There are a few key differences in our work. First, it's a very different system; the prior experiments were done using trapped ions, and "defects" (nitrogen-vacancy centers) in diamond, while our system used nuclear spins. The more important difference is that our system is very ordered, since it took place on an actual crystal lattice with a high degree of symmetry (this matters because some theories proposed the need for this disorder to observe the effect -- the trapped ion experiment even purposely included disorder). This is the reason for our use of the word "ordered" in the title of the paper.
Other differences include our further work to clarify the phemomenon, including the creation of "echoes" to explore the coherence of the system (see my other comments) among other new contributions about the parameter space and behavior of the effect. Finally, it's just surprising to have observed this effect across so many systems which are all so different from each other (very different Hamiltonians).
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!
See my response here, about the way in which the response frequency depends on both the nature of the drive and the nature of the internal interactions in the system:
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.
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.
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."
I notice a lot of questions here about piezoelectric oscillators, which I realize now makes sense given this community. A key difference to understand here is that the phrase "time crystal" is referring to a state of a particular "driven" system. So, the signatures we've observed are properties of not only the nuclear spins, but of their response to our driving pulses. So I could not for example "make an equilibrium time crystal and send it to you." Rather, to duplicate our particular results, you would need a clean MAP crystal, which you would then need to "drive" in a particular way, with energy input.
However, for applications, one could imagine a packaged system+driving apparatus with potentially useful properties... but that is just speculation on my part.
We use a solenoid to drive magnetic fields in our sample (RF frequencies, near field), but yes, we do often envision an absorption or emission event by a given nuclear spin as it changes its spin state in the presence of an even stronger, static magnetic field. We have to carefully match the frequency of the driving magnetic field to the so-called Larmor frequency of the spins, which allows them to absorb the supplied energy.
We're working on understanding possible applications now, and we also wonder whether this is a more commonly available phenomenon than originally thought. As experimentalists, we're very conservative in our claims -- for instance, we explain our observation of the "DTC signature" specifically proposed by theorists, without making claims as to the final interpretation of the results for the existing theory. Instead, our job is to very clearly explain what we did and what resulted, and then we get to see (and in some ways participate in) how the broader condensed matter community comes to understand the phenomena. It's an exciting position to be in, there are still many interesting unknowns!
Let me know if my synopsis above helps, or if you have any specific questions from a high-energy theory point of view. Given your background, you might appreciate that we ran many simulations, to characterize the sample, understand our early results, and build our echo sequence.
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!
Let me know if my attempted synopsis above is helpful or not... I think I can confidently say that the crystal does not travel backwards in time (or forwards in time any faster than the normal rate, as has been pointed out).
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].
Admittedly, if you asked me 20 years ago which one of "time crystal" or "flux capacitor" were actually from a movie called "Back to the Future," I am not confident I would answer correctly.
You're right that the terminology has been tricky to contend with, although it's hard to say what a 'least-confusing' name would be. Other names for the phenomenon include "Pi spin glass" and "Floquet time crystal," neither of which seem to definitely avoid any confusion. The accounts of these phenomena are becoming more clear over time, which will help, but given the name and the images often used in the press, I understand why it can come across as fantastical.
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!
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.
[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.]
That is the kind of thing we are working on understanding right now, and research proposals into this (so-called "quantum metrology") are underway. Is it definitely the case that radio-frequency pulse sequences (related to those used in our work) have been used for extending quantum coherence and making measurements, for instance in MRI. (In fact, that's the kind of work that got me into this!)
I'm not an expert in quartz, but I'd assume there are physical "mechanical" oscillations with a hopefully-small distribution of frequencies around a given frequency, which is known to some particular degree of accuracy.
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.
The state of the nuclear spin (up or down, or superposition) is definitely something that has been proposed as a quantum bit ("q-bit"), and many quantum computer proposals have used the nuclear spin as their proposed q-bit. The tricky thing is that these nuclear spins are all interacting with each other, and exercising control of the full state in the presence of those interactions is very tricky.
As far as I know, there are no implications for how physical structures are organized in space (e.g. spatial crystal lattices). The signatures we've observed were in a crystal with a very well-characterized lattice structure, and could be observed in systems with different geometries as well (i.e., we didn't have to go out of our way to find a "special" crystal lattice).
Sean is the kind of advisor that makes being a graduate student both exciting and sustainable. He's always upbeat, supports us professionally, etc., so it's always particularly sad for me to hear from students who have had bad experiences with their advisors.
Other differences include our further work to clarify the phemomenon, including the creation of "echoes" to explore the coherence of the system (see my other comments) among other new contributions about the parameter space and behavior of the effect. Finally, it's just surprising to have observed this effect across so many systems which are all so different from each other (very different Hamiltonians).