So, what is a “temporal cloak”, anyway?

ResearchBlogging.orgI’ve been saying for a few years that optical science has entered a truly remarkable new era: instead of asking the question, “What are the physical limitations on what light can do?”, we are now asking, “How can we make light do whatever we want it to do?”  Among other things, we can make light travel “faster than light“, we can focus light through a highly scattering material, we can take high-resolution pictures with low-resolution sensors, and even make particles “fly” on a “wind” of light!

Inevitably, though, many of these discoveries get misinterpreted in popular news accounts to the point that their real significance is lost in a haze of science fictional, or even supernatural, hype.  A good example of this is the “picosecond camera” that I described last week, which is an amazing achievement but also possesses a number of technical limitations that make it not quite a “camera” in the ordinary sense of the word.

This week, the experimental realization* of a “space-time cloak” or “temporal cloak” by researchers at Cornell University has made national news.  This novel device differs from the “invisibility cloaks” discussed previously on this blog in that it hides temporal events, not spatial objects.  Loosely speaking, this has also been referred to as a “history editor”.  Naturally, the discussion of “cloaking” has again brought out references to “Harry Potter cloaks” and other dramatic imagery; the reality is much more mundane, but still fascinating — and an amazing achievement.  Let’s take a look at what was done, what was not done — and why it’s quite cool!

First, let’s get rid of some misconceptions that the terminology naturally brings to mind.  The terms “space-time cloak” and “history editor” make it sound like the device is ripping a hole in the fabric of space-time itself — like a time machine equipped with a big eraser!  This is definitely not what is happening here!  There is no manipulation of time itself, but rather a manipulation of a beam of light to hide something that the light would otherwise detect.

It is difficult to come up with a simple analogy to explain what is really going on, but let us imagine a beam of light as a long moving train of hanging curtains, as illustrated below:

We might imagine that these curtains are at an assembly line and have recently been dyed, and are still wet (I told you, analogies for this phenomenon are tough!).  We want to pass objects from one side of the curtains to another, but any attempt to simply push an object between them will mess up the dye and leave a mark.  An elegant solution is to design a system that parts the curtains gently starting at one point of their motion and lowers them gently to their original position at another point:

Anything that happens in the gap in the curtains will not affect the curtains at all; these actions are “hidden” from anyone watching the curtains at the end of the line.

This is, in short, the basic idea of a “temporal cloak”: we take a continuous beam of light, and part it like a curtain at one point, leaving a moving gap within which things can happen which will be completely untouched by the beam of light.  Some distance down the line, we close the gap, so that the light beam which reaches the detector is a continuous, undisturbed beam.  To appreciate how weird this is: we could pass a completely opaque object through the beamline during the gap, and the output light beam will still be a perfectly continuous unbroken stream of light!

You may deduce from this description that the real accomplishment isn’t the creating of a gap in the beam of light, but the seamless closing of that gap; or, to put it another way, creating a gap in such a manner that it can be closed seamlessly.

So that is the idea of a “temporal cloak”; the next natural question to ask is: how is it done?  The key to the phenomenon is a clever application of optical dispersion, which is most clearly manifested on the cover of a classic Pink Floyd album cover (and, come to think of it, in the header of this blog):

The atoms of a material respond differently to light of different frequencies (colors); the result of this is that different colors of light move at different speeds in a material.  This is what is known as dispersion, and this difference of speeds results in different colors of light being refracted at different angles in a prism.

The trick in creating a “temporal cloak” is to take light of a given color, and at the point at which one wants to introduce the “gap”, increase the frequency of light (“blue-shift”) in a region on one side, and decrease the frequency of light (“red-shift”) on the other side.  The device used to do this is called a “split-time lens”; more on this in a moment!  Then the light is passed into an optical fiber with dispersion such that the blue-shifted light moves faster and the red-shifted light moves slower.  This causes the gap to open up in the beam of light.  To close the gap, the light is then passed into a fiber with dispersion such that the red-shifted light moves faster and the blue-shifted light slower.  If the dispersion and the length of the fiber is just right, the gap can be seamlessly closed, leaving no trace of the former existence of the gap!  This process is illustrated schematically below:

A schematic of the actual experimental setup looks not much different from the simple description given above (adapted from the experimental paper):


A laser of a fixed frequency passes through a “split-time lens” which creates the red-shifted and blue-shifted section of the beam.  When this section passes into the optical fiber, ordinary dispersion causes the blue parts to speed up and the red parts to slow down, introducing the gap.  In the event region, an optical event is triggered that would ordinarily effect the beam but which falls in the gap and is therefore “cloaked”.  Then the light enters the dispersion-compensating fiber, which has the opposite dispersion properties of the ordinary fiber — the blue parts move slower and the red parts move faster!  This causes the gap to close, but the beam still has red-shifted and blue-shifted segments.  The second split-time lens reverses the effect of the first and removes the frequency shifts, returning the beam to its original, pristine, state.

If you’re paying careful attention (or are just suspicious of my explanation), you may have noticed a flaw in this scheme, as described.  If I blue-shift one part of the wave uniformly and red-shift the other part uniformly, I would expect the blue part to run into the unshifted part of the wave ahead of it, and the red part to get run into by the unshifted part behind it!  A gap will open, but because the parts of the wave are running into one another, I wouldn’t be able to separate them again.

My picture was in fact a little too simple: the frequency of the light in the red- and blue-shifted regions isn’t changed uniformly, but is in fact “chirped”: the frequency is increased/decreased smoothly and continuously.  (The name “chirp” comes from a bird’s “tweet”, which starts at a low frequency and ends with a high frequency: say “tuh-weet!”)  A plot of a chirped signal, which starts with a low frequency and ends with a higher frequency is illustrated below (source):

This means that the red- and blue-shifted regions of the light contain a range of speeds, with the fastest speeds at the middle of the gap and the slowest speeds on the outside boundary.  The gap therefore opens very much like curtains: the middle of the curtain spreads apart the fastest, and bunches up against the slower-moving outer parts.  I should revise my picture to the more sophisticated one shown below:

With the question of “how” out of the way, now we can focus on some more details, such as,  “How big of a temporal gap was created?”  Don’t start planning your temporally-cloaked bank robbery just yet: the gap width was 50 picoseconds of time, or 50 trillionths of a second!  The event cloaked was a very short nonlinear interaction of light in the “cloaked” region.  With the cloak off, the interaction generated new frequencies in the beam of light, detectable at the output.  With the cloak on, the nonlinear interaction occurred during the short duration of the gap, and produced no noticeable change in the probe beam.

This sort of “temporal cloaking” seems at first glance to be very different from the “spatial cloaking” that has been discussed and investigated for a number of years now.  It is worth noting, however, that the temporal cloak is in fact an almost straightforward extension of the same theoretical ideas that led to the first “invisibility cloaks”.

Physically, the now-traditional form of an invisibility cloak is a device fashioned of material whose optical properties guide light rays around a central “cloaked” region and send them on their way without any deviation (from one of the original 2006 papers**):

It has been noted that, mathematically, the effect of matter on light is equivalent to a distortion of space!  This has led to an entirely new theoretical field of optics, known as transformation optics, in which novel optical devices can be imagined by first assessing the “warping” of space needed, and then determining the material properties that will create this warping.  For instance, an invisibility cloak may be loosely thought of as a stretching of space away from a central, cloaked region, as depicted below.

In early 2011, researchers at Imperial College and the University of Salford realized*** that a medium which has properties which vary in time could produce a similar effective “warping”, but a warping of “space-time”.  We can even use the same warping picture depicted above, but replacing the horizontal position “x” with time:

The picture looks the same, but represents something very different!  Now this is a picture showing the motion of light rays along the y-direction at time t increases; a vertical line represents the position of the light rays at a single instant of time.  When the space-time cloak is active, the rays on the bottom move slower (y increases more slowly as t increases) while rays on the top move faster (y increases faster as t increases).  The “hole” in the middle of the picture represents the gap produced by the space-time cloak.  After a certain period of time, the rays return to their original trajectories and look as if nothing at all happened to them in the interim.

I imagine descriptions like this add to confusion about what exactly a “temporal cloak” is!  People read the phrase “mathematically equivalent to a warp in space-time” and retain, “a warp in space-time”.  As we have noted, though, this temporal cloak is in fact just a clever manipulation of various parts of a continuous stream of light.

It is worth noting that the duration of a cloaked event has a hard limit equal to the amount of time it takes light to pass through the system.  If light takes, say, 20 nanoseconds (20 billionths of a second) to pass through the entire cloaking system, then the theoretical upper limit on the duration would be 20 nanoseconds.  Temporally cloaking an everyday event, even one that lasts a few seconds, seems to be well outside of the reach of such a system, at least as currently conceived.

This does not mean that the temporal cloak doesn’t have potential applications, though.  The authors of the experimental paper suggest that such techniques could be used in optical data processing, for instance in a fiber optics data network.  Being able to split streams of optical data and reconnect them, possibly in a different order, could be a valuable tool in data manipulation.  I imagine such temporal cloaks working much like a railroad switchyard, in which trains of cargo can be separated, moved about, and recombined to send them on to their desired locations.

It will be interesting to see what other ideas and applications related to cloaking people come up with in the future; the temporal cloak shows that the imaginations of physicists in this regard have by no means been exhausted!

***************************

* Fridman, M., Farsi, A., Okawachi, Y., & Gaeta, A. (2012). Demonstration of temporal cloaking Nature, 481 (7379), 62-65 DOI: 10.1038/nature10695

** The original cloaking papers are U. Leonhardt, “Optical conformal mapping,” Science 312 (2006), 1777-1780, and J.B. Pendry, D. Schurig and D.R. Smith, “Controlling electromagnetic fields,” Science 312 (2006), 1780-1782.

*** M.W. McCall, A. Favaro, P. Kinsler and A. Boardman, “A spacetime cloak, or a history editor,” J. Opt. 13 (2011), 024003.

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6 Responses to So, what is a “temporal cloak”, anyway?

  1. Jim Kakalios says:

    That was a wonderful, clear explanation. Fantastic job! I found this site via Jennifer Ouellette and will be coming back in the future.

    Your Friendly Neighborhood Physics Professor,
    Jim Kakalios

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