Canadian researchers devise method to directly measure the quantum wavefunction

Canadian researchers devise method to directly measure the wavefunction
Direct measurement of the photon transverse wavefunction. Image: Nature, doi:10.1038/nature10120

( -- Physics researchers working at the National Research Council in Canada have succeeded in developing a way to directly measure the wavefunction of a photon. The technique, as described in their paper published in Nature, combines both strong and weak measurements, and offers researchers a new tool for use in understanding the intricacies of quantum mechanics. The wavefunction is a mathematical function that describes the quantum state of a particle.

Until now, physicists have had to resort to using quantum to gather information about the real wavefunction (as opposed to the virtual one described by math formulas), a method that relies on indirect measurements and alters the target it’s trying to measure in the process. This is because of Heisenberg’s uncertainty principle, which states that the location and momentum of a single particle can’t be simultaneously measured; because by its very nature, the waveform is altered by direct observation.

To get around that problem, the team, led by Jeff Lundeen, devised a method based on “weak” measurements, whereby an observation is made that only alters the particle just a little tiny bit and gives information about just one property of the particle at a time. Taking multiple such measurements of identical copies of a particle, such as a photon, gives more and more information, eventually approaching a very close approximation to the actual state of the system. In one respect this approach is similar to the way calculus is used to measure irregularly shaped objects by cutting it into a number that approaches infinity, virtual slices, then adding up the results. When combined with more certain “strong” measurement results, the procedure provides an accurate measurement of the wavefunction.

The wavefunction is a big deal in physics because it can be used to predict how a particle will react with other particles, where it will be at a given time, or how fast it will be traveling; that are needed when building microelectronics, or one day perhaps a true quantum computer.

Lundeen points out that this new method doesn’t actually provide any new information about the waveform; it’s more like it provides researchers with a new tool. He also says the technique could be used to measure the waveform of other such as ions, electrons and molecules.

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More information: Direct measurement of the quantum wavefunction, Nature 474, 188–191 (09 June 2011) doi:10.1038/nature10120

The wavefunction is the complex distribution used to completely describe a quantum system, and is central to quantum theory. But despite its fundamental role, it is typically introduced as an abstract element of the theory with no explicit definition. Rather, physicists come to a working understanding of the wavefunction through its use to calculate measurement outcome probabilities by way of the Born rule. At present, the wavefunction is determined through tomographic methods, which estimate the wavefunction most consistent with a diverse collection of measurements. The indirectness of these methods compounds the problem of defining the wavefunction. Here we show that the wavefunction can be measured directly by the sequential measurement of two complementary variables of the system. The crux of our method is that the first measurement is performed in a gentle way through weak measurement, so as not to invalidate the second. The result is that the real and imaginary components of the wavefunction appear directly on our measurement apparatus. We give an experimental example by directly measuring the transverse spatial wavefunction of a single photon, a task not previously realized by any method. We show that the concept is universal, being applicable to other degrees of freedom of the photon, such as polarization or frequency, and to other quantum systems—for example, electron spins, SQUIDs (superconducting quantum interference devices) and trapped ions. Consequently, this method gives the wavefunction a straightforward and general definition in terms of a specific set of experimental operations19. We expect it to expand the range of quantum systems that can be characterized and to initiate new avenues in fundamental quantum theory.

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Jun 16, 2011
The general understanding was, only the probability density distribution is, what remains observable from quantum physics, not the quantum wave as such. But if such view would be true absolutely, than the quantum world would be statical and atemporal. As we can observe with Brownian motion for example, the dynamic nature of quantum mechanics still manifests clearly.

So, where's the trick of this experiment? The quantum wave function still remain unobservable as a whole, or it would violate the uncertainty principle. But the principle of so-called weak measurement enables to observe it with using of so-called stroboscopic effect: during each measurement the quantum waves collapses nearly completely, but it's restored again before a new sample is taken. When the frequency of sampling is synchronized with frequency of quantum wave, then the time evolution of quantum wave can be observed, although we are effectively observing a restored, i.e. not original wave during each sample.

Jun 16, 2011
Recently the similar theorem of Copenhagen interpretation of quantum mechanics was shifted. It basically claims, during double slit experiment the path of photons cannot be observed, or their interference patterns will collapse into Gaussian shape, which the single slit produces.

But as the experiment demonstrated, with careful sampling it's still possible to trace the path of photons in subsequent observations in such a way, their interference is not impacted. Again, the main trick here is in usage of multiple weak measurements, not just single "hard" one, which would collapse the quantum wave undeniably.


Jun 16, 2011
How do they get the "identical copies" of the photon?

Jun 16, 2011
"identical copies" of the photon?
This sentence is a bit misleading, as these Canadians used collinear photons, i.e. photons with the same phase and amplitude, but with perpendicular polarization. Such photons are routinely produced with shinning of near infrared laser to the nonlinear optical crystal of beta barium borate under certain angle. It generates coherent pairs of short wavelength photons, which can be used in subsequent experiments. You can imagine it like laser, which generates two photons during stimulated emission instead of single one. Such lasing is indeed quite rare, but if you pump BBO crystal with sufficiently intensive light from another laser, you can succeed in generation of such entangled pairs.

Jun 16, 2011
The BBO crystal is unique with the fact, it's both birefringent, i.e. its refractive index strongly depends on the direction of polarization of light, both strongly piezoelectric (which means, the impulse of electric field can generate mechanic vibrations of lattice). When laser stimulates some atom in BBO lattice to emission of photon, the corresponding electric impulse deforms lattice in such a way, another photon from neighboring atom is released too at the same moment. When these two photons differ with their polarization sufficiently, they propagate through birefringent crystal with different speed, so they're refracted with its surface under different angle and they can be handled separately.

Jun 16, 2011
Who knows, it might even get a handle on a quantum reason and/or calculation for the speed of light...why it is THAT speed and not ANOTHER speed. Maybe manipulation of wave functions in micro would have an effect in macro as well. Comments?

Jun 19, 2011
Brilliant article and the comments really helped clear up a few misunderstandings for me. Thankyou all!

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