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Crystal to time crystal : Periodic arrangement of atoms in the form of a crystal is well known to us. The periodicity in conventional crystal is  with respect to its spatial co-ordinates. An interesting question is : what if  the periodicity of a crystal is also considered in temporal co-ordinates, that is with respect to time ? Such crystals, in which  atoms (or their equivalents) repeat both in space and time are called time-crystals (specifically space-time crystals).

Origins : Although the term “time crystal” was used in biological context in 1970s, it was a research paper by Alfred Shapere and Frank Wilczek in 2012 which brought this interesting concept into mainstream physics. Wilczek, a Nobel laureate, also postulated the concept of quantum time crystal, which has added great impetus to this exploration. These theoretical concepts were experimentally probed and verified by Zhang’s group at UC Berkeley using ions in a cylindrical arrangement. Since then, there is a lot of research activity in this area. My colleagues at IISER-Pune – Sreejith and Mahesh, have created a new variety of time crystals by subjecting periodic NMR pulses to spins in star-shaped molecules .  

    I should also mentioned that after Wilczek’s results were published, Patric Bruno criticized the quantum counterpart based on No-Go theorem argument. There are some interesting debates which are still going on regarding the thermodynamic aspects of these crystals. Also many new applications have been proposed and tested based on the initial predications. To know more about the history and current trends in time-crystals, I suggest a recent, comprehensive review article.

Choreographic (time) crystals : Dance is something inherent to humans, and may be to other living beings. As per google dictionary, the term choreography means the sequence of steps and movements in dance or figure skating, especially in a ballet or other staged dance. In a choreographic time crystal, the movement of atoms (or their equivalent) are in a sequence of steps and co-ordinated, just as in a dance sequence. This means the spatial and temporal co-ordinates of this crystal varies in a predictable way, and hence represents a space-time crystal.  Such a concept was proposed in a paper in 2016. An interesting issue discussed in this theoretical paper is how Bragg’s diffraction law can be modified and adapted to probe such choreographic crystals. Modification of this law in necessary as atoms in a dancing lattice are in constant motion, and to obtain snapshots of the moving atoms one needs a capture protocol (diffraction in this case).

Colloidal dance : Atoms are tiny objects. If we need to probe the spatial and temporal evolution of atoms in a crystals, then we require sophisticated imaging tools (such as scanning tunneling microscope) to track atoms in space and time in an ultra-high vacuum condition. Is there any alternative, cheaper method to this approach? The answer is yes (with some caveats). One way is to utilize colloids (micron-scale objects floating in a fluid)  and treat them as big atoms. This is of course  an approximation, as colloids are classical objects, but many of the physical concepts that are applicable to atoms may be scaled up to colloidal size, and this scaling has been verified and harnessed to mimic and study collective behavior of atoms.

   Coming back to choreographic time crystal, the obvious question to ask is: can we use colloids to visualize the dance of this crystal ? A recent paper in PRL (arxiv version) addresses this question with numerical simulations. The authors first propose an experimental scheme to create a choreographic optical lattice using light as a tool. They hypothesize optical potential wells that can evolve both in space and time, and numerically study the evolution of colloids in such a choreographic time crystal. An important finding from their study is that they identify three phases of dynamics, in which the interaction between the potential-well  and the colloids is weak, medium and strong. In these three phases, they observe chiral looping of colloids, liquid-like behavior and colloidal choreography. I strongly recommend to have a look at the amazing simulation videos for the three simulated regimes of interaction : weak , strong , medium.

Summary : What I have described above is a metaphorical snapshot of how concepts in physics such as time crystals, optical lattice and colloids can come together on a single platform to collectively give something, which is not feasible to obtain by any of the individual entity. The concept of crystal itself is a manifestation of this ‘emergence’ philosophy. In an essence these ideas are both a tribute to, and reinforcement of, the concept:  “More is Different”…..  adieu Anderson….