Quantum superposition — experimental proof

Consider the average NMR experiment.  A radiowave which is really electromagnetic radiation with a wavelength in meters is absorbed by a single nucleus with a diameter of about 10^-15 meters.  The wavefunction of the photon (which can pass through a brick wall if there’s no magnetic field around to split the energy levels apart enough so it can be absorbed) suddenly is absorbed by just one nucleus.  This is the famed collapse of the wavefunction.  If you think of things at the wave level, the photon is all over the place, yet it is absorbed in just one (very small) place.  So (for the cognoscenti) does every absorption of a photon by an atom or a molecule constitute a quantum mechanical measurement?  Post a comment if you know.  

Zeilinger’s book “The Dance of The Photons” (see previous post) has a marvelous experiment showing that a single photon follows two paths (unless it is measured, causing the wavefunction to ‘collapse’).  An experiment done nearly 20 years ago at the University of Rochester using a Rydberg atom with a very high (50) principal quantum number (its orbit is nearly 1 micron in diameter) showed that the electron in this orbit could be seen in 2 places at once.  I wasn’t smart enough to follow the details and found it hard to believe.   For details see “Doubt and Certainty: The Celebrated Academy Debates on Science, Mysticism, Reality” by Rothman and Sudarshan”(R&S) p. 289.   This is another really good book about the philosophic conundrums of QM.  Even better, Sudarshan brings an Eastern religion perspective to the party.  But be warned — he is very tough intellectually, and not at all touchy feely or newage (thank God). 

Unlike R&S, Zeilinger’s experiment features something every organic chemist knows quite a bit about — polarized light.  He even goes into just how a polarizer works (p.69).  Polarizers “are built up of long chains of molecules with parallel orientation.  An electric charge . . . can move easily along these chains of molecules, but has a very hard time moving in a direction at right angles to them.  So what happens if light comes in?  It tries to bring the electric charges into an oscillatory motion, because the electric field (of the light) itself oscillates. . . If the electric field oscillates parallel to the orientation of the molecules, the electric charges can move easily.  This motion takes up a lot of energy from the light.  In the end, the light loses so much energy that it is completely absorbed . . . In contrast, if the electric field oscillates at right angles to the chains of molecules, the electric charges cannot really move much.  This reduced motion takes only very little energy from the light so the light beam hardly gets reduced and passes through.”  The passage is typical of Zeilinger’s friendly (and very clear) writing style.  I did try to look up just what these “long chains of molecules with parallel orientation” are, but couldn’t find it anywhere.  If anyone knows, post a comment.   Note that the axis of the polarizer is defined by what it passes, not what it absorbs.  

How do you determine the orientation of a polarized beam of light?  If there is a position of the polarizer where no light gets through, the light is polarized. The orientation of the light is taken to be the angle at which transmission is maximal (e.g. at the axis of the polarizer). 

It’s worth being a  bit picky at this point.  How do you tell if a beam of light is polarized?   As you know, the electric field of (linearly) polarized light oscillates along one line (say the x axis) with the magnetic field oscillating along another at right angles to it (say the y axis).  The direction of propagation of the light is perpendicular to both (the z axis).  So shine the beam at a polarizer, then rotate the polarizer.  If the intensity of the transmitted beam doesn’t vary, the beam is unpolarized (e.g. it contains photons with every orientation of the associated fields relative to the axis of the polarizer).  

How do you determine the orientation of a polarized beam of light?  If there is a position of the polarizer where no light gets through, the light is polarized. The orientation of the light is taken to be the angle at which transmission is maximal (e.g. at the axis of the polarizer). 

To the experiment at last:  It involves something called a polarized beam splitter (PBS), which is a device which will split a beam polarized at 45 degrees (relative to horizontal and vertical) into two beams.  The orientation of the beam reaching the PBS is critical.  If the polarized beam is oriented vertically (something you now know how to determine) it goes right through.  If it is oriented horizontally it comes out at a 90 degree angle polarized horizontally. How do you know? Put polarizers in each path and measure what comes out.  

What do the two beams coming out after a beam polarized at 45 degrees enters the PBS look like? The one continuing the original path is vertically polarized, the other at 90 degrees is horizontal.  That’s why its called a beam splitter after all. Zeilinger doesn’t really go into how a PBS works (again, if you know post a comment).  The PBS acts like a vector analyzer, splitting a 45 degree vector into its zero and 90 degree components.

Now the fun begins.  Put a photon counter in each path

  —->   PBS         counter1

             counter2 

Send the photons through one at a time (apparently this can be done).  What happens?  How does the photon ‘decide’ which way to go?  No one knows, and quantum mechanics states that no one will ever be able to tell.  The photon definitely goes one way or the other (at least in this setup).  Either counter1 registers a photon or counter2 does — NEVER both.  Each counter registers a photon roughly half the time.  Zeilinger assures us that this has been tested experimentally many times (p.81).

Now for a more complicated experimental set up.  It involves two PBSs and two mirrors.  Zeilinger doesn’t explain how mirrors work (if anyone knows, post a comment), but work they do.  Just like in billiards the angle of incidence equals the angle of reflection.  They reflect photons without changing their polarization (you know how to check this experimentally).  We’ll throw in the light beam polarized at 45 degrees 

        —->   PBS1 —- vertical —>   \   <– Mirror1

                       |                                    |

                horizontal                   vertical

                       |                                    |

Mirror2–> \   horizontal —>  PBS2

What comes out from PBS2 and which way does it come ?

You should be able to figure out what happens from what you’ve been told.   Think about it and then read the next paragraph.

The vertically polarized beam hitting PBS2 should go straight through.  The horizontally polarized beam hitting PBS2 should be reflected 90 degrees, so we should have a beam coming out the bottom of PBS2 made up of photons, half of which are polarized vertically, the other half polarized horizontally.    The first experiment measured what they are like after hitting PBS1, and how vertical and horizontally polarized beams act when they hit a PBS.  

Nice !   Except this is NOT what happens.  What you get is a beam ALL of whose photons are polarized at 45 degrees.  At least it’s coming out the bottom of PBS2.  It’s as though the photon followed both paths.  Quantum mechanics says that this is exactly what happens, the photon is in a superposition of states of all possible paths. If you force a measurement on the photon after PBS1, the photon is forced in some way to chose a path.  This is called the collapse of the wavefunction.  You’ve just seen it live and in color, along with the photon being in two places (paths) at once as long as you don’t look at it. 

I love it.  This is experimental evidence for superposition of quantum states, based on real measurements, not the statistics of outcomes.

However, statistics of outcomes is exactly how Zeilinger shows that the Bell inequality (for which he has a neat derivation involving twins) proves that quantum mechanics is right and local reality (see previous post and the next post) is wrong.