Time Crystals! | Space Time Journal Club
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Time Crystals! | Space Time Journal Club


MATT O’DOWD: This episode is
supported by the Great Courses Plus. 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. [MUSIC PLAYING] In “Space Time Journal Club,”
we review new scientific papers that are making waves. We pick them apart to
turn the technobabble into simple English, at
least as much as is possible. Then we fight about
it in the comments. This week, we’re going to take
a look at a recent publication by Norman Yao et al. in physical review
letters, entitled “Discreet Time Crystals:
Rigidity, Criticality, and Realizations.” This paper proposed
an approach to making these bizarre objects, a
recipe that two other research teams have now followed
and have actually synthesized these things. But first up, what on
earth are time crystals? The idea was first proposed in
2012 by Nobel laureate Frank Wilczek of 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, but how does that make
it a time crystal? The analogy is that regular
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 his “The Geometry
of Biological Time,” where it’s 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 translational 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 over 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
in the universe are not in 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 states. 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 is 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
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 where the line 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 or frequency. The spin-flip oscillation
will be determined by the period of the laser. That laser is what takes the
system out of equilibrium, because you are basically
pumping in energy. Causing spins to flip in a laser
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 spins should not oscillate at the same
period as the laser, but at an integer multiple
of the driving period. So two, three, four, et cetera
spin oscillations for every EM field oscillation in the laser. Yao et al.’s work
was theoretical, but it involved numerical
calculations that allowed them to draw a phase diagram. This is sort of like the phase
diagram of regular matter in which you plot pressure
versus temperature. Different materials become
solid, 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 become too strong,
then a wormhole forms and sends your
graduate students back to the Paleocene era. I’m kidding. At that point, thermal effects
take over and the rhythm dies. Since Yao and team laid
out a practical approach to building time
crystals, in August 2016 two teams have synthesized
them in the lab 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 10 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 their systems do break continuous time
translational symmetry, they have a different
type of symmetry– discrete time symmetry. That means if you shift
forwards 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 have
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 ones and zeros of a
classical computer in the up-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 calculation. Time crystals with their
resilient spin-flip cycle could be the next step in
building stable quantum memory. Time crystals could
also 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 in relativity,
quantum mechanics treats space and time very
differently to each other. Now that we’ve
seen matter settle into discrete lattices in time
just like in regular crystals, perhaps it’s a first step in
a quantum union of space time. Thanks to the Great Courses Plus
for sponsoring this episode. The Great Courses Plus is
a digital learning service that allows you to learn about a
range of topics from Ivy League professors and other educators
from around the world. Go to thegreatcoursesp
lus.com/spacetime and get access to a library of different
video lectures about science, math, history, literature, or
even how to cook, play chess, or become a photographer. New subjects, lectures,
and professors are added every month. The Nature of Matter
by Professor David Ball may not cover time
crystals, but it does go into some amazing detail
about some other weird and wonderful states of matter. With the Great
Courses Plus, you can watch as many different lectures
as you want anytime, anywhere, without tests or exams. Help support the series and
start your one month trial by clicking on the link
in the description, or going to thegreatcoursesp
lus.com/spacetime. A couple of weeks
ago, we talked about the recent spectacular
discovery of seven terrestrial and potentially habitable
worlds around a nearby red dwarf star, the TRAPPIST-1 system. Solano Felicio asks about the
possibility of stable orbits when planets are
so close together. Well, that’s where orbital
resonance comes in. The planet’s
orbital periods have evolved so that each
pair of planets lines up at regular intervals. That actually
stabilizes the orbits rather than makes
them more chaotic. Some period of instability
would have preceded the system, finding this nice
resonant configuration, and that probably
drove the planets from much larger orbits to their
current locations very close to the star. Matthew Pick asks about
the transit method, and wonders how rare it
is for a planetary system to be lined up so we
actually see the transit. The answer is that,
yeah, it’s rare, but there are a lot of
stars in the galaxy. The Kepler Space
Telescope has so far discovered 2,330
confirmed exoplanets in 578 planetary systems. That’s 578 stars out
of the 100,000 stars that Kepler monitors. That gives you an idea of
the average probability of alignment, but not all
of those will have planets. Yet it’s estimated that a
system with an Earth-like planet orbiting a Sun-like star
has around a 1% chance of transiting from
our perspective. I think my favorite comment
was from WarriorofCathar, who pointed out that we
basically just learned all about a solar system
light years away by studying how faint shadows make
other faint shadows wobble. I agree, Warrior. Damn science, you scary. Scary awesome. [MUSIC PLAYING]