Crystals all the way down: An artistic rendering of a time crystal. (Courtesy: Google Quantum AI)
Crystalline solids such as diamond have a hallmark property: their structure is periodic in space. For much of the past decade, physicists have wondered whether a similarly robust, repeating structure might also exist in time. By analogy with spatial crystals, this structure is known as a time crystal, and whereas diamonds may be forever, time crystals are both forever and forever changing.
Researchers have proposed several physical systems that could host time crystals, including platforms like nitrogen-vacancy (NV) centres and trapped ions. Most recently, a collaboration between researchers at QuTech, TU Delft and UC Berkeley demonstrated long-lived period-doubling oscillations in carbon-13 NV centres across a variety of initial conditions. However, each of these previous platforms lacked the full slate of capabilities to necessary to realize (and verify) a genuine time crystal.
Now, researchers at Google Quantum AI and Stanford University in the US have constructed a time crystal on Google’s Sycamore quantum processor, demonstrating that these exotic objects constitute their own distinct phase of matter. To do so, they ran a series of “experiments” on Sycamore, treating the computer as a laboratory to test whether their proposed time crystal met certain requirements. The result is the first to experimentally verify that a phase of matter can exist outside of thermal equilibrium. It also shows that even in today’s world of noisy intermediate scale quantum (NISQ) computing, quantum processors already have important implications for our understanding of physics.
Phases of matter
Phases of matter come in many varieties, from ubiquitous liquids and gases to quantum phases like superconductors and Bose–Einstein condensates that only crop up under extreme conditions. Regardless of their properties, all phases share a key quality: each one has some notion of order, a way of quantifying the patterning of particles within the collection.
Crystalline solids, for example, exhibit spatial ordering. When a crystal forms, a discrete set of points from the continuous expanse of space become the loci for its evenly spaced atoms. In so doing, the system breaks a well-known physical symmetry: as far as the fundamental laws of physics are concerned, no point in space should have priority over any other. This cosmic apathy is reflected in a set of symmetries, or transformations, under which these laws must remain invariant.
One such symmetry, known as continuous translation symmetry, implies that shifting a closed physical system by any amount in any spatial direction is inconsequential. During formation, crystals spontaneously break this continuous symmetry; in other words, they break it even though the system is not explicitly swayed towards any particular choice of points. The repeating pattern that remains displays only discrete translation symmetry: if every atom is shifted over by one interval, or unit cell, of the crystal, then the same set of spatial positions (apart from the edges) will retain their distinction.
Time crystals enter the fray
The fundamental forces of nature also regard all points in time with indifference. In other words, the laws of physics stay the same from second to second and day to day. This invariance is referred to as continuous time-translation symmetry. Just as crystalline solids disrupt the continuous translation symmetry of space, systems such as pendulums swinging to and fro and planets orbiting stars carve the infinite extent of time into regular, discrete intervals.
Unlike space, however, the passage of time is indelibly coloured by the second law of thermodynamics, which states that entropy – the amount of randomness or disorder in a closed system – cannot decrease over time. Simple systems, like a single pendulum or a planetary orbit, can exhibit stable, long-lived oscillations, as there are few ways for their constituent pieces to interact with each other and exchange energy. In contrast, oscillations quickly fall out of sync in systems with many degrees of freedom (such as a collection of coupled pendulums), as energy surges through every allowed avenue and the system explores many possible states.
In 2012 the physics Nobel laureate Frank Wilczek proposed that an extended phase of matter could exhibit regularity and ordering in time, while also spontaneously breaking time-translation symmetry. Drawing an analogy with the spatially ordered crystalline solid, Wilczek called this proposed phase a quantum time crystal. At that point, it was unclear whether such a phase could truly exist in the physical world, or whether entropy would extinguish all hope for time-crystalline order.
Wilczek’s original proposal involved the ground state, or lowest energy configuration, of a superconducting ring. By itself, this superconductor supports a steady current that flows without resistance. If an alternating pattern of electric charge known as a charge density wave is then superimposed onto this constant current, the ripples of charge would break down the continuous translation symmetry of space into a discrete translation symmetry. Combining the two, Wilczek hypothesized, would result in a stable many-body system with reduced (from continuous to discrete) time-translation symmetry.
Need for non-equilibrium phases
In 2014 theoretical physicists Haruki Watanabe and Masaki Oshikawa dealt a striking blow to Wilczek’s proposal, and to the prospect of time crystals. Their “no-go” theorem stated that any system in thermal equilibrium, including Wilzcek’s, could not be a time crystal. Instead, any time-crystalline phase would need to enter a strange new realm: non-equilibrium physics.
Time crystal theorist: Vedika Khemani is a condensed-matter theorist and associate professor of physics at Stanford University. (Courtesy: Vedika Khemani)
Around the same time, physicists at Princeton University, US and the Max Planck Institute in Dresden, Germany were working in earnest to define such phases. For years, other physicists had pursued similar research programs with little to show for it, but Vedika Khemani (now a professor at Stanford), Roderich Moessner, Shivaji Sondhi and colleagues succeeded, theoretically demonstrating a stable non-equilibrium phase. Their recipe contained two essential physical ingredients: periodic or Floquet driving, and many-body localization (MBL).
When a system is out of equilibrium, its dynamics must depend nontrivially on time, with the state of the system constantly evolving. Floquet driving evokes such dynamics by making the system interact with a laser (or microwave) pulse. The strength of coupling between the system and the laser is varied periodically, and this periodicity modifies the system’s temporal symmetry. While the fundamental forces don’t depend on time, the dynamical pressures generated by the coupled laser are cyclic. From the system’s point of view, time’s translational symmetry is now discrete rather than continuous, and its governing physics looks the same only at times separated by exact multiples of the Floquet driving period.
Reduction in symmetry alone, however, does not a time crystal make. Whereas the continuous translation symmetry breaking in a crystalline solid is spontaneous, symmetry breaking via Floquet driving is induced by coupling the system to the laser. Any time crystal constructed from a Floquet-driven system must therefore spontaneously break the discrete translation symmetry it inherits from the driving mechanism.
In Floquet-driven systems, this is typically done via a phenomenon known as period doubling, where the system falls into a regular cycle that takes twice as long as the period of the process that governs it. The phenomenon dates back to 1837, when Michael Faraday experimented with thin layers of liquid on top of oscillating piston-like platforms, and observed that the standing waves that formed in the liquid moved at half of the oscillator’s frequency. Period doubling does not guarantee a time crystal either. What it does do, when combined with a Floquet-driven many-body system, is to make time crystalline order possible – with one big caveat.
In most Floquet systems, the driving laser imparts energy to the system with every cycle. As the system absorbs this energy, both its temperature and entropy increase. Eventually entropic randomness overwhelms any information contained in spatial or temporal correlations, and the system no longer exhibits any order, crystalline or otherwise.
Many-body localization to the rescue
There is, however, one special class of physical system that overcomes this problem by skirting the encroach of entropy: systems exhibiting many-body localization (MBL). The term “localization” refers broadly to a set of phenomena in which particles or physical properties are confined in their motion. This confinement often stems from disorder. For example, in Anderson localization, named after the late physics Nobel laureate Phil Anderson, disorder in a crystal lattice immobilizes the electrons that would otherwise be free to travel from one atom in the lattice to another.
Whereas an ideal crystal comprises uniform atomic nuclei, leading to a regular lattice structure, in practice crystals can be dotted with defects – that is, with nuclei of different elements randomly interspersed in the lattice. These defects push and pull electrons in different directions, creating complex potential energy landscapes with deep, narrow trenches that act as traps.
