Direct measurement of repulsive and attractive pair potentials using pairs of optical traps

We present a technique for measuring the interactions between pairs of colloidal particles in two optical traps. This method is particularly suitable for measuring strongly attractive potentials, an otherwise challenging task. The interaction energy is calculated from the distribution of inter-particle separations by accounting for the contribution from the optical traps with arbitrary trap profiles. The method is simple to implement and applicable to different types of pair potentials and optical trapping geometries. We apply the method to measure dipolar pair interactions in experiments with paramagnetic colloids in external magnetic fields. We obtain consistent and accurate results in all regimes, from strongly attractive to repulsive potentials. By means of computer simulations, we demonstrate that the proposed method can be successfully applied to systems with complex pair interactions characterized by multiple attractive and repulsive regimes, which are ubiquitous in soft and biological matter.