This project aims to create a time crystal, analogous to a crystal in space, based on a Bose-Einstein condensate of ultracold atoms bouncing resonantly on an oscillating mirror, where the bounce period is equal to an integer multiple of the mirror oscillation period.
In 2015, Krzysztof Sacha from the Jagiellonian University in Krakow (a collaborator on this project) proposed that a periodically driven quantum many-body system, such as a Bose-Einstein condensate bouncing resonantly on an oscillating mirror, can reveal spontaneous breaking of discrete time-translation symmetry and spontaneously start to evolve with a period s-times longer than the driving period T of the mirror to create a time crystal. Such a time crystal is predicted to be robust against external perturbations and to persist indefinitely in the limit of an infinite number of atoms, in analogy with the behaviour of a normal space crystal. When the interaction between atoms is sufficiently strong and attractive, periodically evolving states of the many-body system become Schrödinger cat-like superposition states, so that an infinitesimally small perturbation is sufficient to break the time-translation symmetry and collapse the system into one of the s wave-packets evolving with period sT.
We are setting up an experiment to create a time crystal based on a Bose-Einstein condensate of ultracold potassium-39 atoms bouncing resonantly on an oscillating mirror such that the bounce period is equal to an integer multiple of the mirror oscillation period¹,². An important characteristic of such a ‘gravitational bouncer’ system, compared with, for example, spin-based systems, is accessibility to dramatic breaking of time-translation symmetry with an evolving period that can be orders of magnitude longer than the mirror oscillation period². Such ‘big time crystals’ can involve up to about 100 effective lattice sites in the time dimension and are suitable for implementing a broad range of condensed matter phenomena in the time domain³ such as:
- Anderson localization and many-body localization with temporal disorder.¹,³
- Mott insulator phases in the time domain.
- Time quasi-crystals, ordered but not periodic in time.
- Topological time crystals, involving edge states in time.
- Time crystals with exotic interactions.
- Dynamical quantum phase transitions in the time domain¹.
¹K. Giergiel, A. Kosior, P. Hannaford and K. Sacha, Time crystals: analysis of experimental conditions, Physical Review A 98, 013613 (2018).
²K. Giergiel, T. Tran, A. Zaheer, A. Singh, A. Sidorov, K. Sacha and P. Hannaford, Creating big time crystals with ultracold atoms, New Journal of Physics (in press); arXiv:2004.00755 (2020).
³ P. Hannaford and K. Sacha, Time crystals enter the real world of condensed matter, Physics World 33, 42-46 (2020).