Absence of Far-Detuned Attractive Optical Traps for Alkali Rydberg Atoms

Abstract

Neutral-atom quantum simulation is susceptible to entanglement between the atom's internal electronic state and its center-of-mass position. In many alkali Rydberg platforms, the 'spin-motion coupling' is exacerbated by the free expansion required to avoid ponderomotive anti-trapping from optical fields. A recent proposal (arXiv:2505.01071) claims sufficiently excited Rydberg states could be trapped in a monochromatic, far-detuned, circularly polarized optical field by harnessing a large vector polarizability. We disprove the proposal through analytic calculation and measurement of the vector polarizability of the $54S$, $54P$, and $53D$ orbitals of Cesium. Regarding the optical angular frequency $ω$, we analytically derive that the scalar, vector, and tensor polarizabilities scale as $ω^{-2}$, $ω^{-3}$, and $ω^{-4}$, as opposed to the proposed scaling of $ω^{-2}$, $ω^{-1}$, and $ω^{-2}$. We refine the sum-over-states expression for vector and tensor polarizability to be numerically stable and predict negligible vector and tensor polarizabilities far detuned from resonances, in agreement with our measurements. However, we find vector polarizability can enhance a recent proposal for near-detuned attractive trapping. Furthermore, we evaluate the breakdown of the electric-dipole approximation and derive no effect stronger than ponderomotive repulsion. We conclude that an attractive, monochromatic, far-detuned optical trap for alkali Rydberg states is not possible, regardless of the beam geometry.

Figures (8)

• Figure 1: (a) The polarization ellipse for an electric field with ellipticity $\gamma$, linearity $l=\cos(2\gamma)$, and circularity $c=\sin(2\gamma)$. The electric field is $\vec{E}(t)=\Re(\mathcal{E} \hat{\epsilon}e^{i(kz-\omega t)})$ with the ellipse showing the directions that the electric field points over a period of oscillation. Both the direction of field propagation and the effective magnetic field experienced by the atom are into the page. (b) A schematic for how the scalar, vector, and tensor polarizabilities diagonally perturb the sublevels of a fine structure level of $J=\{1/2,3/2\}$ that are quantized by a DC magnetic field. The sublevels are arranged in order of increasing $m_J$, and the arrows depict how the scalar, vector, and tensor polarizabilities apply a common-mode, antisymmetric, and symmetric change to the energy of the sublevels.
• Figure 2: (a) Experimental apparatus. Atoms are trapped in an optical tweezer array, whose ellipticity is controlled by a waveplate on a motorized rotation mount. (b) Energy levels relevant to this work. Rydberg state $54S_{1/2}$ is reached by two vertical laser beams ('IR' and 'Blue'), and additional states $54P$, $53D$ are addressed by two microwave radiations ('M1' and 'M2'). (c) Pulse sequence for probing polarizability of $54S_{1/2}$ states. Power $P$ of tweezer light is varied only for a target site to excite one atom at a time, and this step is repeated for all sites. (d) Pulse sequence for probing polarizability of $54P$ and $53D$ states. IR/Blue $\pi$-pulse is applied to prepare $54S_{1/2}, m_J = 1/2$ at a target site, and another $\pi$-pulse is applied for read-out. The power of tweezer is varied in between, during which microwave M1 is pulsed to measure light shift (M2 is continuously on).
• Figure 3: Light shift measurement for $54S_{1/2}$. (a) Excitation spectra of $m_j = \pm1/2$ levels at three different tweezer powers $P/P_0 = 0, 0.25, 0.5$, where $P_0$ is the initial trap depth. The y-axis is the probability of remaining in the ground level $6S_{1/2}$ after a Rydberg excitation. The x-axis is a scan of the Blue laser's frequency about 657933.21 GHz with the IR laser at 282286.14 GHz. The trap depths of the detuned sites are maintained at $P_0$. (b) (left) Frequency shift vs. tweezer power for the two $m_j$ levels. The curves represent linear fits. (right) Frequency shift vs. waveplate angle at the tweezer power of $P/P_0 = 0.5$. (c) Effective total magnetic field $B_{\text{tot}}$ as a function of circularity, $c$ (see text).
• Figure 4: Light shift measurements for $54P_{1/2}$ and $54D_{3/2}$. (a,d) Excitation spectra of magnetic sublevels in $54P_{1/2}$ and $53D_{3/2}$ at two different tweezer powers $P/P_0 = 0, 0.6$. The x-axis represents M1 and M2 microwave frequencies, plotted relative to 23.7 GHz and 3.9 GHz, respectively. (b,e) Frequency vs. waveplate angle for the magnetic sublevels, plotted relative to their respective bare resonances without the tweezers. (c,f) Effective total magnetic field as a function of circularity, $c$. Error bars in (b) and (e) are the standard error of mean of centers from Gaussian fits for least 5 measurements, each comprising several hundred runs.
• Figure 5: Light shift measurements for $54D_{5/2}$. (a) Frequency vs. waveplate angle for two magnetic sublevels, $m_J = 5/2,-3/2$, at the tweezer power $P/P_0 = 0.75$. The data is plotted relative to the bare resonances without the tweezers. (The microwave powers of M1 and M2 were reduced for $m_J = 5/2$ to increase resolution, resulting in the overall frequency shift of $\sim 1.5$ MHz due to light shift.) (b) Effective total magnetic field as a function of the circularity, $c$.