Bose-Einstein Condensation of Magnons in Atomic Hydrogen Gas

We report on experimental observation of Bose-Einstein condensation (BEC)-like behavior of quantized electron spin waves (magnons) in a dense gas of spin-polarized atomic hydrogen. The magnons are trapped and controlled with inhomogeneous magnetic fields and described by a Schrödinger-like wave equation, in analogy to the BEC experiments with neutral atoms. We have observed the appearance of a sharp feature in the ESR spectrum displaced from the normal spin wave spectrum. We believe that this observation corresponds to a sudden growth of the ground-state population of the magnons and emergence of their spontaneous coherence for hydrogen gas densities exceeding a critical value, dependent on the trapping potential. We interpret the results as a BEC of nonequilibrium magnons which were formed by applying the rf power.

Figure 1

cw (a) and pulsed (b) ESR spectra with a signal from trapped magnons at five different hydrogen gas densities in the two different trapping geometries (depicted in insets) described in Ref. [19]. In the low density spectra in (a), the left side peak is due to ESR absorption at the rf field maximum, and the right side peak is the signal from the trapped magnons. Because of broadening, the peaks are partially superimposed in the higher density spectra. In (b), only the signal from trapped magnons is visible. In both trapping geometries, the emergence of the spontaneous coherence is visible as a narrow high-amplitude feature. (c) Pulsed ESR (FID) signals below (bottom), above (top), and approximately at the critical hydrogen gas density (middle). In the top panel, the envelopes of the decomposition of the measured signal (blue) into the coherent (red) and incoherent (black) signals is shown. The node in the blue signal is due to destructive interference between coherent and incoherent parts. The continuing growth of the coherent signal amplitude after the end of the excitation pulse is a clear sign of the spontaneity of the coherence. The FIDs are recorded in the toroidal geometry.

Figure 2

Spectra measured with selective excitation pulses. Green and magenta curves show selective excitation pulse shapes and the measured spectra, correspondingly. Excitation in resonance with hydrogen atoms located at the rf field maximum (purple curves), spatially separated from the minimum of the magnon potential, still produces a signal from the bottom of the potential. A similar excitation in resonance with the bottom of the potential (green curves) only produces a signal from the potential minimum. The inset shows the cw spectrum.

Figure 3

Ground-state energies for trapped magnons and coherent peak amplitudes of trapped magnon signals vs hydrogen atom density for three different potentials. Solid lines show the simulated ground-state energies ${\epsilon }_0$ and circles the detected coherent signal amplitudes vs hydrogen atom density. Black line: Toroidal trap, no applied linear gradient. Blue line: Spherical trap with $\approx 20\mathrm{G}/\mathrm{cm}$ gradient. Red line: Spherical trap with $\approx 30\mathrm{G}/\mathrm{cm}$ gradient. A clear density- and potential-dependent criticality is observed in the appearance of the coherent signal.