High harmonic generation from a Bose-Einstein condensate

Lasers provide intense coherent radiation, essential to cool and trap atoms into a Bose-Einstein condensate or can alternatively drive the non-linear dynamics of high-order harmonic generation. Yet, these two fundamental processes remained of independent consideration. Here, we connect matter waves at ultracold temperatures with radiation bursts on the ultrafast attosecond timescale. We do this by exploring high harmonic generation from a Bose-Einstein condensate. We show that the quantum state of the generated harmonics of a driven Bose gas is a classical mixture, while below the critical temperature of Bose-Einstein condensation the emitted harmonic radiation is in a pure quantum state. These states furthermore exhibit squeezing and entanglement across all field modes.