with Monte- Carlo simulation (light-blue, solid border) for $t=5,9,\cdots ,25\mathrm{ms}$. The simulation time starts with a delay of 3.3 ms, taking account of the slowly decaying magnetic field of the MOT. Maximum overlap between experiment and simulated data is obtained for a MOT located at $-0.254\mathrm{mm}$ at a temperature of 1.9 $\mu \mathrm{K}$. The vertical dashed line indicates the position of the potential minimum.

Figure 3

Spatial density distribution of Cs (orange bars) with Rb at $2.2\mu \mathrm{K}$ (blue line) with $6.6\times {10}^3$ (a) and $14\times {10}^3$ thermalized atoms (b) being present in the crossing region of the trap at the time when the nonthermalized fraction of Cs reaches the right turning point in the trap. The fraction of nonthermalized Cs is decreased in (b) due to a higher density of Rb, and thus higher effective cross section for collisions.

Figure 4

Dynamics of single Cs atoms (orange, borderless) without Rb (a) and with Rb (b) at an evolution time of 27 ms, when unperturbed Cs is at a turning point of its axial oscillation. The Rb density profile is shown as a solid blue line and matches the spatial distribution of the thermalized fractions, since the trap frequencies are almost equal for the two species. From the fraction of atoms outside of the blue shaded area in (b), we compute the total fraction of nonthermalized Cs atoms (light-blue, solid border) with the help of (a). In this measurement, 27% of the Cs atoms are not thermalized with Rb and exhibit an unperturbed distribution.

Figure 5

Release-recapture thermometry on the thermalized fraction of single Cs thermometer atoms. Release-recapture curves for Cs with Rb being present in the trap [(a), blue octagons] and the correction curve for Rb being absent [(a), red circles] at an evolution time of 27 ms are shown. An effective release-recapture curve of the thermalized fraction [(b), filled red circles] is computed as the difference between the two curves weighted with the thermalized and nonthermalized fractions' size. From the Monte Carlo simulations we determine a release-recapture temperature of $T_{\mathrm{RR}}=2.3\pm 0.5\mu \mathrm{K}$ (empty blue circles), in good agreement with the Rb time-of-flight temperature $T_{\mathrm{TOF}}=2.15\pm 0.15\mu \mathrm{K}$. Inset of (b): The ${\chi }^2$ values for simulated release-recapture curves at initial temperatures $T_{\mathrm{sim}}$ follow a parabolic shape, while the parabola's slope yields the uncertainty of $T_{\mathrm{RR}}$ as described in the text.

Figure 6

Comparison of release-recapture temperatures $T_{\mathrm{RR}}$ to independently measured time-of-flight temperatures $T_{\mathrm{TOF}}$, with $1\sigma$ confidence intervals. Single-atom thermometry (red squares): The temperatures $T_{\mathrm{RR}}$ of the thermalized fraction of thermometer atoms agree well with the time-of-flight temperatures $T_{\mathrm{TOF}}$ of the cold Rb cloud. Blue diamonds: Release-recapture temperatures of Rb, obtained from the number of recaptured atoms. Systematic errors caused by self-evaporations during the waiting time after recapture lead to overestimated temperatures $T_{\mathrm{RR}}$, increasing with the cloud's temperature $T_{\mathrm{TOF}}$. Green circles: Release-recapture temperatures of Rb, avoiding systematic errors caused by self-evaporation. The gray line serves as a guide to the eye, $T_{\mathrm{RR}}=T_{\mathrm{TOF}}$.

Figure 7

Release-recapture thermometry on a cold Rb cloud at $T_{\mathrm{TOF}}=1.0\pm 0.1\mu \text{K}$. Systematic errors due to self-evaporation are avoided by computing the survival rates from the absorption images (top) as $1-N_{\text{lost}}/N_{\mathrm{tot}}$, 6 ms after the beginning of the release. Experimental survival rates (red dots) best fit a Monte Carlo simulation (blue circles) at a temperature of $T_{\mathrm{RR}}=1.2\mu \text{K}$. The time-of-flight absorption images show recaptured atoms at the top, while atoms lost during the release appear below. The statistical errors do not exceed the size of the markers.