  Bose-Einstein condensates (BECs) are macroscopic coherent matter waves that
have revolutionized quantum science and atomic physics. They are essential to
quantum simulation and sensing, for example underlying atom interferometers in
space and ambitious tests of Einstein's equivalence principle. The key to
dramatically increasing the bandwidth and precision of such matter-wave sensors
lies in sustaining a coherent matter wave indefinitely. Here we demonstrate
continuous Bose-Einstein condensation by creating a continuous-wave (CW)
condensate of strontium atoms that lasts indefinitely. The coherent matter wave
is sustained by amplification through Bose-stimulated gain of atoms from a
thermal bath. By steadily replenishing this bath while achieving 1000x higher
phase-space densities than previous works, we maintain the conditions for
condensation. This advance overcomes a fundamental limitation of all atomic
quantum gas experiments to date: the need to execute several cooling stages
time-sequentially. Continuous matter-wave amplification will make possible CW
atom lasers, atomic counterparts of CW optical lasers that have become
ubiquitous in technology and society. The coherence of such atom lasers will no
longer be fundamentally limited by the atom number in a BEC and can ultimately
reach the standard quantum limit. Our development provides a new, hitherto
missing piece of atom optics, enabling the construction of continuous coherent
matter-wave devices. From infrasound gravitational wave detectors to optical
clocks, the dramatic improvement in coherence, bandwidth and precision now
within reach will be decisive in the creation of a new class of quantum
sensors.
