Experimental observation of Josephson oscillations in a room-temperature Bose-Einstein magnon condensate

The alternating current (ac) Josephson effect in a time-independent spatially inhomogeneous setting is manifested by the occurrence of Josephson oscillations—periodic macroscopic phase-induced collective motions of the quantum condensate. So far, this phenomenon was observed at cryogenic temperatures in superconductors, in superfluid helium, and in Bose-Einstein condensates (BECs) of trapped atoms. Here, we report on the discovery of the ac Josephson effect in a magnon BEC carried by a room-temperature ferrimagnetic film. The BEC is formed in a parametrically populated magnon gas in the spatial vicinity of a magnetic trench created by a dc electric current. The appearance of the Josephson effect is manifested by oscillations of the magnon BEC density in the trench, caused by a coherent phase shift between this BEC and the BEC in the nearby regions. Our findings advance the physics of room-temperature macroscopic quantum phenomena and will allow for their application for data processing in magnon spintronics devices.

Figure 1

Spectrum of the fundamental magnon mode in a 5.1-$\mu \mathrm{m}$-thick YIG film magnetized in plane by a bias magnetic field $H=1520\mathrm{Oe}$, shown for the wave vector $\mathit{q}\parallel \mathit{H}$ (lower part of the spectrum, blue and green curves), for $\mathit{q}\perp \mathit{H}$ (upper part, magenta curves), and also for several intermediate directions of wave vectors (grey curves). The orange arrows illustrate the magnon injection process by means of parallel parametric pumping. The horizontal black arrows illustrate scattering of the pumped magnons into secondary magnon states. The blue and green dotted arrows symbolize the flow of thermalizing magnons to the bottom of the spectrum. The blue and green dots indicate the positions of the frequency minima ${\omega }_{\text{min}}(+{\mathit{q}}_{\text{min}})$ and ${\omega }_{\text{min}}(-{\mathit{q}}_{\text{min}}$) occupied by the $+q$- and $-q$-BECs of magnons.

Figure 2

Experimental setup and Josephson oscillations. (a) Sketch of the experimental setup. A YIG film magnetized in plane by a magnetic field $\mathit{H}$ is placed on top of a 50-$\mu \mathrm{m}$-wide microstrip. The red and orange branches represent the circuits for the generation of dc and microwave currents. The red arrows illustrate the magnetic field $\mathit{h}$ induced by a dc current. The green part describes a tool for optical detection of magnons by means of Brillouin light scattering (BLS) spectroscopy. A pulse generator triggers dc and microwave generation, and synchronizes the time-resolved BLS analysis. (b) The calculated profile of a potential trench $-f\left(x\right)$ controlling the energy of BECs in different zones of the sample. The bidirectional dashed arrows indicate two alternating magnon supercurrents related to the oscillations of $+q$-BEC (black arrow) and $-q$-BEC (red arrow) densities $N_{+}^{\text{center}}$ and $N_{-}^{\text{center}}$, observed in the central zone of the potential trench. Panels (c)–(e) present the BLS intensity in the central zone, which is proportional to the magnon density at the bottom of spin-wave spectrum, versus time. (c) Josephson oscillations in two systems, $+q$-BEC (black line) and $-q$-BEC (red line). Time intervals 1–4 in (c) mark: 1—the time, when magnons are excited by parametric pumping, 2—the time interval during which the BEC forms, 3—the time interval during which the first oscillation appears, and 4—the rest of the observation time. Panels (d) and (e) present the summarized dynamics of two BEC systems $(N_{+}^{\text{center}}+N_{-}^{\text{center}})$ for different bias dc currents: (d) Potential ridge formed by dc currents from 0 to $+500\mathrm{mA}$. (e) Potential trench formed by dc currents from 0 to $-500\mathrm{mA}$.

Figure 3

Time dependence of spatial magnon distributions in different potential profiles. Distribution of magnons perpendicular to the antenna. Rows 1–4 show integrated data over different time intervals of the time-resolved measurement data, as shown in Fig. 2. The intensity of the $+q$-BEC- and $-q$-BEC are shown by black solid and red dashed lines, respectively. The difference in the intensities of these condensates refers to the difference in the efficiency of the Stokes and anti-Stokes scattering processes (see Appendix). The first column (A) shows data for the magnetic ridge with the applied current $I=500\mathrm{mA}$, while the second column (B) corresponds to the magnetic trench with the applied current $I=-500\mathrm{mA}$. Note the change in the BLS intensity scale.

Figure 4

Magnon frequency shift in the middle of the central zone of a potential profile. The center frequencies (found by a Gaussian fit) of the measured magnon spectra near $+q_{\min }$ (black lines and squares) and $-q_{\min }$ (red lines and dots) are shown as a function of the applied bias current $I$.

Figure 5

Determination of Josephson oscillation frequencies. (a), (b) Time dependencies of the BLS intensity measured for various negative dc currents are shown after noise filtering and attenuation compensation. (a) The BLS intensity increases with the increase in current from $-400\mathrm{mA}$ to $-560\mathrm{mA}$ in $20\mathrm{mA}$ steps. (b) The BLS intensity decreases with the increase in current from $-560\mathrm{mA}$ to $-700\mathrm{mA}$ in $20\mathrm{mA}$ steps. (c) Time positions of the first (black squares) and the second (red circles) oscillation peaks. Grey triangles mark the beginning of the coherent BEC motion after the pumping pulse is switched off. (d) Frequency of the Josephson oscillations (blue triangles) versus applied current in the strip. Vertical bars show 95% confidence intervals. The measurement error increases for the smallest and highest currents due to the reduced amplitude of the Josephson oscillations. The solid red line is a linear fit by the weighted least squares.

Figure 6

Numerical solutions of Eq. (8) with parameters and initial conditions taken from the experiment. The data in panels (a1)–(a4) and (b) were obtained for a trench depth of 80 MHz, corresponding to a bias current $I=-500\mathrm{mA}$. The solid red lines in panels (a1)–(a4) show the spatial distribution of the BEC density $\overline{{\left|C(x,t)\right|}^2}$ for four consecutive moments of time, marked by circles in panel (b). The dotted blue lines indicate the initial BEC distribution at zero moment of time. For a better comparison with the experimental data, the BEC distributions were smoothed by a Gaussian filter with a width matching the diameter of the focal spot of the probing laser beam. The vertical dashed lines and shaded colored areas mark the potential trench and different areas of the sample, similar to Figs. 1 and 3. Panel (b) plots the BEC density $\overline{{\left|C(0,t)\right|}^2}$ in the trench as a function of time. The inset displays the corresponding Fourier spectrum. The dominant spectral peak with a frequency of 2.5 MHz is marked with a dashed red line. Panel (c) shows the dependence of the Josephson frequency ${\mathrm{\Omega }}_{\text{num}}^{\text{osc}}$ on the trench depth $|{\mathrm{\Omega }}_0|$. The error-bar values refer to the widths of the corresponding Fourier spectral lines.