Guiding slow polar molecules with a charged wire

We demonstrate experimentally the guiding of cold and slow ND${}_3$ molecules along a thin charged wire over a distance of $\sim 0.34$ m through an entire molecular beam apparatus. Trajectory simulations confirm that both linear and quadratic high-field-seeking Stark states can be efficiently guided from the beam source up to the detector. A density enhancement up to a factor 7 is reached for beams with velocities ranging down to $\sim 150$m/s generated by the rotating nozzle technique.

Figure 1

Schematic representation of the experimental setup used for guiding slow polar molecules along a thin charged wire.

Figure 2

(a) Transverse guide potential of ND${}_3$ molecules in rotational states $|J,KM\rangle =|0,0\rangle$ (quadratic Stark effect) and $|1,1\rangle$ (linear Stark effect). A wire diameter of $50\mu$m and an applied voltage $U=1.5$ kV is assumed. (b) Potential of ND${}_3$ molecules in rotational states $|J,KM\rangle =|1,-1\rangle$ and $|0,0\rangle$ transverse to the quadrupole electrodes ($U=1.5$ kV).

Figure 3

Selected trajectories of ND${}_3$ molecules in the $|0,0\rangle$ ground state propagating in the potential of the wire guide at various values of the initial transverse velocity components $v_x$ and $v_y$. The longitudinal velocity $v_z=200$ m/s, the wire voltage $U=2$ kV, and the distance between the nozzle and the center of the wire, $\Delta x=350\mu$m, are held constant.

Figure 4

Contour plots illustrating the acceptance of the wire guide for ND${}_3$ molecules in the ground state $|0,0\rangle$ in terms of initial transverse velocity components $v_x$ and $v_y$: (a) the wire voltage $U$ and the longitudinal velocity $v_z$ are varied at constant $\Delta x=350\mu$m; (b) the $\Delta x$ dependence for $U=2$ kV and $v_z=200$ m/s. (c) and (d) The corresponding distributions of the total (bottom scale) and kinetic (top scale) energy of the transverse motion.

Figure 5

(a) Absolute peak densities of beams of velocity-controlled ND${}_3$ molecules detected behind the wire guide for wire voltage on (2kV) and off (0V). The dashed line represents a model of the free jet expansion based on Gaussian transverse velocity distributions. (b) Relative enhancement of the peak density due to guiding by the charged wire (2kV; left scale). The solid lines show the result of trajectory simulations (see text; right scale).

Figure 6

(a) Simulated relative enhancement of the peak density of ND${}_3$ molecules in the high-field-seeking states $|J,KM\rangle =|0,0\rangle$ and $|1,1\rangle$ due to guiding by the charged wire as a function of wire voltage for a beam velocity $v_z=150$ m/s. (b) Enhancement of the measured ND${}_3$ peak density for various beam velocities (symbols; left scale). The calculations show the average of trajectory simulations for the low-energy Stark states correlating to $J=0$ and $J=1$ and for two effective detector cross sections with radius $R_D=0.5$ mm and $R_D=0.9$ mm (upper and lower lines, respectively; right scale).

Figure 7

(b) Relative enhancement of the measured ND${}_3$ peak density due to guiding in a linear quadrupole for a beam velocity $v_z=290$ m/s as a function of the applied voltage (left scale). The calculations show the results of trajectory simulations for two effective detector cross sections with radius $R_D=0.5$ mm and $R_D=0.9$ mm (upper and lower lines, respectively; right scale).

Figure 8

Measured (symbols; left scale) and simulated (lines; right scale) enhancement of the ND${}_3$ peak density due to guiding by the charged wire as a function of the distance $\Delta x$ between the center of the nozzle orifice and the center of the wire. The beam velocity and wire voltage are fixed to $v_z=310$ m/s and $U=1.5$ kV, respectively.

Figure 9

(a) Electric field according to Eq. (1) at a distance $\Delta x=375\mu$m from the wire center as a function of the wire radius. (b) Simulated behavior of the ND${}_3$ peak density due to guiding by the charged wire as a function of the wire radius for $\Delta x=375\mu$m and $\Delta x=475\mu$m (upper and lower lines, respectively). The beam velocity and the wire voltage are fixed to $v_z=310$ m/s and $U=1.5$ kV, respectively.

Figure 10

(a) Electric field according to Eq. (1) at $\Delta x=375\mu$m as a function of the tube radius. (b) Simulated enhancement of the ND${}_3$ peak density as a function of the tube radius. The beam velocity and the wire voltage are fixed to $v_z=310$ m/s and $U=1.5$ kV, respectively.

Figure 11

Simulated density enhancement of ND${}_3$ molecules in the ground state $|0,0\rangle$ as a function of velocity down to $v_z\sim 20$ m/s (solid line; left scale). The dashed line indicates the number of molecules that hit the wire on their way from the nozzle to the detector in proportion to the number of detected molecules (right scale).