First author here -- happy to take any questions!
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...
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 :(
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.
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.
(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)
Also, what is the size of the crystal that you're looking at in these experiments (sorry if I missed that)
If the atoms "flip" when exposed to an electromagnetic pulse, it seems like this could be used to represent state at the atomic level, so highly relevant for computing.
Is there any current indication of how "stable" this flipped/non-flipped state is?
>In about 1220, the rite of public penance in Siena for those who had committed murder required the penitent to throw himself on the ground three times, saying: Mea culpa; peccavi; Domine miserere mei ("Through my fault. I have sinned. Lord, have mercy on me").
So that's a reasonable approximation. The vowels are off. If you know Spanish pronunciation, it's exactly the same for this word.
Specifically, The E sound is actually the single-vowel /e/, not the diphthong /aɪ/. The "uh" in both words is closer to "ah".
What's the layman's 2-minute definition of a time crystal?
The name makes it sound very sci-fi, like it might have the ability to travel through time (!)
Time crystal is a kind of crystal that has repeatable structure over time. It just means it changes its "shape" in a repeated fashion over time. Usually an external force is required to force a crystal to change its shape over time such as with the piezoelectric effect. Time crystal is supposed to just keep changing its "shape" over time by itself. In the Yale case, the changing of "shape" is the flipping of the nuclear-spin magnetization periodically.
However, now it seems to be changed to that an external energy source is driving the frequency of the structural change of the crystal over time. Like in the Yale experiment, an external pulsing light shines at the system at certain pulsing frequency and they found the system reverses its nuclear spin at twice as slow as the light's pulsing frequency. There's no intrinsic timing property shown in the crystal, so it cannot be used as a source of time information. I've asked the same question. [2]
However, it is a seemingly miraculous trick of spin systems that we are able to use pulses to effectively reverse the time evolution of the system and produce echoes. When looking at one new pulse sequence which had many pulses, the discoverer of the spin echo (Erwin Hahn) said "With that many pulses I could bring back the Messiah!" [1].
[1, PDF] https://pines.berkeley.edu/sites/default/files/publications/...
(Sorry that may be a bit vague)
"Chrystal with periodically re-arranged structure"?
However, for applications, one could imagine a packaged system+driving apparatus with potentially useful properties... but that is just speculation on my part.
eli5 please
If an external periodic pulse is required to drive the crystal to change its structure periodically, the time aspect is coming from the external pulse. The crystal itself doesn't have an intrinsic structural periodicity. The periodicity comes from the external pulsing. Is it still qualified to be called a "time crystal"?
The 2X slower reversing rate does show it has a time magnifying aspect, which can be huge.
https://news.ycombinator.com/item?id=16999031
The idea of a ground state time crystal was shown to be impossible, which led to the proposals for a non-equilibrium time crystal, connecting the idea (serendipitously) to the research that was already taking place in non-equilibrium systems by condensed matter physicists.
While we do think that each of the 4 existing experiments on discrete time crystals are showing the same effect, we're not yet sure how these observed "signatures of DTC order" will be eventually interpreted relative to the original idea of the time crystal (hence our conservatively named papers/descriptions). Sean's lab used subtleties of complex pulse systems to enable high-resolution MRI imaging in solids like bone (!), and we're pretty sure (not certain) that there's a connection between some of the effects related to those pulse sequences, and what we're now observing in these "DTC signatures"... that's what got us looking at these non-equilibrium ideas originally, and we're pursuing the possible connection.
Here's the point group (rotational symmetries around a lattice point) for a typical cubic lattice found in many metals: http://materials.cmu.edu/degraef/pg/pg_mbar3m.gif
Here's the space group (rotational symmetries combined with lattice/translational symmetries): http://img.chem.ucl.ac.uk/sgp/large/225az1.htm This is for face-centered cubic crystals. That's 48 symmetry operations, for one of the most common crystal systems used. However, they don't exist in higher dimensions because they're not fully independent. You can construct the full symmetry from just a handful of operators.
>That’s the “ticking.” In addition, the ticking in a time crystal is locked at a particular frequency, even when the pulse flips are imperfect.
I assume this is not true for quartz?
The "ticking" in our system is a periodically flipping nuclear-spin magnetization (rather than mechanical oscillations) whose period is definitely centered at twice the input drive period.
Time crystal I gather just vibrates (ticking) by itself with no external power, which is amazing. In this case, it's at the sub-atomic level rather than at the crystal lattice level of the quartz.
See also the reply here: https://news.ycombinator.com/item?id=16996766
It was shown after the original proposal in 2012 that these signatures can only be observed in "non-equilibrium" systems, so we are actually supplying the pulses, which drive the ticking. The quantum basis for the robust frequency of the ticking relies on dipole-dipole interactions among the nuclear spins.
It is very difficult to understand the complex state of the system after many of these interactions, but in our papers we explore how "coherent" the interactions are by "resurrecting" the signal in what are called spin echoes [1]. Simply speaking, after many interactions the "order" of the system lies not in the nuclear spins individually, but in a complex network of interactions among the spins -- this complex order is not observable (and so the signal appears to "decay away" over time).
Using techniques developed in nuclear magnetic resonance (NMR), we are able to put this "order" back into an observable state, and watch it return. It feels like reversing time, I never get used to it!
It is very difficult to understand the complex state of the system after many of these interactions, but in our papers we explore how "coherent" the interactions are by "resurrecting" the signal in what are called spin echoes [1]. Simply speaking, after many interactions the "order" of the system lies not in the nuclear spins individually, but in a complex network of interactions among the spins -- this complex order is not observable (and so the signal appears to "decay away" over time).
Using techniques developed in nuclear magnetic resonance (NMR), we are able to put this "order" back into an observable state, and watch it return. It feels like reversing time, I never get used to it!