ac electric trapping of neutral atoms

We study the dynamic behavior of ultracold neutral atoms in a macroscopic ac electric trap. Confinement in such a trap is achieved by switching between two saddle-point configurations of the electric field. The gradual formation of a stably trapped cloud is observed and the trap performance is studied versus the switching frequency and the symmetry of the switching cycle. Additionally, the electric field in the trap is mapped out by imaging the atom cloud while the fields are still on. Finally, the phase-space acceptance of the trap is probed by introducing a modified switching cycle. The experimental results are reproduced using full three-dimensional trajectory calculations.

Figure 1

(Color online) Photograph of the ac trap. The inset on the left shows a schematic of the trap where the dimensions of the electrodes and the distances between them are indicated. The voltages applied to the electrodes during the $\rho$-focusing ($z$-focusing) phase are written on each electrode.

Figure 2

(Color online) Calculated electric field (in kV/cm) in the trap for the $\rho$-focusing (a) and $z$-focusing (b) configurations.

Figure 3

(Color online) Stark shift of the $5{{}^{2}S}_{1/2}\left(F=2\right)\to 5{{}^{2}P}_{3/2}\left(F=3\right)$ transition used for probing. For the upper state the Stark shift is different for the $\left|m_F\right|$ sublevels, while for the lower state all $m_F$ sublevels are degenerate. This can also be seen in the inset which shows the probing transition. All degenerate sublevels of the $5{{}^{2}S}_{1/2}\left(F=2\right)$ state are populated in the trap; the linearly polarized probe beam drives only transitions with $\Delta m_F=0$. The relative transition strengths are indicated next to the arrows.

Figure 4

(Color online) Absorption images (a)–(j) and simulations (A)–(J) of the atom cloud for different probe detunings with the electric fields still on. The first column displays images recorded during $\rho$ focusing, when the atoms are kept in the trap for 9.83 ms. For the second column, the atoms are probed in the $z$-focusing configuration after a trapping time of 9.84 ms. All absorption images are averaged five times. The pictures in the third and fourth columns show the corresponding simulations.

Figure 5

(Color online) Gradual formation of the trapped atom cloud. The pictures are taken at a switching frequency of 60 Hz and show the cloud after $N=1$, 2, 3, 4, 5, 10, 30, 60, and 240 full switching cycles. All images are averaged five times. The corresponding optical density is indicated by the color scale.

Figure 6

(Color online) Lifetime measurement of the ac trapped atom cloud. The experiment is performed at 60 Hz, and all the data points are single-shot measurements. The solid line is a double-exponential fit to the data points, while the dashed curves show each exponential individually.

Figure 7

(Color online) Absorption images (a)-(d) of the atom cloud at different phases within the 61st switching cycle at a trapping frequency of 60 Hz. The pictures (A)–(D) are simulation results of the atomic distribution, labeled with matching capital letters. The schematic shows the applied switching cycle, where the appropriate phases are also indicated. The measurements are averaged five times, and the optical density is shown in the color scale.

Figure 8

Radial (first row) and axial (second row) simulated phase-space distributions of the atoms at different trap phases during the 61st switching cycle. The phase space plots are obtained for the same switch-off times A–D used in Fig. 7, as indicated for each column. Note that for the simulations in $\rho$ a finer grid is used for small velocities and small positions, thus increasing the density of particles around zero.

Figure 9

(Color online) (a) Ballistic expansion measurements of the ac trapped cloud after a trapping time of 1016 ms at 60 Hz. Plotted are the measured FWHM of the cloud in the $\rho$ (squares) and $z$ (circles) directions versus the TOF. The solid lines show the corresponding fits. (b) Mean kinetic energies $E_{\rho }$ (squares) and $E_z$ (circles) of the atoms for various ac trapping times within the 61st switching cycle. The dashed lines indicate the times A–D in the switching cycle. All data points are plotted together with the associated error bars, which are the standard deviations of the fit.

Figure 10

(Color online) Frequency scan for two different sets of voltages. The squares show measurements where the voltages from Fig. 1 are employed. The solid curve is the corresponding theory prediction. The circles display measurements where higher voltages are used, resulting in electric fields that are 1.2 times stronger. The frequencies for stable trapping are then shifted to higher values. The number of atoms is measured after a trapping time of 5 s, and ten pictures are averaged for each data point.

Figure 11

(Color online) Atom number versus $\rho$-focusing fraction in a switching cycle of 16.7 ms corresponding to a switching frequency of 60 Hz. The data are taken after 1 s of trapping, and the measurements are averaged five times. The solid black curve is the simulation result.

Figure 12

(Color online) Pictures of the atom cloud after 60 switching cycles at 60 Hz followed by a phase jump. For the first column (a)–(e), $\rho$ focusing is on for only 1/4 of its usual duration and $z$ focusing is on for 3/4 of its usual setting. For the second column (f)–(j), a symmetric phase jump is performed with 1/2 $\rho$ focusing and 1/2 $z$ focusing. In the third column (k)–(o), 3/4 of $\rho$ focusing is followed by 1/4 of $z$ focusing. Each column shows the atoms imaged directly after the phase jump (first row), after an additional $\rho$-focusing phase applied after the phase jump (second row), after a full switching cycle applied after the phase jump (third row), after a full cycle and a $\rho$-focusing phase (fourth row), and when 30 full switching cycles have been applied after the phase jump (last row). All pictures are averaged five times.

Figure 13

(Color online) Simulated phase-space distributions where $v_z$ is plotted versus $z$. The figures show those atoms that survive the symmetric phase jump and the subsequently applied 30 full switching cycles. In (a), the phase-space distribution after the $\rho$-focusing stage of the phase jump [light gray (orange online)] is plotted, along with the distributions already shown in plots B (black and D [dark gray (magenta online)] of Fig. 8. In (b), this distribution [light gray (orange online)] is shown again, along with the distributions after the entire phase jump [black (blue online), corresponding to Fig. 12f], and after an additional $\rho$-focusing stage [dark gray (red online), corresponding to Fig. 12g].