Yeah, I know this is the middle of the year, but year boundaries are so arbitrary. Once upon a time (even here in America, prior to 1752), New Years Day was March 25, so…whatever….

However you mark the passage of time, there have been some exciting experimental breakthroughs in the world of experimental quantum mechanics over the last 12 months. I’m not talking about exotic experiments designed to look for dark matter or the Higgs boson, or attempts to confirm or refute String Theory or SUSY, but rather experiments which probe and test the most basic fundamentals of quantum theory. (Well, in all fairness, one of the experiments I’m about to mention could be used to probe some aspects of String Theory, as well as other candidates for a quantum theory of gravity, and another has results which seem to invalidate some predictions made by SUSY.) Here are some of the highlights:

## Confirmation of the Born Rule via a triple-slit experiment

Young’s double-slit experiment has long been a mainstay for both demonstrating and testing some of the more bizarre and counter-intuitive aspects of quantum mechanics (so fundamental, in fact, that almost every book Feynman ever wrote about QED seems to start with an analysis of it, and it occupies a big chunk of his more famous lectures), especially the Born Rule, one of the most fundamental elements of quantum mechanics, which tells us how to mathematically combine quantum probability amplitudes in order to calculate the probability of a given outcome.

Remember that, in quantum mechanics, probabilities are calculated differently than in any other discipline. The probability of any event A taking place, P(A), is calculated by taking the absolute square of a probability amplitude, a, which is a complex number, and may be a function of time and/or position, so P(A)=|a(x,t)|^{2}. Now, the rules for combining probability amplitudes for various competing outcomes are where things get complicated. In the case of the double-slit experiment, we have a probability a_{1} that the particle will pass through the first slit, and a probability a_{2}, that it will pass through the second slit. Classically, we would expect that the overall resulting probability would be a simple superposition of the two cases, P=|a_{1}|^{2}+|a_{2}|^{2}, but this is not at all what we see experimentally (unless we modify the experiment to detect which slit the particle actually came through, but then we are changing the problem). What we actually see is P=|a_{1}+ a_{2}|^{2 }= |a_{1}|^{2}+|a_{2}|^{2}+2|a_{1}a_{2}|, where the last term is what introduces interference effects.

But what if we add a third slit? Do we get some crazy probability distribution with higher order terms? The Born Rule says no, and these experiments confirm that.

Sinha

et al., “A Triple Slit Test for Quantum Mechanics”,Physics in Canada. Vol. 66, No. 2 (Apr.-June 2010), pp. 83-86Sinha

et al., (23 July 2010). “Ruling Out Multi-Order Interference in Quantum Mechanics”.Science329(5990): 418-421. Bibcode 2010Sci…329..418S. doi:10.1126/science.1190545. PMID 20651147Sanders et al., (14 August 2010). “Triple slits don’t add interference”.

Science News178(4): 12. Bibcode2010Sci…329..418S. doi:10.1126/science.1190545. PMID 20651147

## Observation of gravitational quantum states of cold neutrons

I had actually referenced this in an earlier post. It had long been thought that quantum gravitational effects would be far too weak to measure in the Earth’s anemic gravitational field. (It would be much easier to measure quantum gravitational effects on, for example, the surface of a neutron star. Well, aside from the intense gravity of the neutron star crushing any measuring apparatus placed upon it into oblivion, but I digress….) This difficulty in experimentally probing the quantum mechanical aspects of gravitational phenomena is precisely what makes it so challenging for physicists to construct a workable theory of quantum gravity.

Well, some clever scientists have figured out a way to do it, by, of all things, bouncing cold neutrons. Seriously.

Jason Palmer “Neutrons could test Newton’s gravity and string theory”, BBC Online (17 April 2011).

Tobias Jenke

et al.“Realization of a gravity-resonance-spectroscopy technique”,Nature Physics(17 April 2011) | doi:10.1038/nphys1970Valery V. Nesvizhevsky

et al. “Quantum states of neutrons in the Earth’s gravitational field”,Nature415, 297-299 (17 January 2002) | doi:10.1038/415297a

## Using “weak measurement” of a photon’s momentum to reconstruct average photon trajectories through a double-slit experiment

Returning to the topic of the double-slit experiment, some rascally researchers have found a way to push Heisenberg’s Uncertainty Principle to its limits in such an experiment. The Uncertainty Principle states that the product of the uncertainties in the values of any pair of canonically conjugate quantum observables (for example, momentum and position) must be greater than or equal to the reduced Planck constant divided by 2:

Mind you, the right-hand side of that expression is a pretty tiny value, and can be taken to equal zero in the classical limit (which is essentially the mathematical definition of taking a quantum system to the classical limit), so at the classical scale, it doesn’t mean much. But in the microscopic world of quantum mechanics, the Uncertainty Principle rules all, setting severe limits on what we can or cannot know about a system, not as a consequence of how sensitive or cleverly designed our instruments are, but rather as a result of fundamental limitations of reality. (Exactly why that is the case is a bit beyond the scope of this posting. Think about the Fourier Transform of a particle’s quantum state function and what it means to pluck exact values for both position and momentum out of that, and you might grasp why. For the moment, just roll with it.)

The upshot of the Uncertainty Principle is that making precise measurements of a particle’s momentum effectively destroys the precision with which we can measure its position, and vice-versa. But, to know a particle’s trajectory (in the classical sense, at least), we need at least some information about both. What these clever researchers have done is to make intentionally imprecise (“weak”) measurements of the particle’s momentum, thus giving themselves some breathing room for measurement of the particle’s position.

Jason Palmer, “Quantum mechanics rule ‘bent’ in classic experiment”, BBC News Online (3 June 2011).

Kocsis

et al., “Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer”,Science, 3 June 2011: Vol.332no. 6034, pp. 1170-1173. DOI: 10.1126/science.1202218

## Observation of quantum interference with large organic molecules

Young’s double-slit experiment (Yep, we are still talking about that!) was initially conducted with light, but has since been performed with electrons, neutrons, and even atoms, all with the result of an interference pattern consistent with quantum mechanical behavior. (These experiments have even been performed with “feeble” sources, trickling one particle at a time through the apparatus and still producing interference, demonstrating that the particles are interfering with themselves, not with one another.) The tricky part is that the more massive the particles with which we conduct the experiment, the smaller the wavelength of the interference phenomenon. Moving up in scale, we eventual reach a point at which the quantum interference is drowned out, and the results give way to classical behavior. This fuzzy boundary between quantum and classical behavior is an illustration of what is known as quantum decoherence, and is a particularly fascinating area of research.

Recently, researchers have pushed the boundary of this quantum/classical transition further than ever before by observing quantum interference with large organic molecules. Such experiments had previously been performed with carbon-60 (“buckyballs”). These molecules are particularly well suited since their spherical shape makes them relatively compact, keeping their physical extent from overwhelming the interference effects. The researchers are considering continuing their work using spherical viruses.

“Researchers Find ‘Fattest Schrodinger Cats Realized to Date”, Discover Blogs, April 7, 2011.

“Wave-particle duality seen in carbon-60 molecules”, PhysicsWorld, Oct 15, 1999.

Gerlich, S.

et al. “Quantum interference of large organic molecules”.Nat. Commun.2:263 doi: 10.1038/ncomms1263.

## A high-precision measurement of the electric dipole moment of the electron.

The word “shape” in the title of the paper describing this work is rather misleading, as an electron technically has no shape. It is generally regarded as a point charge (albeit a rather fuzzy point thanks to the Heisenberg Uncertainty Principle), thus having no spacial extent, and thus no surface. What “shape” really refers to here is the shape of the electron’s electric field. The QED predicts that the electric field of an electron is perfectly spherical, with the exception of a tiny deviation known as the electric dipole moment (EDM). The Standard Model predicts that the EDM is too small by several orders of magnitude to be measurable by currently available methods (not to be confused with the magnetic dipole moment due to the electron’s intrinsic angular momentum, or “spin,” which has been readily measurable since the days of the 1922 Stern-Gerlack experiment). However, there are extensions to the Standard Model which predict values for the EDM which are in ranges which are measurable today, making such measurements a useful tool for testing the validity of those extensions. The upshot of the experiment is that an upper bound was placed on the value of the EDM which essentially rules out those particular extensions to the Standard Model (yet another coffin nail for SUSY, but that would be the subject of a future post).

Hudson,

et al., “Improved measurement of the shape of the electron”,Nature473, 493-496 (26 May 2011). doi:10.1038/nature10104