Direct observation of the transition from spin waves to the magnon Bose condensate.

Bose-Einstein condensation occurs at an appropriate density of bosonic particles, depending on their mass and temperature. The transition from the semiclassical paradigm of spin waves to the magnon Bose-Einstein condensed state (mBEC) was obtained experimentally with increasing magnon density. We used the Faraday rotation effect to study the spatial distribution of the magnon density and phase far from their excitation region. A coherent magnetization precession was observed throughout the sample, which indicates the formation of a magnon BEC. It is shown that this result under experimental conditions goes beyond the applicability of the Landau-Lifshitz-Gilbert semiclassical theory.

Optical registration of a coherent magnon state outside of the excitation region.

Magnons have demonstrated enormous potential for the next generation of information technology and quantum computing. In particular, the coherent state of magnons resulting from their Bose-Einstein condensation (mBEC) is of great interest. Typically, mBEC is formed in the magnon excitation region. Here we demonstrate for the first time by optical methods the permanent existence of mBEC at large distances from the magnon excitation region. The homogeneity of the mBEC phase is also demonstrated. The experiments were carried out on films of yttrium iron garnet magnetized perpendicular to the surface and at room temperature. We use the method described in this article to develop coherent magnonics and quantum logic devices.

Magneto-optical imaging of coherent spin dynamics in ferrites.

The explosive development of quantum magnonics is associated with the possibility of its use as macroscopic quantum systems. In particular, they can find an application for quantum computing processors and other devices. The recently discovered phenomenon of magnon Bose-Einstein condensation and coherent precession of magnetization can be used for these purposes. Our letter describes a method for the optical observation of the coherently precessing magnetization in conditions when the concentration of magnons reaches the value necessary for their quantum condensation. The investigations were conducted in the out-of-plane magnetized yttrium iron garnet films. The required magnon density was achieved by magnetic resonance technique. The magneto-optical imaging method provides such important parameters of the coherent spin dynamics as the amplitude and phase distributed all over the sample. It should become an indispensable read-out tool for the upcoming quantum technologies based on the magnon Bose-Einstein condensation.

Quantum paradigm of the foldover magnetic resonance.

The explosive development of quantum magnonics requires the consideration of several previously known effects from a new angle. In particular, taking into account the quantum behavior of magnons is essential at high excitations of the magnetic system, under the conditions of the so-called phenomenon of "foldover" (bi-stable) magnetic resonance. Previously, this effect was considered in the quasi-classical macrospin approximation. However, at large angles of magnetization precession, the magnon density exceeds the critical value for the formation of a magnon Bose condensate (mBEC). Naturally, this purely quantum phenomenon does not exist in the classical approximation. In addition, mBEC leads to superfluid transfer of magnetization, which suppresses the macroinhomogeneity of the samples. The experiments presented in the article show that quantum phenomena well describes the experimental results of nonlinear magnetic resonance in yttrium iron garnet. Thus, we remove the questions that arose earlier when considering this effect without taking into account quantum phenomena. This discovery paves the way for many quantum applications of supermagnonics, such as the magnetic Josephson effect, long-range spin transport, Q-bits, quantum logic, magnetic sensors, and others.