Each of the two orthogonal AODs (AOD-x/y) is driven by the same two RF tones at frequencies 1 and 1 + , which creates 2 x 2 laser beams. We use a slit to select the two beams that have equal optical frequencies, while the distance between the beams can be tuned by changing the RF tone frequency difference . The Dove prism rotates the optical plane to place the beams into the plane of the optical table. The beams are subsequently focused in the vacuum chamber to form two traps at a distance d 0. The light back-scattered by the particles is reflected with a Faraday rotator (FR) and a polarizing beamsplitter (PBS) and sent to two independent heterodyne detectors monitoring particle motion. Inset: two particles are trapped and interact anti-reciprocally with the coupling rate g a tuned by the polarization angle , which we set with a HWP in front of the vacuum chamber.