Fig. 1: System of two magnon Bose–Einstein condensates (BECs).

a The green and blue dots at the north and south poles of the Bloch sphere represent pure \(\left|+\right\rangle\) and \(\left|-\right\rangle\) states of the double magnon condensate BEC^± formed in two different global energy minima of the magnon system, while the red dot shows the position of a mixed state of BEC⁺ and BEC⁻. b Schematic spectrum of magnons and BEC generation via parametric pumping using microwave photons of frequency ω_p with small wavenumbers q_p ≈ 0. The green and blue thick lines schematically depict the dispersion branches of the lowest-frequency magnon mode for the positive and negative wavevectors q_z along the magnetization direction z. The red dashed arrows indicate the process of decaying the pump photon into two magnons of half the pump frequency and opposite wavevectors. The green and blue dots mark the spectral positions of the BEC⁺ and BEC⁻ formed in the two global energy minima at \({q}_{z}=+{q}_{{}_{{{{{{{{\rm{BEC}}}}}}}}}}\) and \({q}_{z}=-{q}_{{}_{{{{{{{{\rm{BEC}}}}}}}}}}\). The green and blue shaded areas symbolize the corresponding magnon gaseous states. c Numerical simulation of the condensation process of parametrically populated magnon gas in an yttrium-iron-garnet (YIG) ferrimagnetic film. The fine structure of the magnon gas population corresponds to the thickness magnon modes of this film. The YIG film-thickness is 5 μm. The pumping frequency ω_p/(2π) is 7.5 GHz with a pump duration of 50 ns. The bias magnetic field is 100 mT. d Spatial interference pattern formed by the superposition of the BEC⁺ and BEC⁻ states along the magnetization direction z. The magnon density stripes along the perpendicular direction y correspond to the BEC wave fronts. The color code indicates the normalized magnon density in c and d. The quite regular structure of the interference pattern corresponds to a relatively high degree of spatial coherence of the magnon BEC.