[jdrov]

There are a few questions about an "overview," so I'll give that a shot here. This is some imagery I've been using recently, about how our observed signatures are related to crystals.

Sometimes physicists think of phase transitions in terms of "symmetry breaking." Imagine zooming in very close on the molecules in a glass of liquid water, all tumbling quickly into and out of your field of view. The situation is highly "symmetric": if you closed your eyes and I shifted the field of view slightly to the left, you wouldn't know what I'd done when you opened your eyes again.

Now suppose the water freezes into a crystal of ice, so that the molecules are arranged on a regular lattice. If I repeat my "shift-slightly-to-the-left" experiment, you'd be able to tell I moved things. That is, somehow the molecules chose a particular location for the lattice, even though any other location of the lattice could have done just as well. In jargon, we say the water "spontaneously broke the continuous translational symmetry": the defining equations of motion are agnostic about the particular location in space, but the state of the system chose a location anyways.

In our experiment, we do something similar in time rather than space. We drive the system with pulses once every time period "T", so the equations of motion are identical under this "discrete" shift in time. However, the state of the system (in our case, the direction of the nuclear magnetization) only goes back to itself every time 2T, and so "breaks discrete time translational symmetry."

There is one more important feature of the observed signature in this analogy: if you nudge an atom that is in a crystal lattice, it will want to return to its original position. Similarly, the period of the magnetization's direction-reversal is robust to our pulse imperfections, if we allow the quantum interactions long enough to act. So, the "region" of parameter space where you can observe this effect is not confined to perfectly ideal pulses, but is instead robust to our pulse imperfections -- the "robustness" depends on the amount of time we allow the nuclear spin interactions to take place.

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I hope this helps. I recommend the synopses available at prl.aps.org, and searching for the PDF preprints on the Arxiv (not yet quite as good as the published versions), if you don't have Physical Review access.

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[Edit for links]

[2012 overview] https://physics.aps.org/articles/v5/116

[2013 overview] https://physics.aps.org/articles/v6/31

[2013 quanta mag.] https://www.quantamagazine.org/perpetual-motion-test-could-a...

[2017 overviews: "recipe" and first two results]

https://physics.aps.org/articles/v10/5

https://www.nature.com/news/the-quest-to-crystallize-time-1....

[2018 announcement] https://physics.aps.org/synopsis-for/10.1103/PhysRevLett.120...

[A different background by (the great) Natalie Wolchover of Quanta Mag., which provides context for the original thrust of one branch of this research. Our first significant involvement was after a talk about "Time Translational Symmetry Breaking" by Chetan Nayak of Microsoft's Station Q.]

https://www.quantamagazine.org/physicists-aim-to-classify-al...

[brandmeyer]

Is there any relationship between this kind of lossless vibration, and other lossless processes like superconductivity or superfluidity?

[jdrov]

I'm not confident that what we're observing are "lossless vibrations," but it is the case that there is something that is "lossless" about what we call "unitary evolution." The signal we start with decays to zero after a while, but we are able to show that this signal can be (in large part) restored, demonstrating that much of what initially looked like irretrievable loss is actually what we think of as "evolution towards a complicated but coherent state."

[brandmeyer]

I'm more confused, now. Some of the articles you linked to talk about time crystals as a type of perpetual motion machine, albeit one that is "exactly unity" instead of "over unity" as the crackpots would say.

If you have to hit the system with an impulse every once in a while to keep it toggling, how is it different than any other kind of resonant oscillating system? Is it that the cycle goes through states like:

* disorganized

* organized, directional

* disorganized

* organized, opposite direction

I still feel like the part of this system that is special and interesting is getting lost in the translation to lay language :(

[jdrov]

This is a good question. The "directions" you mention would, in our system, typically be considered to depend on the nature of the drive. For instance, if you repeatedly rotate the magnetization by 180 degrees, you can imagine the magnetization going up-down-up-down-... repeatedly, whereas if you instead used rotations of 181 degrees, it would take a long time for the state to come back around to pointing along its exact original orientation.

The proposed signature of a "discrete time crystal" was to observe the magnetization point up-down-up-down-... even when you used e.g. 181 degree rotations, if you allow dipole-dipole interactions to act for long enough between rotations. This is what we observe: "wrapped" magnetization when we use imperfect rotations with short nuclear spin interaction times, then locked up-down-up-down-... magnetization when we use imperfect rotations with longer nuclear spin interaction times.

A last subtelty when comparing to traditional oscillating systems is that the response is not at the same frequency as the drive, but will have a period determined by both the drive period T and the symmetry of the dipole interactions. Our system's interactions have 2 symmetric states, so the response period is at 2T. Other systems have other symmetries; for instance, the research team at Harvard showed oscillations at 3T using a spin system with different interaction symmetries.

[brandmeyer]

(HN doesn't do private messages, or this would be sent privately)

Thanks for coming out here and fielding our totally ignorant questions. Its an amazing and beautiful world out there, thank you for sharing your discoveries about it.

[jdrov]

Thanks for the kind words. I've focused a good deal in the past few years on teaching/communication (see my profile for a link to some of my basic-physics lectures for student taking the MCAT), and I'm very grateful for the opportunity to discuss our work with this community. Thanks for your interest and great questions!

[downer68]

Actually, HN does do /almost/ private messages, if you hellban your account, and the recipient of your reply comment has “show dead” turned on.

(of course, anybody can activate the “show dead” option, but, in reality, there’s no such thing as privacy on a web server, since there’s always a system administrator noticing unhashed passwords scroll through the log stream)

[ww520]

That's a great insight. That's probably why it's 2X slower in changing spin direction.

[samstave]

This may be a stupid question, but, is there any possibility to store data with this?

Also, what is the size of the crystal that you're looking at in these experiments (sorry if I missed that)

[rcthompson]

Based on what you describe, it seems to me that a macroscopic example of "symmetry breaking" in the time domain would be the piston of any internal combustion engine. The linear back-and-forth motion of the piston is converted to rotational motion, but in theory the rotation could equally well be in either direction. So when the piston starts moving and picks one or the other direction for the rotation, symmetry is broken. (Obviously real ICE pistons have some way to ensure that the rotation always happens in the same direction.) Have I got that right?

[masteranza]

With all fairness don't you think this is not really time-crystal formation in the strict sense (those have been shown to be impossible), but rather an analogue to a "forced" crystal formation? I.e. the direct analogue would be setting up some spatially periodic potential and trapping some atoms in it then finding out it took every second spot. I admit that the doubling appears a bit mysterious from a condensed-matter point of view, but on the other hand period doubling is a well known phenomena in classical physics. I'm a physicist, though not working on time-crystals - some of my friends do.

[watersb]

This overview helps. Thanks much. More to think about...