Collisional perturbation of radio-frequency $E1$ transitions in an atomic beam of dysprosium

We have studied collisional perturbations of radio-frequency (rf) electric-dipole $\left(E1\right)$ transitions between the nearly degenerate opposite-parity levels in atomic dysprosium (Dy) in the presence of 10 to $80\mathrm{\mu }\mathrm{Torr}$ of ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, He, Ar, Ne, Kr, and Xe. Collisional broadening and shift of the resonance, as well as the attenuation of the signal amplitude are observed to be proportional to the foreign-gas density with the exception of ${\mathrm{H}}_2$ and Ne, for which no shifts were observed. Corresponding rates and cross sections are presented. In addition, rates and cross sections for ${\mathrm{O}}_2$ are extracted from measurements using air as foreign gas. The primary motivation for this study is the need for accurate determination of the shift rates, which are needed in a laboratory search for the temporal variation of the fine-structure constant [A. T. Nguyen, D. Budker, S. K. Lamoreaux, and J. R. Torgerson, Phys. Rev. A 69, 22105 (2004)].

Figure 1

Relevant levels and transitions in atomic dysprosium. Population and detection scheme: Level $B$ is populated in a three-step process. The atoms are excited to level $f$ in the first two steps using 833- and 699-nm laser light (solid arrows). The third step is a spontaneous decay (labeled by a short-dashed arrow) from level $f$ to level $B$ with $\sim 30\%$ branching ratio. The population is transferred to level $A$ by the rf electric field (curved long-dashed lines). Atoms in level $A$ decay to level $c$ and then to the ground state. The fluorescence from the second decay $\left(564\mathrm{nm}\right)$ is used for detection. Inset: Hyperfine structure of levels $A$ and $B$ for ${}^{163}\mathrm{Dy}$. Zero energy is chosen to coincide with the lowest hyperfine component.

Figure 2

Experimental setup (not shown to scale): (a) Atomic beam produced by effusive oven source at $\sim 1500\mathrm{K}$; (b) atomic-beam collimator; (c) oven light collimator; (d) cylindrical lenses to diverge laser beams; (e) interaction region of atoms with the electric field enclosed in a magnetic shield (not shown); (f) cylindrical mirror to collect fluorescent light; (g) lucite light pipe; (h) interference filter; and (i) short-pass filter.

Figure 3

Schematic diagram of the rf-generation, control, and pressure-measurement systems. The rf synthesizer is referenced to a Cs standard, which is compared to a CDMA (Code Division Multiple Access) primary reference source. Both clocks have a long term stability of $\sim {10}^{-11}$. The output of the synthesizer is amplified and then sent to the electric-field plates and a $50\mathrm{\Omega }$ power-resistor termination in series with the larger impedance of the plates. The output of the photomultiplier tube is sent to the lock-in amplifier for detection and acquisition.

Figure 4

First- and second-harmonic signals for 10-kHz frequency modulation. The solid line is a fit to the function derived from first-order time-dependent perturbation theory.

Figure 5

Shift of the resonance frequency for both transitions due to the presence of krypton. $\mathrm{\Delta }\nu$ is the difference between the transition frequency and the fixed rf synthesizer carrier frequency ($3074000\mathrm{Hz}$ and $234661000\mathrm{Hz}$ for the two transitions). The solid lines are the least-squares linear fits to the data.

Figure 6

Collisional broadening for the 235-MHz transition due to Kr without the phasing-effect correction. On the $y$ axis, the inverse of the normalized first harmonic slope, which is directly proportional to the linewidth is plotted. The solid line is the least-squares linear fit to the data.

Figure 7

Decrease in the second harmonic signal for the 235-MHz transition due to Xe. The signal has been normalized to one at zero pressure. The solid line is the least-squares fit to the data.

Figure 8

Shifts due to collision of the Dy atoms in the beam. Beam density was varied by changing the oven temperature from 1170 °C to 1077 °C which correspond to the estimated atomic densities in the interaction region shown in the plots.