The Heisenberg limit, corresponding to a root mean square error vanishing as N-1 with the number N of independent processes probed in an experiment, is widely believed to be an ultimate limit to the precision of quantum metrology. Here, we experimentally demonstrate a quantum metrology protocol surpassing the Heisenberg limit by probing two groups of independent processes in a superposition of two alternative orders. Each process creates a phase space displacement, and our setup achieves the super-Heisenberg limit N-2 in the estimation of a geometric phase associated to two sets of N displacements. In stark contrast with previous works, our results only require a single-photon probe whose initial energy is independent of N, and outperform every setup where the displacements are probed in a definite order.