Abstract Bose–Einstein condensates (BECs) are macroscopic coherent matter waves that have revolutionized quantum science and atomic physics. They are important to quantum simulation1 and sensing2,3, for example, underlying atom interferometers in space4 and ambitious tests of Einstein’s equivalence principle5,6. A long-standing constraint for quantum gas devices has been the need to execute cooling stages time-sequentially, restricting these devices to pulsed operation. 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 1,000 times higher phase-space densities than previous works7,8, we maintain the conditions for condensation. Our experiment is the matter wave analogue of a CW optical laser with fully reflective cavity mirrors. This proof-of-principle demonstration provides a new, hitherto missing piece of atom optics, enabling the construction of continuous coherent-matter-wave devices.
The conventional magnon Bose-Einstein condensation (BEC of magnons with k = 0) is a coherent state of excited magnons described by a common wave function. It was observed first in antiferromagnetic superfluid states of 3He. Here we report on the discovery of a very similar magnon BEC in ferrimagnetic film at room temperature. The experiments were performed in Yttrium Iron Garnet (YIG) films at a magnetic field oriented perpendicular to the film. The high-density quasiequilibrium state of excited magnon was formed by methods of pulse and/or Continuous Waves (CW) magnetic resonance. We have observed a Long Lived Induction Decay Signals (LLIDS), well known as a signature of spin superfluidity. We demonstrate that the BEC state may maintain permanently by continuous replenishment of magnons with a small radiofrequency (RF) field. Our finding opens the way for development of potential supermagnonic applications at an ambient conditions.
We analyze sound waves (phonons, i.e. Bogoliubov excitations) propagating on continuous-wave (cw) solutions of repulsive
F=1 spinor Bose-Einstein condensates (BECs) such as
23Na (which is antiferromagnetic or polar) and
87Rb (which is ferromagnetic). Zeeman splitting by a uniform magnetic field is included. All cw solutions to ferromagnetic BECs with vanishing
MF=0 particle density and nonzero components in both ${M}_{F}=\ifmmode\pm\else\textpm\fi{}1$ fields are subject to modulational instability (MI). Modulational instability increases with increasing particle density. Modulational instability also increases with differences in the components' wave numbers; this effect is larger at lower densities but becomes insignificant at higher particle densities. Continuous-wave solutions to antiferromagnetic (polar) BECs with vanishing
MF=0 particle density and nonzero components in both ${M}_{F}=\ifmmode\pm\else\textpm\fi{}1$ fields do not suffer MI if the wave numbers of the components are the same. If there is a wave-number difference, MI initially increases with increasing particle density and then peaks before dropping to zero beyond a given particle density. The cw solutions with particles in both ${M}_{F}=\ifmmode\pm\else\textpm\fi{}1$ components and nonvanishing
MF=0 components do not have MI if the wave numbers of the components are the same, but do exhibit MI when the wave numbers are different. Direct numerical simulations of a continuous wave with weak white noise confirm that weak noise grows fastest at wave numbers with the largest MI and show some of the results beyond small-amplitude perturbations. Phonon dispersion curves are computed numerically; we find analytic solutions for the phonon dispersion in a variety of limiting cases.