# Anisotropic Interactions in Electric Field Polarized Ultracold Rydberg Gases

## TL;DR

This paper calculates and compares interaction potentials of Rydberg atoms in an electric field, showing improved agreement with experiments for anisotropic dipole-dipole and van der Waals interactions near the blockade radius.

## Contribution

It provides detailed calculations of anisotropic Rydberg interactions in an electric field, improving agreement with experimental data over previous independent atom models.

## Key findings

- Calculated $C_6$ within 8% of experiment
- Calculated $C_3$ within 20% of experiment
- Molecular calculations outperform independent atom models near blockade radius

## Abstract

We calculate pair potential curves for interacting Rydberg atoms in a constant electric field and use them to determine the effective $C_3$ dipole-dipole and $C_6$ van der Waals coefficients. We compare the $C_3$ and $C_6$ with experiments where the angle of a polarizing electric field is varied with respect to the axis of a quasi-1-dimensional trap at ultracold temperatures. The dipoles produced via polarization of the atoms have an angular dependent dipole-dipole interaction. We focus on the interaction potential of two rubidium Rydberg atoms in $50S_{1/2}$ states in the blockade regime. For internuclear distances close to the blockade radius, $R_{bl} \approx 4 - 6\,\mu$m, molecular calculations are in much better agreement with experimental results than those based on the properties of single atoms and independent calculations of $C_3$ and $C_6$ which were used to analyze the original experiment. We find that the calculated $C_6$ coefficient is within $8\%$ of the experimental value while the $C_3$ coefficient is within $20\%$ of the experimental value.