Time Crystals

Jim talks to Randy about structures that are periodic in time like crystals are periodic in space. This idea came from Frank Wilczek in 2012, and was realized just recently, providing an extraordinary turn-around time from theory to observation.

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Notes:

1. The papers we read for this program:

• Quantum Time Crystals, Wilczek,, F. Physical Review Letters 109, 160401 (2012) [arXiv]
• Discrete Time Crystals: Rigidity, Criticality, and Realizations,Yao, Potter, Potirniche, and Vishwanath. Physical Review Letters119 030401 (2017) [arXiv]
• Observation of Discrete Time Crystal, Zhang, Hess, Kyprianidis, Becker, Lee, Smith, Pagano, Potirniche, Potter, Vishwanath, Yao, and Monroe. Nature 543 217 (2017) [arXiv]
• Observation of discrete time-crystalline order in a disordered dipolar many-body system, Choi, Choi, Landig, Kucsko, Zhou, Isoya, Jelezko, Onoda, Sumiya, Khemani, von Keyerlingk, Yao, Demler, and Lukin. Nature 543 221 (2017) [arXiv]

2. Our subreddit.

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The following post was made to the arXiv_plus subreddit about these papers:

This was an interesting one. Frank Wilczek hypothesized, here, that there would be structures that were periodic in time the way crystals are periodic in space. The wave functions, in time, would be similar to the Bloch functions of condensed matter. The character of the wave functions would be a little like solitons, with an attractive nonlinearity balanced by uncertainty-related dispersion. His original model was to look at coupled superconducting rings. The coupling would repeatedly and periodically reproduce the same state.

In Discrete time crystals: rigidity, criticality, and realizations, Yao, et al., showed that the ground state wave function cannot have the periodicity required -- but an excited state could. What you would need to do is produce a Hamiltonian that did three things, successively: orient the system, order the system, and finally randomly disorder it.

Two groups wasted no time at all producing these excited "time crystals," simultaneously publishing in Nature about a year ago. One group looked at what I'd think of as a very artificial system, a few optically-trapped, ultra-cold atoms. In this case each of the effects was programmed by laser interactions. The other group used a real crystal: diamond with nitrogen vacancies at room temperature.

Both groups successfully reproduced the phenomena of Yao's paper. The nature of the Hamiltonians, if I'm free to interpret them, is a successive Zeeman interaction to align the spins of the atoms, an exchange term like the Heisenberg Hamiltonian, and a diffusion term.

There is some similarity to spin echos here, but the effects are much more coherent.