Determination of the ground state polarizability of $^{162}$Dy near 530 nm

Abstract

Open-shell lanthanide atoms, and dysprosium in particular, combine a large ground-state angular momentum with dense electronic spectra, making their dynamical polarizability strongly dependent on wavelength and internal state and therefore particularly challenging to characterize accurately. This issue has become especially relevant with the recent development of single-atom trapping of dysprosium in optical-tweezer arrays, where precise knowledge of the polarizability is needed to design optimized trapping architectures. Here, we exploit the strong spin-dependent light shift near the $J'=J-1$ intercombination line at 530.306 nm to determine the background scalar and vector polarizabilities of $^{162}$Dy in its ground state near this wavelength. Our measurements quantitatively agree with atomic-structure calculations and provide new insight into the contributions of nearby transitions in a spectral region relevant to emerging dysprosium tweezer platforms.

Figures (4)

• Figure 1: Schematic representation of the polarization dependence of the light shift. For a polarization set by the angle $\theta$, we obtain a repulsive (attractive) optical potential for $\theta$ above (below) the cancellation angle $\theta_{\rm cancel}$. At $\theta=\theta_{\rm cancel}$, the polarizability (and thus the light shift) vanishes. This behavior is illustrated schematically in the top row (left to right). The bottom panels are absorption images representative of the three corresponding cases.
• Figure 2: Zero-crossing of the polarizability from time-of-flight expansion in the presence of the SLS beam at a detuning $\Delta = 815.9GHz$. Top panels: azimuthally integrated optical density $\tilde{n}(r)$ as a function of the distance from the cloud center, $r$, for three different polarizations of the spin-dependent light-shift (SLS) laser beam. Black curves correspond to the expansion without the SLS beam (reference), while green curves show the expansion in the presence of the SLS beam. From left to right we realize an attractive potential ($U_{\rm LS}<0$), an almost vanishing potential ($U_{\rm LS}\approx 0$), and a a repulsive potential ($U_{\rm LS}>0$). Vertical dashed lines indicate the extracted peak radius $\tilde{r}_{\rm peak}$. Bottom panel: relative peak radius $\tilde{r}_{\rm rel}$ (see main text) as a function of the angle of the half-wave plate, $\vartheta_{2}$ for $\vartheta_{4} = 160^\circ$. The dashed horizontal line at $\tilde{r}_{\rm rel.}=1$ marks the condition where the SLS beam does not modify the expansion, corresponding to a cancellation of the light shift.
• Figure 3: Polarizability cancellation for different detunings. Each panel shows the polarizability $\alpha$ (in units of $\alpha_0$) of the state $\left\vert-J\right\rangle$ as a function of the half-wave-plate angle $\vartheta_{2}$ and quarter-wave-plate angle $\vartheta_{4}$, computed using the fitted background polarizabilities $\alpha^{\rm{bg}}_{st} = 399\,\alpha_0$ and $\alpha^{\rm{bg}}_{v} = 41\,\alpha_0$. Since the polarizability is insensitive to the phase $\varphi$ and depends only on the degree of circular polarization $\theta$, continuous sets of combinations $(\vartheta_{2}, \vartheta_{4})$ yield the same value of $\alpha$. The panels correspond to different detunings $\Delta$ of the SLS beam, from left to right: $\Delta/(2\pi) = 100.7,\ 500.3,\ 815.9,\ 902.8,$ and $1009.9~\mathrm{GHz}$. The Jones matrix $M$ (see main text) is the same for all panels. Red disks indicate the experimental zero crossings extracted from the expansion measurements, while solid black lines show the calculated zero-polarizability contours. Dashed and dash-dotted contours illustrate the expected shift of the zero-crossing lines when $\alpha^{\mathrm{bg}}_{\mathrm{st}}$ is varied by $+30\,\alpha_0$ and $-30\,\alpha_0$, respectively.
• Figure 4: Calibration of the linewidth $\Gamma_0$. (a) Schematic representation of the spectroscopy method (see text). (b) Fraction of atoms transferred to the state $\left\vert-7\right\rangle$ by the Raman coupling, for an SLS detuning of $\Delta/(2\pi) = 7.88GHz$ and for different SLS powers, as a function of the two-photon detuning measured with respect to the Raman resonance in the absence of the SLS beam. The resonant condition depends on the intensity of the SLS beam. An offset is added to each curve for visibility. (c) Raman resonance frequencies variation with SLS power and detuning. The slope of the linear fit is used to determine the ordinary dipole matrix element $d$, directly related to the linewidth $\Gamma_0$ of the transition.