Time Crystals Script (Patreon)

What exactly ARE time crystals? Are they the bling inside your time turner? The flux in your flux capacitor? Are they the heart of the TARDIS? In today’s edition of Space Time Journal Club we find out.

In Space Time Journal Club we review new scientific papers that are making waves. We pick them apart to turn the techno-babble into simple english - at least as much as possible. Then we fight about it in the comments. This week we’re going to take a look at the recent publication by Yao, Potter, Potirniche & Vishwanath in Physical Review Letters entitled “Discrete time crystals: rigidity, criticality, and realizations.” This paper proposed an approach to making these bizarre objects: a recipe t two other research teams have now followed and actually synthesized these things. But first up, what on earth are time crystals? 

The idea was proposed in 2012 by Nobel laureate Frank Wilczek at MIT. He suggested a type of matter that exhibits a sort of fundamental oscillation over time. So some property of the material goes through a repeating cycle.  How does that make it a time crystal? The analogy is that crystals have a periodic cycle through space. Molecular patterns repeat again and again along their lattices. Time crystals repeat some internal state with constant separations in time. The name “time crystal” is somewhat out there, but Wilczek wasn’t the first to use it in reference to a regularly repeating system. That may have been Arthur Winfree in The Geometry of Biological Time, where it is used to describe periodic biological systems. But Wilczek was clever to apply it here, because the name made the internet go completely bonkers. And so here we are.

Wilczek came up with a simple model in which charged particles in a superconducting ring break what we call continuous time translation symmetry. That’s a fancy way of saying that the system looks different on a global level from one instant to the next. Normal matter that is in what we call thermal equilibrium only has random internal motion – in solid matter that would be the vibrational buzz of its constituent atoms. But from one instant to the next that buzz stays random. In regular matter in equilibrium, statistical properties stay the same over time. Wilczek’s imaginary system broke this time translational symmetry because there ARE global statistical differences in the state of the matter - non random patterns that change with time.

Big deal. Lots of things change over time – cups of coffee cool down, planets orbit the Sun, the universe expands. But cups of coffee and the universe are not in thermal equilibrium, and the planets are macroscopic moving objects. Wilczek proposed an actual substance that was in perpetual motion while in equilibrium – more, he imagined a substance for which oscillations were the most fundamental, lowest energy, or ground state. This would break time translational symmetry, which makes most physicists nervous.

Well physicists can chill. In 2015, Haruki Watanabe of UC Berkeley and Masaki Oshikawa of the University of Tokyo showed from theoretical arguments that time translational symmetry can’t be broken by a quantum system in equilibrium. That sounds bad for time crystals, but that’s where this new paper by Yao et al comes in. Their answer was to throw away this equilibrium thing. Thermal equilibrium means a closed system; no energy in, no energy out. Norman Yao, also at UC Berkeley, and his team proposed a way to make time crystals by using some sort of external input of energy to force the oscillating states.

The idea goes like this: set up a chain of ions – so electrically charged atoms. These atoms have spin values – quantum mechanical angular momenta from their electrons. Spins in nearby atoms like to line up with each other due to their interacting magnetic fields – either direct alignment or opposite alignment are both a lower-energy state than random alignment. This is the same effect that results in magnetic materials. So you prepare a string of ions with aligned spins. Now, cause those spins to flip back and forth using a laser. A laser is just a very well-ordered, electromagnetic wave with a known period. The spin-flip oscillation will be determined by the period of the laser.

That laser beam is what takes the system out of equilibrium, because you’re pumping in energy. Causing spins to flip in a laser beam isn’t particularly exciting. I mean, you’re basically grabbing the electrons and forcing them to oscillate. But the paper proposes that if you let go of the electrons their spin oscillations should continue – they should be sustained internally. That means they should resist a change in the frequency of the input laser, or continue oscillating at least for a while if the input EM field is randomized. In addition, other researchers theorized that the spins should not oscillate at the same period as the laser but at an integer multiple of the driving period. So 2, 3, 4, etc spin oscillations for every EM field oscillation in the laser.

Yao et al’s work was theoretical, but involved numerical calculations that allowed them to calculate a phase diagram. This is sort of like the phase diagram of regular matter, in which you plot pressure versus temperature. Different materials become sold, liquid, gas, or plasma at different locations on THAT phase diagram. The analogous phase diagram for time crystals plots interaction strength between atoms versus imperfection in the spin-flip-driving signal. This triangle at the bottom is where time crystals live. If the variations in the forcing signal become too messy and the interaction strength is too weak, then the time crystal effectively “melts” into regular time-symmetric matter, in which the ion chain follows the rhythm of the driving signal perfectly, with no independent rhythm of its own.

This right side of the graph is also interesting. If the connections between the spins of the ions becomes too strong then you get this interesting quantum mechanical effect in which the ion locations gain quantum uncertainty -  imprecise positions that mess everything up. At that point a wormhole forms and sends your graduate student back to the paleocene era. Kidding. At that point thermal effects take over and the rhythm  dies.

This right side of the graph is also interesting. If the connections between the spins of the ions becomes too strong then a wormhole forms and sends your graduate student back to the paleocene era. Kidding. At that point thermal effects take over and the rhythm  dies.

Since Yao et al. laid out a practical approach to building time crystals in August 2016, two teams have synthesized them in the laboratory, in completely different ways. Chris Monroe’s team at the University of Maryland followed Yao’s suggestions for setting up a chain of ions, linking ten ytterbium ions and driving them with a laser. Mikhail Lukin’s Harvard team tried something completely different. They used microwaves to generate oscillations in the spins of nitrogen impurities inside a diamond. A time crystal within a space crystal.

Both spin systems developed periods that were integer multiples of the drivers, the ytterbium ions oscillations were twice the laser period, the diamond flaws three times the microwave period. Both resisted changes in the driving period, keeping up their own rhythms. Finally, both fit the predicted phase diagram, their time asymmetry melting when subjected to too much perturbation or too little interaction strength. So two teams verified this result in completely different ways. That means time crystals, at least by Yao et al’s definition of them, can exist. By the way, these two lab results have been submitted to journals but as of the filming of this journal club the peer review isn't complete.

I should also add that while these systems do break continuous time translational symmetry, they have a different type of symmetry – discrete time symmetry. That means that that if you shift forward or backwards in time in steps of exactly their period they will return to the same state. Scientists are using the term discrete time crystals to describe such systems.

Time crystals could see their first application in quantum computing. Perhaps the most popular approach to building a quantum computing memory element is to use electron spins, which can represent the 1’s and 0’s of a classical computer in the up or down direction of the spin. One of the most serious challenges is that these quantum states are really hard to maintain. It doesn’t take much random motion from heat to scramble a carefully-prepared array of entangled spin alignments, completely messing up your calculations. Time crystals, with their resilient spin-flip cycle, could be the next step in building stable quantum memory.   Time crystals could help bridge the gap between quantum mechanics and general relativity. Before this year, time stood out as a major symmetry that hadn’t been broken. And, unlike relativity, quantum mechanics treats space and time very differently to each other. Now we’ve seen matter settle into a discrete lattices in time, just like regular crystals. Perhaps a first step in a quantum union of space-time.