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We demonstrate a density-dependent gauge field, induced by atomicinteractions, for quantum gases. The gauge field results from the synchronouscoupling between the interactions and micromotion of the atoms in a modulatedtwo-dimensional optical lattice. As a first step, we show that a coherentshaking of the lattice in two directions can couple the momentum andinteractions of atoms and break the four-fold symmetry of the lattice. We thencreate a full interaction-induced gauge field by modulating the interactionstrength in synchrony with the lattice shaking. When a condensate is loadedinto this shaken lattice, the gauge field acts to preferentially prepare thesystem in different quasimomentum ground states depending on the modulationphase. We envision that these interaction-induced fields, created by finecontrol of micromotion, will provide a stepping stone to model new quantumphenomena within and beyond condensed matter physics.

Observation of density-dependent gauge fields in a Bose-Einstein condensate based on micromotion control in a shaken two-dimensional lattice