It’s Time for Time Crystals

To a layperson, the words “Time Crystal” probably evokes images of scientific magic, like phasers, flying DeLoreans and flubber. Real-world time crystals are likely not as exciting as whatever sci-fi gobbledygook you might have imagined (Physicists are very good marketers). But their potential applications in quantum computing are genuinely something to pay attention to in the coming years.

Google’s sycamore microprocessor. In 2021, Google’s Quantum AI team, in collaboration with researchers from the Max Planck Institute for Physics of Complex Systems, Stanford and Oxford managed to create a 20-atom time crystal on the sycamore microprocessor chip. Credit: Erik Lucero

The earliest modern proposal of time crystals was made in 2012 by Nobel Laureate, Frank Wilczek in his paper titled ‘Quantum Time Crystals’. To understand Wilczek’s proposal, we should first consider a regular crystal. Crystals are ordered periodically in space. The pattern of a crystal repeats across space.

This is ‘discrete space translational symmetry’. In the crystal structure above, you have to walk some discrete distance to get from one black atom to the closest black atom, and the same distance to get from one white atom to the closest white atom. Crystals are said to spontaneously break ‘continuous space translational symmetry’ as the crystal is not spatially homogenous. Wilczek wondered if there was a system that could break ‘continuous time translational symmetry’ spontaneously. Rather than the discrete ordering of atoms, this system would be characterised by the discrete temporal ordering of events. He dubbed such a system a ‘Time Crystal’ ¹. The idea is that time crystals repeat some state periodically after some period of time. What could this look like? Wilczek originally supposed a superconducting ring of atoms carrying a current. The ring is threaded by a small magnetic flux. This generates a constant current in the lowest energy or ‘ground’ state. The charged particles could then be ordered to travel in “lumps” that complete the loop in a constant period, indefinitely, giving us our conditions for a time crystal [1].

Wilczek’s time crystal exists in thermal equilibrium – The system does not require any energy exchange with the surroundings. If the indefinite motion of charge around the ring seems wrong to you, you’re not alone. What Wilczek proposed is ‘Perpetual Motion’ in the ground state. The idea of macroscopic perpetual motion has been discredited among scientists since the 1700s. Technically, Wilczek’s proposal doesn’t violate the current laws of thermodynamics, as no mechanical work can be extracted from the ground state system [2]. However, Wilczek’s superconductor model was shown to be impossible in a paper from Patrick Bruno in equilibrium in 2012.² Kablamo! Your theory is dead, Wilczek. It was good while it lasted.

Woah, not so fast. What if we also let go of our equilibrium condition. What if we allowed an external energy source to drive the system. And what if our system was arranged so that none of this energy was absorbed or dissipated by the system, so it could behave as though it was in equilibrium. A paper from Yao et al suggested just this in 2016! Yao et al posited that an array of 1D ions could be created as shown.

Certain isotopes have a ‘spin-state’. The concept of spin is too complex to dissect in this blog. The spin axes align parallel and antiparallel with each other as these states are lower energy than random orientations due to their interacting magnetic fields. Suppose these alignments are along the z axis. Normally, as our system would tend towards equilibrium, the arrangement of these spins would randomise. This is ‘thermalisation’. But we want temporal order so we can’t permit this to happen. What if the atoms were radiated with pulses of electromagnetic radiation which caused each of the spins to rotate 180 degrees about the x-axis.

This sort of system is a ‘Discrete Time Crystal’ because the atoms return to their initial state after some multiple integer of the period of the driving force. It’s not spontaneous like Wilczek originally suggested, but it’s good enough. The period of the time crystal would be twice the period of the laser as it oscillates between the two states. Imperfections in the laser could destabilise the ions if the interaction strength between ions is not strong enough. Additionally, if the interaction is too strong, the system would thermalise. The existence of such a system outlined by Yao et al was confirmed by Monroe et al in 2016. They used an array of ten ¹⁷¹Yb⁺ ions which were oscillated using a Raman laser.

The paper from Yao et al also suggests that this periodic behaviour should continue for extended periods of time if the driving beam is stopped (provided that the frequency of the laser was sufficiently high). These so-called ‘Pre-Thermal Time Crystals’ were observed by Monroe et al in 2021.

In 2021, the researchers at Google’s Quantum AI team, in collaboration with researchers from Stanford, Oxford and the Max Planck Institute of Physics of Complex Systems managed to create a time crystal of 20 qubits on Google’s Sycamore processor [3-4]. Not to be outdone by Google, two physicists from the University of Melbourne, Philipp Frey and Stephan Rachel, managed to create a time crystal of 57 qubits using IBM’s Brooklyn and Manhattan processors [5-6].

Quantum Computing

One possible pathway for quantum computing is spintronics. Currently data in computers is binary. It consists of an array of 1s and 0s. These 1s and 0s are bits. In quantum computing, information is stored by ‘Qubits’, which can be 1, 0 or a ‘superposition’ of the two. The essence of spintronics is using the spin-states of particles as our qubits. One of the challenges of quantum computing is finding a sustainable way of storing these 1s and 0s as information across long periods of time in an energy-efficient manner. These systems are easily disturbed by heat and the preservation of the memory often entails cooling the qubits to temperatures on the scale of tens of millikelvins [7]. The stable oscillations of the discrete time crystals could open the door to long-term, energy-efficient, quantum-memory storage.

The future of quantum computers is, however, still uncertain. What does the future hold for time crystals? Time will tell.

¹ Wilczek was not the first to use the term ‘Time Crystal’ to describe periodically repeating systems. Biologist Arthur Winfree gave the name to biological systems that repeat periodically in his book, The Geometry of Biological Time in 1980.

² Additionally in 2015, a paper from Haruki Watanabe and Masaki Oshikawa purported to disprove time crystals in equilibrium. However, this proof contained a discrete error, as outlined in the appendix of a paper from Khemani et al [8]. However the authors of this paper agreed that the conclusion of the falsified proof is likely correct.

References

[1]: Zakrzewski, J., 2012. Crystals of Time. [online] Physics. Available at: <https://physics.aps.org/articles/v5/116> [Accessed 10 May 2022].

[2] Andersen, T., 2021. Here’s how time crystals really work. [online] Medium. Available at: <https://medium.com/the-infinite-universe/heres-how-time-crystals-really-work-b487fbe03523> [Accessed 12 May 2022].

[3] Mi, X., Ippoliti, M., Quintana, C. et al. Time-crystalline eigenstate order on a quantum processor. Nature 601, 531–536 (2022). https://doi.org/10.1038/s41586-021-04257-w

[4] University, S., 2021. Time crystal in a quantum computer | Stanford News. [online] Stanford News. Available at: <https://news.stanford.edu/2021/11/30/time-crystal-quantum-computer/> [Accessed 11 May 2022].

[5] Frey, P. and Rachel, S., 2022. Realization of a discrete time crystal on 57 qubits of a quantum computer. [online] science.org. Available at: <https://www.science.org/doi/10.1126/sciadv.abm7652> [Accessed 13 May 2022].

[6] Cho, A., 2022. Physicists produce biggest time crystal yet. [online] Science.org. Available at: <https://www.science.org/content/article/physicists-produce-biggest-time-crystal-yet> [Accessed 13 May 2022].

[7] Moss, S., 2021. Cooling Quantum Computers. [online] datacenterdynamics.com. Available at: <https://www.datacenterdynamics.com/en/analysis/cooling-quantum-computers/> [Accessed 10 May 2022].

[8] Khemani, V., Moessner, R. and Sondhi, S., 2019. A Brief History of Time Crystals. [online] Available at: <https://arxiv.org/pdf/1910.10745.pdf> [Accessed 12 May 2022].