Transmission-line decelerators for atoms in high Rydberg states

Beams of helium atoms in Rydberg states with principal quantum number $n=52$, and traveling with an initial speed of 1950 m/s, have been accelerated, decelerated, and guided while confined in moving electric traps generated above a curved, surface-based electrical transmission line with a segmented center conductor. Experiments have been performed with atoms guided at constant speed, and with accelerations exceeding ${10}^7$ $\mathrm{m}/\mathrm{s}{}^2$. In each case, the manipulated atoms were detected by spatially resolved, pulsed electric field ionization. The effects of tangential and centripetal accelerations on the effective trapping potentials experienced by the atoms in the decelerator have been studied, with the resulting observations highlighting contributions from the density of excited Rydberg atoms to the acceleration, deceleration, and guiding efficiencies in the experiments.

Figure 1

(a) Schematic diagram of the transmission-line decelerator. Electric field distributions in (b) the $xy$ plane, and (c) the $zy$ plane, for $V_0=+120$ V, and $V_{\mathrm{u}}=-V_0/2$. The color scale in the lower right of the figure is common to (b) and (c).

Figure 2

(a) Electric field distributions in the $zy$ plane for traps located (i) above a decelerator segment, (ii) one quarter of the way between two segments, and (iii) halfway between two segments. In each case, contours of equal electric field strength are displayed in increments of 20 V/cm, from 20 to 160 V/cm, and the positions of the decelerator segments are indicated by the thick bars on the horizontal axis. (b) The dependence of the position of the electric field minimum in the $y$ dimension upon its location along the decelerator axis when a potential $V_{\text{gp}}=0$ V is applied to the ground planes (dashed red curve), and when the potential $V_{\text{gp}}=-0.045V_{0}cos\left(5\omega t\right)$ is applied (continuous black curve).

Figure 3

(a) Electric field distributions in (i) the $zy$ plane and (ii) the $xy$ plane, containing an electric field minimum located one quarter of the way between two decelerator segments. Contours of equal electric field strength are displayed in increments of 20 V/cm beginning at 20 V/cm. (b)–(d) Potential energy distributions in (i) the $zy$ plane and (ii) the $xy$ plane, experienced by a He atom in the $|n,k\rangle =|52,35\rangle$ Rydberg-Stark state. In (c)-(i) and (d)-(i), a pseudopotential is included to account for tangential accelerations of $-0.5\times {10}^7$ $\mathrm{m}/\mathrm{s}{}^2$ and $-1.15\times {10}^7$ $\mathrm{m}/\mathrm{s}{}^2$, respectively. In (c)-(ii) and (d)-(ii), the effects of centripetal accelerations of $-0.47\times {10}^7$ $\mathrm{m}/\mathrm{s}{}^2$ and $-0.71\times {10}^7$ $\mathrm{m}/\mathrm{s}{}^2$ are included. In the curved decelerator described here, these centripetal accelerations correspond to tangential velocities of 1950 and 2400 m/s, respectively. In (b)–(d), contour lines of equal potential energy are displayed in terms of a temperature, i.e., $E/k_{\text{B}}$, in increments of 2 K beginning at 1 K.

Figure 4

Effective depth of the moving decelerator traps for He atoms in the $|n,k\rangle =|52,35\rangle$ Rydberg-Stark state, when $V_0=+120$ V. Data for five different centripetal accelerations, $a_{\mathrm{c}}=0$ $\mathrm{m}/\mathrm{s}{}^2$ ($v_{\mathrm{t}}=0$ m/s, continuous black curve), $a_{\mathrm{c}}=-0.22\times {10}^7$ $\mathrm{m}/\mathrm{s}{}^2$ ($v_{\mathrm{t}}=1350$ m/s, dotted red curve), $a_{\mathrm{c}}=-0.47\times {10}^7$ $\mathrm{m}/\mathrm{s}{}^2$ ($v_{\mathrm{t}}=1950$ m/s, dashed-dotted green curve), $a_{\mathrm{c}}=-0.71\times {10}^7$ $\mathrm{m}/\mathrm{s}{}^2$ ($v_{\mathrm{t}}=2400$ m/s, dashed blue curve), and $a_{\mathrm{c}}=-0.90\times {10}^7$ $\mathrm{m}/\mathrm{s}{}^2$ ($v_{\mathrm{t}}=2700$ m/s, dashed–double-dotted magenta curve), are displayed.

Figure 5

Schematic diagram of the experimental apparatus (not to scale). Photoexcitation of the metastable He atoms to selected Rydberg-Stark states is carried out between the electrodes labeled E1 and E2. After traveling through the decelerator, the Rydberg atoms are detected by pulsed electric field ionization upon the application of a potential of $+3.5$ kV to the electrode labeled E3. The resulting ${\mathrm{He}}^{+}$ ions are then accelerated through the aperture in the grounded electrode labeled E4 to an MCP detector.

Figure 6

${\mathrm{He}}^{+}$ time-of-flight distributions recorded following pulsed electric field ionization of the He Rydberg atoms. When the decelerator is operated to guide atoms at a constant speed of 1950 m/s, the maximum of the time-of-flight distribution (dashed blue curve) arrives $\sim 25$ ns later than that recorded with the decelerator inactive (continuous black curve). The time-of-flight distribution recorded with the decelerator active has been scaled by a factor of 0.5 (see text for details).

Figure 7

Dependence of the integrated ${\mathrm{He}}^{+}$ signal on the activation time of the oscillating decelerator potentials, for a He atom flight time from the photoexcitation region to the detection region of $82.5\mu \mathrm{s}$, when the decelerator is operated in a guiding mode at a constant speed of 1950 m/s.

Figure 8

(a) Time-of-flight distribution of the unperturbed beam of He Rydberg atoms recorded with the decelerator off. (b) He atom time-of-flight distributions recorded with the decelerator operated to guide atoms at constant speeds ranging from 1750 to 2350 m/s as indicated.

Figure 9

Dependence of the experimentally determined efficiency with which atoms were guided at constant speed through the transmission-line decelerator, upon the tangential velocity of the moving traps (blue circles, left vertical axis). The linear dependence of the effective depth of the moving traps upon their tangential velocity (see Sec. 2) is indicated by the dashed red line (right vertical axis).

Figure 10

Acceleration and deceleration of He Rydberg atoms in the transmission-line decelerator. For reference, the time-of-flight distribution of atoms guided at a constant speed of 1950 m/s is included in data set (iv). Accelerations as high as $a_{\text{t}}=+2.0\times {10}^7$ $\mathrm{m}/\mathrm{s}{}^2$ permit final velocities of 2700 m/s to be achieved (vi), while with $a_{\text{t}}=-1.15\times {10}^7$ $\mathrm{m}/\mathrm{s}{}^2$, deceleration to a final velocity of 1350 m/s is demonstrated (i).