Shrödinger’s hat (not cat . . . in the hat)

Ah, physics humor.  Anyway, it’s been too long since I made a pure science post.  I’ve been trying to wean myself off, but when I saw Jon Cartwright’s article on, I couldn’t help myself.  According to the article, an international team of physicists has proposed a new device that could detect the presence of waves or particles while barely disturbing them. Called a “Schrödinger’s hat”, the device has not yet been built in the lab but the team believes that it could someday be used as a new type of sensor for quantum-information systems.

Hat for the cat . . . in the hat.Let’s start with why this is important.  In the microscopic world of quantum mechanics, direct observation of the property of a particle – the position of an electron, for example – causes the collapse of the particle’s wavefunction. The result is that the particle that you set out to measure has been changed in a significant way.  Basically, anytime you look at what you are trying to observe, you change it.  In a very simplistic way, this is the idea behind Schrödinger’s cat – that it is both alive and dead at the same time, but once you open the box to look at it, it is now one or the other.  In short, by looking at something, you change it.  Makes it tough to do, well, pretty much anything.

So, if we know the problem, then how can we solve it?  In the early 1990s, physicists Avshalom Elitzur and Lev Vaidman at Tel Aviv University in Israel pointed out that it is not always necessary to observe particles directly to learn something of their nature. The researchers imagined a pile of bombs, each of which is designed to be triggered by the absorption of a single photon. Some of the bombs are duds; through these, photons pass unimpeded. One could check whether a bomb is working by firing a photon at it but, if the bomb were indeed to be working, it would be destroyed in the process. Would there be a way to weed out some of the working bombs without destroying them?

The answer is yes, say Elitzur and Vaidman. They considered an interferometer: a device through which a photon’s path is split into two arms, only to recombine at a set of detectors some distance away. To test a bomb, it would have to be placed in one arm of the interferometer. A dud bomb would have no effect on the photon, and the photon would pass through both arms, generating an interference pattern at the detectors. A working bomb, on the other hand, would force the photon to “choose” through which arm it passes. If it took the bomb’s arm, the bomb would, regrettably, be triggered. If the photon took the empty arm, it would reach the detectors unimpeded – but since the other arm was blocked, there would be no interference pattern. This lack of an interference pattern would reveal the existence of the working bomb without having triggered it.

In 1994 Anton Zeilinger of the University of Innsbruck, Austria, and colleagues demonstrated in a real experiment that such “interaction-free” measurements are indeed possible. Now, however, mathematician Gunther Uhlmann at the University of Washington in Seattle and colleagues may have come up with an easier way to perform such measurements – with a little help from the science of invisibility cloaks.

First demonstrated in 2006, invisibility cloaks can be understood through an analogy with Einstein’s general theory of relativity. This theory shows how very massive objects distort the underlying fabric of the universe, space–time. In the same way, certain man-made structures known as metamaterials distort an equivalent fabric, a virtual “optical space”. Metamaterials distort optical space through a spatially varying refractive index, the property that governs how light bends as it goes from one medium to another. By stretching out a hole in optical space, invisibility cloaks can shield a small object from light; the light rays pass around smoothly, as though the object were not there.

In practice, however, not all the light passes around invisibility cloaks – often, a small amount will leak in. If the inside of the cloak had almost the same resonant frequency as that of the incoming light, say Uhlmann and colleagues, that wave’s energy would build up, forming a localized excitation. This excitation behaves much like a particle, which the group has dubbed a “quasmon”. This quasmon could then be released by making a slight alteration to the cloak’s resonant frequency, perhaps through the application of a weak magnetic field.

Matti Lassas, a member of Uhlmann’s group based at the University of Helsinki, explains that the team calls the modified invisibility cloak a Schrödinger’s hat because tiny “parts” of waves or wavefunctions can be secretly stored, rather like a magician’s hat, and detected. And the trick is that the rest of the wave would be scarcely changed. Outside the Schrödinger’s hat, says Lassas, the wavefunction would be “the old wavefunction multiplied by a constant, [which] may be very small”.

The potential of a Schrödinger’s hat can be seen in the example of an electron in a box. Although the electron’s wavefunction is spread throughout the box, a scientist may be able to guess the location of areas where it drops to zero. That scientist could then position a Schrödinger’s hat at such a location, with no fear of the electron “noticing” the sensor’s presence and collapsing into a definite state. If the experiment were to be repeated several times, the scientist might be able to map out where the electron definitely is not – and in doing so, learn something about where it actually is.

Igor Smolyaninov at the University of Maryland, College Park, US, describes such a measurement as “an interesting proposal”. Smolyaninov – who was not involved in the research – says that “Measuring the quantum wavefunction without much perturbation would find important applications in many fields of basic science and, in particular, quantum computing.” He adds, however, that a Schrödinger hat will be difficult to make, since it will need properties that vary wildly in a very narrow region.

Ulf Leonhardt, a member of Uhlmann’s group based at the University of St Andrews in the UK, says that a device that works for microwaves could be made using circuit-board materials. A device for plasmons – waves of electrons in metals – could be made from metal and plastic rings. He thinks a Schrödinger hat could even be developed for sound – allowing its users to eavesdrop on sound without disturbing it.

The work will be described in an forthcoming paper in theProceedings of the National Academy of Sciences.

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