Investigation of ac Stark shifts in excited states of dysprosium relevant to testing fundamental symmetries

We report on measurements of the differential polarizability between the nearly degenerate, opposite parity states in atomic dysprosium at 19 797.96 cm${}^{-1}$, and the differential blackbody radiation induced Stark shift of these states. The differential scalar and tensor polarizabilities due to additional states were measured for the $\left|M\right|=7,\cdots ,10$ sublevels in ${}^{164}$Dy and ${}^{162}$Dy and determined to be ${\overline{\alpha }}_{BA}^{\left(0\right)}=180{\left(45\right)}_{\mathrm{stat}}{\left(8\right)}_{\mathrm{sys}}$ $\text{mHz}/{(\mathrm{V}/\mathrm{cm})}^2$ and ${\overline{\alpha }}_{BA}^{\left(2\right)}=-163{\left(65\right)}_{\mathrm{stat}}{\left(5\right)}_{\mathrm{sys}}$ $\text{mHz}/{(\mathrm{V}/\mathrm{cm})}^2$, respectively. The average blackbody radiation induced Stark shift of the Zeeman spectrum was measured around 300 K and found to be $-34\left(4\right)$ mHz/K and $+29\left(4\right)$ mHz/K for ${}^{164}$Dy and ${}^{162}$Dy, respectively. We conclude that ac Stark related systematics will not limit a search for variation of the fine-structure constant, using dysprosium, down to the level of $|\dot{\alpha }/\alpha |=2.6\times {10}^{-17}$ yr${}^{-1}$, for two measurements of the transition frequency one year apart.

Figure 1

Partial energy levels diagram of dysprosium. Solid (dashed) arrows indicate induced (spontaneous) transitions.

Figure 2

Frequency of the $M=+10$, $M=-10$, and the $M=\pm 10$ average Zeeman transition, offset for presentation. Over the course of this measurement, the individual Zeeman transition frequencies changed by $\approx$3500 Hz, while the $\pm M$ average changed by $\approx$8 Hz, demonstrating a suppression of $\approx$450. The actual separation between the $M=+10$ and $M=-10$ transition is $\approx$$3\times {10}^6$ Hz. These data were taken while the interaction region was cooled toward liquid nitrogen temperatures. The relatively large drift in magnetic field of $>$1 mG is believed to be due to thermoelectric currents induced by temperature gradients between dissimilar metals.

Figure 3

The Zeeman structure of the $B\to A$ transition is resolved with a 550 mG field. The ratio $R$, as determined by Eq. (13), is measured at the probe-field frequencies ${\nu }_i$ for $i=1,....,6$.

Figure 4

Section view of the atomic-beam apparatus. (a) Oven chamber, (b) gate valve, (c) interaction-region chamber, (d) Dy oven, (e) vacuum chokes, (f) laser access/in-vacuum polarizer, (g) magnetic coils, (h) light pipe, (i) rf electrodes, (j) light-collection mirrors, and (k) two-layer magnetic shielding.

Figure 5

Radio-frequency setup for the measurement of ac Stark shifts. The probe field and a second off-resonant electric field are provided by two separately amplified signal generators. Radio-frequency circulators isolate the amplifiers from reflections from the rf region. Rf splitter and combiner ensure a symmetric feed of the signals into the rf region. The directional couplers allow us to monitor the rf power before the apparatus.

Figure 6

The mean ac Stark shift of the $\pm M$ transitions in ${}^{162}$Dy and ${}^{164}$Dy as a function of mean-squared electric-field amplitude $E^2$. Lines of best fit are obtained from least-squares fit of Eq. (15) to the data. Measurements for different Zeeman transitions are offset from each other for display purposes. Note the difference in horizontal scale.

Figure 7

Average ac Stark shift of the $\pm M$ sublevels as a function of the Stark field frequency ${\nu }_S$. The zero crossings at the centers of the dispersive resonances indicate the approximate location of the individual Zeeman transition frequencies. The mean-squared amplitude of the Stark field is $\approx$9 (V/cm)${}^2$.

Figure 8

Change in the frequency of the unresolved $B\to A$ transition as a function of interaction region temperature.