New Limits on Variation of the Fine-Structure Constant Using Atomic Dysprosium

We report on the spectroscopy of radio-frequency transitions between nearly degenerate, opposite-parity excited states in atomic dysprosium (Dy). Theoretical calculations predict that these states are very sensitive to variation of the fine-structure constant $\alpha$ owing to large relativistic corrections of opposite sign for the opposite-parity levels. The near degeneracy reduces the relative precision necessary to place constraints on variation of $\alpha$, competitive with results obtained from the best atomic clocks in the world. Additionally, the existence of several abundant isotopes of Dy allows isotopic comparisons that suppress common-mode systematic errors. The frequencies of the 754-MHz transition in ${}^{164}\mathrm{Dy}$ and 235-MHz transition in ${}^{162}\mathrm{Dy}$ are measured over the span of two years. The linear variation of $\alpha$ is $\dot{\alpha }/\alpha =(-5.8\pm {6.9}_{[1\sigma ]})\times {10}^{-17}{\mathrm{yr}}^{-1}$, consistent with zero. The same data are used to constrain the dimensionless parameter $k_{\alpha }$ characterizing a possible coupling of $\alpha$ to a changing gravitational potential. We find that $k_{\alpha }=(-5.5\pm {5.2}_{[1\sigma ]})\times {10}^{-7}$, essentially consistent with zero and the best constraint to date.

Figure 1

Partial energy diagram for Dy showing states of interest. Preparation of atoms is accomplished via two laser excitations and a spontaneous decay with 30% branching ratio into metastable state $B$. Atoms are excited from state $B$ to $A$ by a resonant, frequency-modulated rf electric field. State $A$ decays with lifetime $\sim 8\mu \mathrm{s}$. A photomultiplier tube and lock-in amplifier detect the 564-nm fluorescence. The bottom right inset shows typical lock-in signals for the 753.5-MHz transition in ${}^{164}\mathrm{Dy}$ at the first (top) and second (bottom) harmonics of the modulation frequency. Residual errors of line shape fits are magnified $5\times$ and shown as empty circles.

Figure 2

Schematic of the experimental setup. Argon-ion lasers pump a dye laser producing 669-nm light and a Ti:sapphire laser producing 833-nm light. Components in vacuum are within the dashed boundaries. (a) Skimmers collimate the atomic beam and act as conductance chokes for differential pumping between the oven chamber and interaction chamber. (b) Lenses diverge the laser light to match the atomic-beam divergence. (c) In-vacuum linear polarizers are the last optical element for the laser light before interacting with Dy atoms. (d) A central conductor surrounded by a grounded shell on all sides defines the rf electric-field region. (e) Polished aluminum mirrors guide fluorescence to a photomultiplier tube. (f) An interference filter with peak transmission at 564 nm suppresses stray laser and oven light. (g) A glass pipe guides fluorescent light to a PMT for detection with a lock-in amplifier.

Figure 3

Changes in the transition frequencies for ${}^{162}\mathrm{Dy}$ (filled circles) and ${}^{164}\mathrm{Dy}$ (empty circles) over the span of two years. The frequencies for ${}^{162}\mathrm{Dy}$ and ${}^{164}\mathrm{Dy}$ are displayed with respect to 234 661 102 and 753 513 708 Hz, respectively. (a) The data are fit by linear functions with equal magnitude slopes of opposite sign (solid) and same sign (dashed). (b) The data are fit by cosine functions with equal amplitudes but 180° phase difference (solid) and 0° phase difference (dashed). The variation of the dimensionless gravitational potential scaled in relative units by $5\times {10}^{10}$ is shown by the light solid line.