Observation of time quasicrystal and its transition to superfluid time crystal (1712.06877v5)

Abstract: 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 super-crystal.

Observation of Time Quasicrystal and Its Transition to Superfluid Time Crystal

The paper explores a notable advancement in the paper of time crystals, specifically focusing on the experimental realization of a quantum time quasicrystal and its subsequent transformation into a quantum time crystal. This research broadens the understanding of time-translation symmetry and its spontaneous breaking in condensed matter physics.

The authors have explored the Bose-Einstein condensation (BEC) of magnons associated with coherent spin precession within superfluid $^3$He-B. Under the influence of a periodic drive utilizing an oscillating magnetic field, the system demonstrates stabilization at a precession frequency lower than that of the applied drive. This manifestation of spontaneous symmetry breaking, where the precession frequency is incommensurate with the driving frequency, characterizes the state as a time quasicrystal. Upon the cessation of the driving force, the system evolves into a time crystal, exhibiting broken symmetry concerning continuous time translations with a macroscopic lifetime of coherent precession.

The authors contend with the no-go theorem, which initially posed constraints on the realization of time crystals in their ground state by exploring systems with off-diagonal long-range order, such as superfluids. In such systems, the number of particles is quasi-conserved, allowing for the potential observation of periodic oscillations in environments where traditional conservation laws, like that of the number of atoms, do not strictly apply.

Experimentally, the magnon BEC is realized in superfluid $^3$He-B, providing scenarios where the relaxation time for the number of magnons ($\tau_N$) significantly exceeds the energy relaxation time ($\tau_E$). This condition allows the paper of time crystals within manageable experimental timescales. A crucial aspect of the investigation is the employment of a flexible magnetic trap, which adapts to the magnon BEC, thus modifying the energy levels and resulting in an effective interaction akin to phenomena studied within quantum chromodynamics.

The implications of this research extend beyond mere theoretical interest. By realizing a time quasicrystal, where discrete time symmetry is spontaneously broken under a periodic drive, the paper demonstrates the potential of time crystals to exhibit quasicrystalline structures with two incommensurate periods. The subsequent transition to a superfluid time crystal introduces the observation of coherent precession states reminiscent of excited eigenstates, proposing a shared phenomenology between macroscopic quantum states and systems driven out of equilibrium.

Future research might explore applications in designing robust quantum systems that exploit the properties of time crystals and quasicrystals, perhaps in quantum computing and information storage, where stability and coherence are paramount. Additionally, the interplay between applied drives and spontaneous symmetry breaking opens new avenues to paper and harness non-equilibrium dynamics in condensed matter systems.

The results presented here pave the way for further experimental and theoretical investigations into the field of time crystals, presenting novel insights into symmetry, coherence, and macroscopic manifestations of quantum phenomena. The marriage of experimental rigor with theoretical innovation in this paper underscores the potential for such systems to illuminate future paths in quantum physics and material science.