Preparation of one $^{87}$Rb and one $^{133}$Cs atom in a single optical tweezer

We report the preparation of exactly one $^{87}$Rb atom and one $^{133}$Cs atom in the same optical tweezer as the essential first step towards the construction of a tweezer array of individually trapped $^{87}$Rb$^{133}$Cs molecules. Through careful selection of the tweezer wavelengths, we show how to engineer species-selective trapping potentials suitable for high-fidelity preparation of Rb $+$ Cs atom pairs. Using a wavelength of 814~nm to trap Rb and 938~nm to trap Cs, we achieve loading probabilities of $0.508(6)$ for Rb and $0.547(6)$ for Cs using standard red-detuned molasses cooling. Loading the traps sequentially yields exactly one Rb and one Cs atom in $28.4(6)\,\%$ of experimental runs. Using a combination of an acousto-optic deflector and a piezo-controlled mirror to control the relative position of the tweezers, we merge the two tweezers, retaining the atom pair with a probability of $0.99^{(+0.01)}_{(-0.02)}$. We use this capability to study hyperfine-state-dependent collisions of Rb and Cs in the combined tweezer and compare the measured two-body loss rates with coupled-channel quantum scattering calculations.