Microscopic Rydberg electron orbit manipulation with optical tweezers

Abstract

Laser cooling and trapping of atomic matter waves in optical potentials has enabled rapid progress in quantum science, particularly when combined with Rydberg excitation of the atoms to induce long-range interactions. Here, we propose the local manipulation and spatio-temporal sculpting of the electronic matter wave of a Rydberg atom by a laser field focused so that its beam width is smaller than the Rydberg electron orbit. We compute the electronic eigenstates in the presence of a sharply focused Gaussian laser beam, and find strong Rydberg state mixing leading to large kilo-Debye dipole moments. These can be modulated with high bandwidth controlled by the local tweezer intensity. Oscillations in the position-dependent level shifts, analogous to the potential wells allowing ultralong-range Rydberg molecules to form, provide opportunities to trap the Rydberg atom in an eccentric way via ponderomotive forces acting on sub-orbital length scales.

Figures (9)

• Figure 1: Experimental scheme and definition of coordinate system: A tweezer beam is focused at the origin of the coordinate system. The ionic core of the Rydberg atom (red sphere) is located at $\boldsymbol{R}_c$, the Rydberg electron (blue sphere) is located at $\boldsymbol{X}$. The tightly focused laser beam strongly perturbs the quasi-degenerate Rydberg levels, resulting in localized electronic states reminiscent of the "trilobite" orbitals in long-range Rydberg molecules (blue density plot).
• Figure 2: Energies $U_{\nu f}$ and electric dipole moment magnitude $\mathcal{D}_x=e \langle x \rangle$ for $\nu=60$ as a function of the core position $\boldsymbol{R}_c=R_c \, \hat{\boldsymbol{x}}_B$, shown for different $\eta$ values. As reference, $s_{60}=380$ nm and the gray dashed line indicates $R_c=w_0$. The right column shows the electron density $|\psi(\boldsymbol{r};R_c)|^2$ for the eigenstates in the blue (top) and red (bottom) $\eta=1/10$ PECs at core position indicated by the arrow. The white surface represents the 30 % intensity iso-surface of the beam. To expose the small breaking of inversion symmetry along the $x$ axis, we show in the insets the relative asymmetry in the reduced $x$ density $\rho_x(x)= \int |\psi(\boldsymbol{r})|^2 \, \mathrm{d}y \, \mathrm{d}z$ defined as $\Delta(x)=(\rho_x(x)-\rho_x(-x))/(\rho_x(x)+\rho_x(-x))$ at a given $R_c$.
• Figure 3: (a) Ponderomotive energies $U_{\nu f}$ as function of scaled displacement $R_c/\nu^2$ for $\eta=0.11$ and different $\nu$. (b) Extrapolated total PECs $\mathcal{U}_{\nu f}$ including $\hat{V}_{\mathrm{core}}$ in the Hamiltonian for $\nu{=}200$ and a tweezer with $\lambda{=}460$ nm and $w_0{=}480$ nm (resulting in $\eta{=}0.11$). The inset in (b) shows the full scale shifts.
• Figure 4: Energies $U_{\nu \ell_{ \mathrm h}}$ and dipole moments for the $\nu=60$ high-$\ell$ manifold as a function of the core position $R_c$ and different reduced waists $\eta$. The displayed dipole moments correspond to the five highest energy states.
• Figure 5: Electron density $|\psi(\boldsymbol{r};R_c)|^2$ for the red- and blue-highlighted PECs in Fig. \ref{['fig:high_l']} at core position marked by the gray arrow. Panels (a) and (b) correspond to $\eta=1/200$, while panels (c) and (d) correspond to $\eta=1/2$. The beam iso-surface is set to 30 % of the on-axis intensity.