From a continuous to a discrete time crystal

31 July 2024

Photo: AG Hemmerich

An atomic Bose-Einstein condensate is strongly coupled to a periodically pumped ultrahigh finesse optical cavity, and the system’s response locks to the subharmonic of the modulation frequency ωdr.

An international team of physicists from Universität Hamburg, the University of the Philippines, and the University of São Paulo has recently observed a phase transition from a continuous to a discrete time crystal. This work has now been published by the renowned scientific journal "Reports on Progress in Physics".

Time crystals are novel dynamical many-body states, that are characterized by robust self-sustained oscillations, emerging via spontaneous breaking of time translation symmetry. Research distinguishes between discrete (DTCs) and continuous (CTCs) time crystals: DTCs are periodically driven systems that oscillate with a subharmonic of the external drive, while CTCs are continuously driven and oscillate with a frequency intrinsic to the system.

For the experiments that the researchers now report, a CTC with a characteristic oscillation frequency ω_CTC is prepared by strongly coupling of an atomic Bose-Einstein condensate to a continuously pumped ultrahigh finesse optical cavity. Modulating the pump intensity of the CTC with a frequency ω_dr close to two ω_CTC leads to robust locking of ω_CTC to half of the drive frequency ω_dr /2, and hence a DTC arises.

Interface between non-linear dynamics and time crystals

“In biological systems, the phenomenon that a non-linear oscillator in its limit cycle state locks to a periodic drive, is called entrainment”, says Hans Keßler from the Institute for Quantum Physics in Hamburg. A response with a frequency smaller than the modulation frequency, as it is here the case, is called subharmonic entrainment. In physics, the terms phase or injection locking are more familiar. Here, the scientists observe the physics of subharmonic injection locking arising as a phase transition in a many-body system with long range interaction.

“We establish a non-trivial interface between classical non-linear dynamics and time crystals, which allows to access a vast range of dynamical phenomena to be understood and established in time crystals and related dynamical many-body states”, Andreas Hemmerich concludes, who is a professor at the Department of Physics and a researcher at the Cluster of Excellence “CUI: Advanced Imaging of Matter”.

Reference

P. Kongkhambut, J. G. Cosme, J. Skulte, M. A. Moreno Armijos, L. Mathey, A. Hemmerich and H. Keßler

“Observation of a phase transition from a continuous to a discrete time crystal”

Rep. Prog. Phys. 87 080502 (2024)

DOI 10.1088/1361-6633/ad6585