Imaging the vacuum fluctuations of a quantum field

Heisenberg uncertainties lead to inevitable fluctuations in the measurement outcomes for quantum-mechanical observables. For quantum fields, these uncertainties result in random spatial structures in snapshots of a field, even when the field is in its ground (vacuum) state. Such `vacuum fluctuations' are at the heart of a wide range of phenomena, from spontaneous decay processes to the Casimir force and Hawking radiation. Their existence is a key manifestation of the quantumness of the physical world, but usually it is only their consequences that are directly observed. Here, we directly observe spatial vacuum fluctuations of a bosonic quantum field. Our experiments are based on a homogeneous planar atomic Bose--Einstein condensate. The condensate comprises two coherently coupled interacting components (spin states), and the quantum field describes its spin degrees of freedom. In the regime where the interactions dominate over the coherent coupling, our system emulates a (massive relativistic) sine-Gordon field. Images of the field reveal simultaneous fluctuations on different length scales, with scale-dependent amplitudes consistent with theoretical predictions for a vacuum state. Observing such fluctuations in the sine-Gordon limit opens many possibilities for laboratory simulations of relativistic fields in regimes that are presently not theoretically tractable.