We report experimental realization of a quantum time quasicrystal and its transformation to a quantum time crystal We study Bose-Einstein condensation of magnons, associated with coherent spin precession, created in a flexible trap in superfluid ^{3}He-B Under a periodic drive with an oscillating magnetic field, the coherent spin precession is stabilized at a frequency smaller than that of the drive, demonstrating spontaneous breaking of discrete time translation symmetry The induced precession frequency is incommensurate with the drive, and hence, the obtained state is a time quasicrystal When the drive is turned off, the self-sustained coherent precession lives a macroscopically long time, now representing a time crystal with broken symmetry with respect to continuous time translations Additionally, the magnon condensate manifests spin superfluidity, justifying calling the obtained state a time supersolid or a time supercrystal

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Observation of a Time Quasicrystal and Its Transition to a Superfluid Time Crystal.

Studies of supercurrent phenomena, such as superconductivity and superfluidity, are usually restricted to cryogenic temperatures, but evidence suggests that a magnon supercurrent can be excited in a Bose–Einstein magnon condensate at room temperature.

Supercurrent in a room-temperature Bose-Einstein magnon condensate

The possibility of Bose-Einstein condensation of excitations has been discussed for a long time. The phenomenon of the phase-coherent precession of magnetization in superfluid 3He and the related effects of spin superfluidity are based on the true Bose-Einstein condensation of magnons. Several different states of coherent precession has been observed in 3He-B: homogeneously precessing domain (HPD); persistent signal formed by Q-balls at very low temperatures; coherent precession with fractional magnetization; and a mode of the coherent precession in compressed aerogel. The coherent precession has been also found in 3He-A in compressed aerogel. Here we demonstrate that all these cases are examples of a Bose-Einstein condensation of magnons, with the magnon interaction term in the Gross-Pitaevskii equation being provided by different types of spin-orbit coupling in the background of the coherent precession.

Bose-Einstein Condensation of Magnons in Superfluid 3 He

We report the observation of the unusual behavior of induction decay signals in antiferromagnetic monocrystals with Suhl-Nakamura interactions. The signals show the formation of the Bose-Einstein condensation (BEC) of magnons and the existence of spin supercurrent, in complete analogy with the spin superfluidity in the superfluid (3)He and the atomic BEC of quantum gases. In the experiments described here, the temperature of the magnon BEC is a thousand times larger than in the superfluid (3)He. It opens a possibility to apply the spin supercurrent for various magnetic spintronics applications.

High-Tc spin superfluidity in antiferromagnets.

A macroscopic collective motion of a Bose–Einstein condensate (BEC) is commonly associated with phenomena such as superconductivity and superfluidity, often generalised by the term supercurrent. Another type of motion of a quantum condensate is second sound—a wave of condensate’s parameters. Recently, we reported on the decay of a BEC of magnons caused by a supercurrent outflow of the BEC from the locally heated area of a room temperature magnetic film. Here, we present the observation of a macroscopic BEC transport mechanism related to the excitation of second sound. The condensed magnons, being propelled out of the heated area, form compact humps of BEC density, which propagate many hundreds of micrometers in the form of distinct second sound—Bogoliubov waves. This discovery advances the physics of quasiparticles and allows for the application of related transport phenomena for low-loss data transfer in magnon spintronics devices. Exploration of magnon Bose–Einstein condensate (BEC) may enable intriguing applications in magnonic devices. Here the authors show experimentally the condensed magnons forming compact humps of BEC density can propagate many hundreds of micrometers in the form of Bogoliubov waves.

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Bogoliubov waves and distant transport of magnon condensate at room temperature

The frequency of the ''long-lived'' induction signal in /sup 3/He-B depends on the time, and the rate of change of this frequency increases with increasing field gradient. Experiments confirm Fomin's theoretical explanation of this phenomenon, according to which a /sup 3/He-B sample in which a uniform magnetization precession is excited breaks up into two phases. In one, the magnetization is parallel to the field and does not precess; in the other, the magnetization precesses with a deflection angle of approximately 104/sup 0/.

a.Y.M. Mukharskii

Papers

Long-lived induction signal in superfluid /sup 3/He-B