Google recently created the world’s first time crystal using their Sycamore quantum computer. A time crystal is a system of particles that exhibit periodic motion without any sort of energy loss. It cycles between states indefinitely, essentially achieving perpetual motion which has long been deemed impossible.
This unique behavior can be attributed to the fact that time crystals are the first material to break time-translational symmetry. To explore what this means, let’s first take a look at normal crystals and how they are able to break space-translational symmetry in a similar way.
If an object remains unchanged after a translation, said object exhibits translational symmetry. Take for example the set of all integers. Shifting the number line in either direction does nothing to alter the set of integers and therefore it exhibits a form of translational symmetry.
More visually, imagine an infinite 2D plane. Walking in any direction, you will see the exact same landscape: another manifestation of this symmetry.
Empty space always has translational symmetry: space-translational symmetry. Moving around in space does nothing to change the properties or behaviors of an object; a particle in a vacuum acts the same regardless of its position. Noether’s theorem states that such symmetries lay the basis for the conservation of momentum and energy we experience in our world.
Crystals such as diamonds are different. Though pattern driven and composed of highly ordered lattices, crystals break space-translational symmetry. A particle traveling through a crystal will experience very dissimilar dynamics based on its relative position.
The particle will only act equivalently if translated at discrete intervals along a principal crystalline axis of symmetry. These intervals must be a multiple of the distance between atoms in the crystal’s lattice. Otherwise, the particle will not maintain its dynamics.
This indicates that crystals have discrete translational symmetries rather than continuous, breaking typical space-translational symmetry. Again, the distinguishing factor is that crystals show discrete symmetry and space shows continuous symmetry.
We can go further and break the discrete symmetry of a crystal by freezing water into its lattice. Because the water’s dynamics vary across the crystal, it will form a less symmetric lattice inside the structure. This is called a sub-lattice. Due to a general decrease in symmetry, the original discrete translational symmetry of our system vanishes.
Just as we can break spatial symmetries, we can break temporal symmetries using a time crystal.
Compared to crystals which have a periodic spatial arrangement, time crystals have indefinite periodicity of motion in time. They cycle through a sequence of states infinitely, meaning no energy is lost. In fact, time crystals exist in their ground state where they have little to no energy to begin with. Most of these time crystals require an energy injection to change states, but absorb no net energy.
Let’s assume an energy injection is required to initiate the time crystal’s motion. Since we are now working in the realm of quantum mechanics, energy has become discrete. There is a minimum amount of energy that can be added to a system called a quanta. If energy more significant than the quanta is added to the system over time, it tends to spread evenly across the energy levels and atoms, greatly slowing the heating of the system.
This potential heat release is trapped by a process called many body localization, reducing the system’s energy loss to zero despite the time crystal’s seeming perpetual motion: motion generally produces heat. In practice, a time crystal will still heat during energy injection, so some must be dissipated in order to reach permanent stability.
Time-translation symmetry upholds that stable objects do not change through time if not acted upon. Time crystals oscillate for infinity, see no increase in entropy, and are stable, constituting a break in such a symmetry. They are stable, yet changing through time. Much like crystals break continuous space-translational symmetry in favor of discrete, time crystals do similarly in the temporal domain.
Due to their uniqueness, time crystals have been titled a new state of matter. Their specific properties will likely be used for quantum information processing in the future. Other applications such as precisely measuring time may be fitting given their forever periodic nature.
Researchers are also theorizing as to how they can remove the energy injection step from the creation process, moving ever closer to a true time crystal.
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