Bose–Einstein condensation of quasiparticles by rapid cooling

Abstract

The fundamental phenomenon of Bose–Einstein condensation has been observed in different systems of real particles and quasiparticles. The condensation of real particles is achieved through a major reduction in temperature, while for quasiparticles, a mechanism of external injection of bosons by irradiation is required. Here, we present a new and universal approach to enable Bose–Einstein condensation of quasiparticles and to corroborate it experimentally by using magnons as the Bose-particle model system. The critical point to this approach is the introduction of a disequilibrium of magnons with the phonon bath. After heating to an elevated temperature, a sudden decrease in the temperature of the phonons, which is approximately instant on the time scales of the magnon system, results in a large excess of incoherent magnons. The consequent spectral redistribution of these magnons triggers the Bose–Einstein condensation.

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Fig. 1: Theoretical modelling of the BEC by rapid cooling and experimental approach.
Fig. 2: BLS measurements of BEC by rapid cooling.
Fig. 3: Threshold behaviour of the BEC.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

This research was funded by ERC Starting Grant 678309 MagnonCircuits and ERC Advanced Grant 694709 Super-Magnonics, as well as by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) TRR 173—268565370 and Project DU 1427/2-1, by grants no. EFMA-1641989 and no. ECCS-1708982 from the National Science Foundation of the United States, and by the U.S. AFOSR under the MURI grant # FA9550-19-1-0307.

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Contributions

M.S. and D.B. performed the measurements and analysed the experimental results. T.B. and A.V.C. supervised the measurements. T.B., P.P., A.A.S. and A.V.C. planned the experiment. M.S., B. Heinz and T.M. developed the experimental setup. V.L. performed FMR characterizations and preliminary experiments. C.D. grew the LPE YIG films. S.K. and E.Th.P. deposited the Pt overlayer. M.S., B. Heinz, B.L., T.L. and D.B. fabricated the structures under investigation. V.S.T. developed the quasi-analytical model of the magnon spectral redistribution. D.A.B., H.Yu.M.-S., V.S.T. and A.N.S. performed the theoretical calculations. M.S. and F.H. performed the COMSOL simulations. Q.W. and P.P. performed the MuMax3 simulations. B. Hillebrands and A.V.C. led the project. All authors discussed the results and wrote the manuscript.

Corresponding authors

Correspondence to Michael Schneider or Andrii V. Chumak.

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Extended data

Extended Data Fig. 1 Parameters used for the calculations of the magnon density.

The table shows the parameters according to the developed quasi-analytical theoretical model for two different experimentally investigated strips.

Extended Data Fig. 2 Temperature profile and time evolution of the temperature gradient.

a, Temperature across the layers at the end of a 120-ns-long heating pulse simulated with COMSOL (corresponding to the experiment shown in Fig. 2b in the main manuscript). b, Temperature (red curve, left axis) and temperature gradient (black curve, right axis) as a function of time simulated with COMSOL (corresponding to the experiment shown in Fig. 2b in the main manuscript).

Extended Data Fig. 3 Rapid cooling BEC generated in an Au/Al/YIG structure.

a, Time resolved BLS spectrum for the case when a 50-ns-long pulse is applied b, Integrated BLS intensity over the frequency range shown in a.

Extended Data Fig. 4 BEC by rapid cooling for different geometries of the external field.

a, BLS spectrum as a function of time. The BLS signal (colour-coded, log scale) is proportional to the density of magnons. FM indicates the fundamental mode, EM – the edge mode, and 1st M – the first thickness mode. The vertical dashed lines indicate the start and the end of the pulse (τP = 150 ns, U = 0.9 V). The external field was parallel to the short axis of the strip (B||y). c, BLS spectrum as a function of time for the case when the external magnetic field is parallel to long axis of the strip (B||x), (τP = 120 ns, U = 0.9 V). b,d, Normalized magnon intensity integrated from 4.95 GHz to 8.1 GHz as a function of time for the cases in a,c. The insets show the sample and measurement geometry.

Supplementary information

Supplementary Information

Supplementary discussion, Figs. 1–11 and Tables 1–2.

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Schneider, M., Brächer, T., Breitbach, D. et al. Bose–Einstein condensation of quasiparticles by rapid cooling. Nat. Nanotechnol. 15, 457–461 (2020). https://doi.org/10.1038/s41565-020-0671-z

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