Caroline Thompson's Physics

http://freespace.virgin.net/ch.thompson1/

Experiments in the headlines: key experiments and papers relating to quantum entanglement

[See also an old file of mine, “Impressions from the quant-ph archive”]

Contents

·        Introduction

·        Charles Santori et al, “Indistinguishable photons from a single-photon device”, Nature 419, 594-597, 10 October 2002

·        “‘Two-photon’ coincidence imaging with a classical source”, Ryan C Bennink, Sean J Bentley and Robert W Boyd, Phys. Rev. Lett. 89 (11), 113601 (2002)

·        "Plasmon-assisted transmission of entangled photons", Altewischer, E, M P van Exter and J P Woerdman, Nature 418, 304 (2002)

·        Edamatsu, Keiichi, Ryosuke Shimizu and Tadashi Itoh, “Measurement  of the photonic de Broglie wavelength of biphotons generated by spontaneous parametric down-converion”, Phys. Rev. Lett. 89, 213601 (2002), quant-ph/0109005

·        “Ladder Proof of Nonlocality without Inequalities: Theoretical and Experimental Results” (Boschi, D, S Branca, F de Martini and L Hardy, Physical Review Letters 79, 2755 (1997))

·        Strekalov, D V et al., “Observation of two-photon "ghost" interference and diffraction”, Physical Review Letters 74, 3600-3603 (1995)

·        Tonomura, Akita, J Endo, T Matsuda and T Kawasaki, “Demonstration of single-electron buildup of an interference pattern”, American Journal of Physics 57, 117 (1989)

·        “Experimental evidence for a photon anticorrelation effect on a beam splitter: a new light on single-photon interferences”, Grangier, P, G Roger and A Aspect, Europhysics Letters 1, 173-179 (1986)

Introduction

 

Since about 1993 I have been trying to find out what really happened in experiments that claim the impossible – “quantum entanglement” of separated particles.  Often I have needed more information.  Often I’ve written to the experimenters concerned, occasionally receiving a reply.  Always I’ve been able to see that “local realist” explanations are possible, but without access to the full details or the possibility of doing a few subsidiary experiments they are usually incomplete.

 

It seems clear that it is not “the truth” that the experimenters are seeking!  When they talk of the “classical prediction”, it is invariably a prediction based on very limited understanding of the possibilities.  They are, after all, trained in quantum theory, not classical wave theory.  It is not for them to try and model things as they really are.  They do not, I suspect, feel much obligation to understand the test they apply: it is sufficient that somebody else has used it -- maybe under different conditions, but, not having themselves actually studied how the tests work, they are not in a position to judge whether or not the differences matter.  What they seem to aim at is finding out is if, by hook or crook, they can persuade their apparatus to simulate quantum mechanics! 

 

Quantum mechanics deals only with perfect systems (though certain experts are allowed to tweak the rules just a little when they think fit)!  The imperfections that allow the realist explanations work are known as “loopholes”.  Note that there are quite a few more than you might think (see the "loopholes" appendix to my Tangled Methods paper, or new [October 2002] Bell test paper), and which ones are relevant depends on both the experimental setup and on the particular test that is used.  Bell’s original test is never used.  It had to be modified, and additional assumptions made, to allow for the real conditions.  (Clauser and Horne’s very straightforward proof of their 1974 version (from Physical Review D, 10, 526-35 (1974)) is reproduced as an appendix to my paper on the subtraction of accidentals etc. )

 

I fear that there is no easy way out!  If you want to understand my explanations you will pretty certainly need to spend some time studying the papers I’m talking about!  They are presented in reverse chronological order.

·        Charles Santori et al, “Indistinguishable photons from a single-photon device”, Nature 419, 594-597, 10 October 2002

Santori et al produce very uniform pulses of light by using short (3 ps) pulses from a “pump” laser to illuminate “quantum dots”.  Pairs of induced pulses 2 ns apart emitted from an individual dot show signs of interfering with each other when passed through an optical system that splits them and introduces a delay so that part of each (or in quantum theory language, “some of them”) reach(es) a beamsplitter simultaneously.  The interference (inferred from the fact that there is a significant “Mandel dip” in the coincidences observed after this beamsplitter) is attributed in quantum theory to the “photons” being “indistinguishable” or (as Philippe Grangier said (p 577 of the same volume)) “knowing something about each other despite never having met”. 

 

But what is really happening?  Is it really a mystery?  It would be if the pulses were genuinely independent, but correpondence with Santori has revealed that there is rather more reason for them to be dependent than one might at first think.  It seems that the way in which the pairs of pulses from the pump laser (which is of long coherence length) are produced is by splitting individual ones and delaying one half.  The members of a pair will thus be very very similar, being of exactly the same frequency and, moreover with an exact phase relationship.  Such a phase relationship could conceivably cause a similar relationship in the induced pulses for, though 3 ps is short, it is not that short (not the 100 fs or so that can nowadays be achieved).  It may be long enough to cause coupling. 

 

There is, however, a possible snag with this hypothesis:  the observed coincidences are not sensitive to slight changes in the interferometer arm lengths.  Correspondence with Santori is continuing [19:01:03], investigating another idea (necessary in any case to explain the first, single photon, part of the experiment) -- that the illusion of whole photons going one way or the other at beamsplitters is due to interference effects within the beamsplitter.  At least for the single photon case, it may be necessary to take account of reflections from the far side of the splitting region, producing sometimes constructive, sometimes destructive interference at the near side, thus leading, via interaction with the material of the beamsplitter, to whole beams being either transmitted or reflected.  When the phase difference is nowhere near to either of these cases, perhaps the beam emerges from both ports but in a weakened state, a high proportion of the energy getting lost?  It’s just a thought.  To account for the lack of sensitivity to arm length in the two-photon experiment, one must remember that not all pulses are of exactly the same frequency so there will be some washing out of the underlying coincidence pattern.  [I assume, as in many of my other explanations, that any individual pulse will be effectively monochromatic, despite short coherence length.]

 

·        “‘Two-photon’ coincidence imaging with a classical source”, Ryan C Bennink, Sean J Bentley and Robert W Boyd, Phys. Rev. Lett. 89 (11), 113601 (2002)

It is shown how the supposedly quantum effect whereby an image can be built up by observing the exact position at which the correlated “photon” is detected [*] can be reproduced using ordinary correlation if we assume the light is concentrated in narrow rays.  There is no need for quantum entanglement, only parallel (or maybe conjugate) directions. 

 

The authors think this same kind of explanation apply in so-called  “ghost diffraction” (see e.g. Strekalov, D V et al., “Observation of two-photon "ghost" interference and diffraction”, Physical Review Letters 74, 3600-3603 (1995)) and “coincidence holography”.  In my view, however, ghost diffraction may be rather more complicated, depending on the wave nature of light.  It may even depend on a feature of the experiment that seems to be ignored – the fact that the beam passes through a small hole – and may not be as closely related to two-slit interference as has been assumed.

 

I asked the authors how the paper had been received – see correspondence (with permission).

 

[*] T B Pittman, Y H Shih, D V Strekalov and A V Sergienko, Phys. Rev. A 52, R3429 (1995)

 

·        "Plasmon-assisted transmission of entangled photons", Altewischer, E, M P van Exter and J P Woerdman, Nature 418, 304 (2002)

There are no more “entangled photons” in this experiment than in any other.  The Bell test infringement is all due to the kind of mechanism I discuss in "Rotational invariance, phase relationships and the quantum entanglement illusion", quant-ph/9912082 .  What we are in fact dealing with is phase differences between light pulses that are produced simultaneously with orthogonal polarization.  By passing them through a polariser at 45 deg interference becomes possible.  Basically, the source used (as per Kwiat et al, “New High-Intensity source of polarization-entangled photon pairs”, Phys Rev Lett 75, 4337-4341 (1995)) creates the pairs in two possible main groups, corresponding to right or left circular polarization when the orthogonal components are combined.  There may be variations superposed on this picture if the frequency spread is not very low, but the important thing is that any such additional phase difference is the same for each of the two points of intersection of Kwiat’s “cones”.  There is high ordinary correlation.  It is remarkable, of course, that this is preserved when the light goes through the array of holes, but the infringement of Bell tests means nothing more than that, as ever, the assumptions have not been met.  The logic is similar to that of Gregor Weihs’experiment (see below).

 

See some correspondence, including passage from a letter to Altewischer.

 

Popular accounts:

"News and views" by William Barnes, "Survival of the entangled", Nature 418, 281 (2002),

 

http://www.newscientist.com/news/print.jsp?id=ns99992564:

or

http://www.acm.org/technews/articles/2002-4/0719f.html#item13

# "Quantum Entanglement Stronger Than Suspected"
New Scientist Online (07/17/02); Sample, Ian

and Physics World, August 2002: Post-Deadline, p3: “Quantum Mechanics at large”,

·        Edamatsu, Keiichi, Ryosuke Shimizu and Tadashi Itoh, “Measurement  of the photonic de Broglie wavelength of biphotons generated by spontaneous parametric down-converion”, Phys. Rev. Lett. 89, 213601 (2002), http://arxiv.org/abs/quant-ph/0109005

This is a tough one that I have not yet fully comprehended, but one thing is certain: the behaviour of the light has very little to do with DeBroglie’s ideas on the relationship between frequency and momentum!

 

What we are seeing is pulses at one frequency induced by parametric down-conversion using a pump laser at double that frequency.  The pump has very long coherence length.  The induced pulses all have phases related to that of the pump, so that though half tend to be linked to the “even” wave peaks and half to the “odd” ones (so that there is a strong tendency for any “first-order” interference effects to be washed out), long trains of them share the link back to the same pump phase.  [The idea of some linking with even and some with odd is a matter of simple logic, together with the assumption that the laser is the cause of the outputs.  Since the outputs only have half as many peaks per second as the inputs, in each case Nature has to make a choice which subset to link to.  There is (so far as we know!) nothing to choose between them so, on average, the choice is bound to be 50-50.]

 

It is possible that the full explanation for the results depends on the fascinating phenomenon of interference between pulses arriving at a detector at slightly different times.  [I had until recently (May 2003) thought that Kim’s experiment of 1999 demonstrated this, but am now much less sure.]  It is not otherwise at all easy to explain the behaviour at the second beamsplitter, in which we apparently get interference despite the fact that the majority of the time there is nothing for the light to interfere with, the signal having travelled either along the top route or the bottom one!

 

However, don’t hold me to this!  I have written [November, 2002] to the authors asking for more information.  If large numbers of  “accidentals” were subtracted (as they may well have been in Hong, Ou and Mandel’s well-known experiment, PRL 59, 2044 (1987), which Edamatsu follows) this would change the picture.  It is admittedly at present confusing, seeming to require detectors that react very fast to individual pulses when used to study the “Mandel dip” but blur successive ones at a later stage.

·        “Recent Results in Trapped-Ion Quantum Computing”, David Kielpinski et al, http://arxiv.org/abs/quant-ph/0102086 , and M Rowe et al,  Nature 409, 791 (2001)  

See popular articles such as Physics World, “Quantum Loophole Shut”, March 2001, p3.

 

Acclaimed in the press as having blocked the detection loophole (the efficiencies are very high), there is in fact no justification for applying a Bell test in this experiment, let alone claiming to have demonstrated entanglement.  The ions concerned are not “separated”, being very close together in the same trap.  Discussion in the newsgroups all agreed on this (see also an article by Lev Vaidman).  I did not, however, receive any response to my letter to Kielpinski, and Physics World did not publish my letter to Jim Ryder, which made the same point.  Jim did reply, briefly, saying he was glad his article had “touched on [my] own concerns about making physics common sense”.

 

I now think that the actual thing that matters in the experiment could be the fact that they do not have full control over the settings of the two detectors.  In all discussions of Bell tests it is assumed that the experimenter can choose these independently, at will.  In Rowe’s experiment there is some uncertainty in the settings and the way they are controlled means that the errors could be correlated – as if the logic was not already complicated enough!

 

See also Philippe Grangier’s comment on the experiment, “Count them all”, Nature 409, 774, 15 February 2001.  His diagram of the ion trap is slightly less misleading than Rowe’s stylised version, which anyone might be forgiven as interpreting as showing separated particles with independent detector settings and measurements.  Grangier’s report is very inconsistent, though!  At least, on page 775, we find that he does recognise that the situation re local realism will remain open until both (or, it should be, all – See my list of loopholes ) loopholes are closed in the same experiment, but, as so often in the current literature, he feels that: “the results continue to agree with quantum-mechanical predictions.  This appears rather compelling evidence to me that quantum mechanics is right, and cannot be reconciled with classical physics.”

 

We shall see!

 

·        "Quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement" (Jian-Wel Pan et al, Nature, 403, 515-518 (2000))

This experiment does not demonstrate GHZ entanglement (whatever that may be)!  The detection efficiency was very low and the “detection loophole” invalidates the test they use.  It has occurred to me recently that, in addition to the points I raise in my letter to Pan et al, they could have got their wires crossed, as it is most unusual for the supposed realist prediction to be opposite to the quantum mechanical one!  Could they have confused the two outputs from a beamsplitter?  Polarisation directions get changed in transit along a fibre-optic cable if it is twisted, so that the only way to know which is vertical and which horizontal (with respect to the axes of the crystal used in the production of the light) is by trial and error.

 

More notes

 

 

·        The speed of quantum information?  Gisin N, V Scarani, W Tittel, H Zbinden, “Optical tests of quantum nonlocality: from EPR-Bell tests towards experiments with moving observers”, http://arxiv.org/abs/quant-ph/0009055 (2000)

 

Abstract:   “Past, present and future experimental tests of quantum nonlocality are discussed. Consequences of assuming that the state-vector collapse is a real physical phenomenon in space-time are developed. These lead to experiments feasible with today's technology.”

 

Yes, but are they worth doing?  Gisin thinks so, despite his statement that “It is not difficult at all to devise models explaining all existing results using only local variables”, or, in other words, his recognition of the lack of valid evidence for nonlocality.  Why does he consider it worth trying to find the speed of something that we do not even know to exist (and which, of course, realists are convinced cannot exist).

 

See my letter to Ian Percival, CC Gisin et al..

 

Also of some relevance:

 

Zbinden, H, J Brendel, N Gisin and W Tittel, “Experimental test of non-local quantum correlation in relativistic configurations”, quant-ph/0007009

 

Scarini, Valerio, Wolfgang Tittel, Hugo Zbinden and Nicolas Gisin, “The speed of quantum information and the preferred fame: analysis of experimental data”, quant-ph/0007008

 

And perhaps also: Gisin, Nicolas, “Sundays in a Quantum Engineer’s Life”, quant-ph/0104140 (2001)

·        Kim, Yoon-Ho et al, “First-order interference of nonclassical light emitted spontaneously at different times”, Physical Review A, Vol. 61, 051803 (1-4), April 2000, quant-ph/9911014

May, 2003:  I’ve changed my mind on this, after reviewing the details in the light of one of Kim’s more recent experiments (“Two-Photon Interference without Bunching Two Photons”, quant-ph/0304030).  Kim has almost certainly not, as I had at first thought re 9911014, demonstrated memory effects of the detector.  He has merely, I think, cleverly manipulated two components of the same signal so as to first separate them in time and then split them and arrange that the faster component of one part catches up with the slower component of the other!  It’s very neat, and I have not quite got to the bottom of it (there is a problem with the polarisation directions: the two parts that I assume to interfere are orthogonal) but I’m withdrawing my idea that the detector memory played a part.  It would have had to hold on to oscillations from one pulse for about 0.5 ps in order for the next pulse to suffer interference.

 

The clue to my new interpretation lies in the length of the nonlinear crystal used for down-conversion.  It is of the same order as that of the quartz rods used to apply the initial time separation.  The paper uses the notation for “very much greater than” where it means just “greater than”, and the diagram of the apparatus is distinctly misleading, showing a thin crystal.

 

Note that the interference pattern is not very strong.  Another possible explanation for it is that there could be a faint residual pulse travelling through the system from the original laser  -- the 800 nm one responsible for the “frequency doubling” and providing the 400 nm pulses that Kim wants.  The final signal involves 800 nm pulses, after “down-conversion”.  I just wonder.  Correspondence with the author has not succeeded in clarifying this.  We just don’t know.

 

A further possibility: the coherence lengths of the pulses he is dealing with may be longer than he thinks, so that what we are really seeing is simply the overlap of one with the tail of its predecessor.  Coherence lengths of pairs produced by splitting individual pulses tend to be considerably greater than the lengths as estimated from whole ensembles, due to the varying frequencies in the latter.  The convential relationship between frequency bandwidth and coherence length, based on a combination of the classical Fourier analysis approach and Heisenberg Uncertainty, is relied upon in quantum optics experiments far more often than it deserves.

 

Anyway, I shall have to withdraw one of my possible explanations for some other experiments, such as Edamatsu’s.  I am sure the detector does have some memory – it does require some finite integration time, so if phase changes during this time interference is inevitable – but I have not yet seen experimental proof.

 

 

·        "Wave-particle duality of C60 molecules" (Arndt, M. et al, Nature 401, 680-682 (1999),  http://www.quantum.univie.ac.at/research/matterwave/c60/index.html

 

Announced in New Scientist (16 October 1999, p27)  Physics World (November 1999, p5) and elsewhere, and discussed in groups such as sci.physics, this experiment is reported as showing that large molecules, in particular C60, commonly known as “buckyballs”, show diffraction.  Under quantum theory, this means that they exist in a superposition of states.  This is not the same as nonlocality, but is equally unacceptable as far as realism is concerned.  However, if you read the paper carefully you will find that, for one thing, the observed interference patterns were not as expected and some very strange theory concerning the distribution of hole sizes in the screen had to be called upon to “explain” them.  For another, the low parts of the pattern were not low enough to be able to say that they had definitely seen the destructive interference that might prove their case. 

 

Later experiments [*] are claimed to have been better, but closer inspection reveals that some of the most “conclusive” ones used a completely different experimental setup, with “Talbot Lau” interferometers.  Using the same grating period for each of three gratings, there is the possibility that what is being seen is basically just a shadowing effect.  If this is the case, low minima are of no significance.   The gratings used, incidentally, are not quite as suggested in the “artist’s impressions” published.  They have supporting bars across them at intervals (see http://www.quantum.univie.ac.at/research/matterwave/c60/index.html for the presumably similar design used in the 1999 experiment).  These may turn out to be critical, when combined with considerations of bending of beams due to gravity and of slowing due to interaction with the residual gas.  The curves followed by individual molecules will not be exactly parabolic.  I have not yet [April 2004] obtained sufficient information on the geometry or on the way the actual counts (as opposed to just the “visibility”) vary to fully evaluate the possibilities.

 

Yet other experiments [**] claim to have observed interference effects using a grating formed from a standing laser beam.  Here again we are likely to be seeing an illusion.  My current hypothesis (still [April 2004] under investigation) is that the grating beam heats individual molecules (we are talking mainly here about their internal degrees of freedom, and they have many) differentially, and this strongly affects the interaction with the “ionising” beam that is an essential part of the detection system.  The detector is described in J Mod Opt 47, 2811 (2000).

 

My earlier hypothesis concerning a “whistling” effect caused when the beam of hot fullerenes passes through narrow slits has turned out to be a non-starter.  The molecules are about 100 nm in diameter and the wavelengths supposed to be involved (De Broglie waves) very much smaller.  It does not make sense to talk of acoustic-type waves in what is effectively a rarefied gas in these circumstances.

 

[*]        Nairz, Olef, Markus Arndt and Anton Zeilinger, “Experimental challenges in fullerene interferometry”, Journal of Modern Optics 47, 2811 (2000)

 

Björn Brezger, Lucia Hackermüller, Stefan Uttenthaler, Julia Petschinka, Markus Arndt, and Anton Zeilinger, “Matter-wave interferometer for large molecules”, Physical Review Letters 88, 100404 (2002), quant-ph/0202158

 

Lucia Hackermüller, Klaus Hornberger, Björn Brezger, Anton Zeilinger and Markus Arndt, “Decoherence in a Talbot Lau interferometer: the influence of molecular scattering”, Applied Physics B, 77, 781 (2003), quant-ph/0307238

 

Nairz, Olef, Markus Arndt and Anton Zeilinger, “Quantum interference experiments with large molecules”, American Journal of Physics 74, 319 (2003)

 

[**]      Nairz, Olef, Björn Brezger, Markus Arndt and Anton Zeilinger, “Diffraction of complex molecules by structures made of light”, Physical Review Letters 87, 160401 (2001), quant-ph/0110012

 

·         “Violation of Bell’s inequality under strict Einstein locality conditions” (Weihs, Gregor et al., Physical Review Letters 81, 5039 (1998) and http://arxiv.org/abs/quant-ph/9810080 )

 

Gregor Weihs’ paper is claimed to be an improvement over Alain Aspect’s final experiment.  Both aimed at blocking the so-called “locality” or “light-cone” loophole, though how this loophole could conceivably account for the results even if not blocked nobody has ever explained!  The idea of both experiments is that the detector settings are switched during transit of the signals, so that the detectors cannot (using communication at the speed of light) “know” each other’s decisions in time to be influenced by them.

 

The test used in the 1998 paper is invalidated by the detection loophole (as the authors recognize).  It is likely (and I have discussed this with Weihs) that the published graphs are misleading as the experiment lacked “rotational invariance”.  See http://arxiv.org/abs/quant-ph/9912082 , which it inspired.

 

·        “Experimental demonstration of quantum-correlations over more than 10 kilometers” (Tittel, W, J Brendel, B Gisin, T Herzog and N Gisin,  http://arxiv.org/abs/quant-ph/9707042, revised and published as Physical Review A 57, 3229 (1998))

See:

Thompson. C H: “Subtraction of  `accidentals` and the validity of Bell tests”, various versions submitted to PRL and PRA and rejected, 1998-9, http://arxiv.org/abs/quant-ph/9903066

 

This Geneva experiment hit the headlines as the first long-distance EPR test.   It is easy to see, though, from a graph in the paper that  without the adjustment of the data by subtraction of accidentals, the Bell test would not be violated.  The experimenters later agreed that the test was not valid.  Subsequent experiments violate the experiment without subtraction but, unfortunately, these have other faults!  Their next experiment used a different Bell test, invalidated by the detection loophole.  See:

Tittel, W et al., “Violation of Bell inequalities by photons more than 10 km apart”, Physical Review Letters 81, 3563 (1998), http://arxiv.org/abs/quant-ph/9806043

 

Before we can untangle this kind of experiment, it would help if we could be sure if we were dealing with positive or negative correlations.  Quantum theory says that they are negative, but the simplest realist explanation I can come up with says otherwise, and they have not been able to persuade me that they can really tell from their data.

 

·        “Ladder Proof of Nonlocality without Inequalities: Theoretical and Experimental Results” (Boschi, D, S Branca, F de Martini and L Hardy, Physical Review Letters 79, 2755 (1997))

This is a very delicate and complicated experiment, which, despite the title, does use inequalities, subject to the same kind of weakness as the standard –2 <= S <= 2 Bell test.  The test used is undoubtedly (as Lucien Hardy admitted at a conference I attended) subject to the “detection loophole”.  I have not been able to persuade him that this totally invalidates his conclusion.  (See my Tangled Methods paper )

 

For details see one of my letters to Hardy and de Martini, and a few notes.  My letter tries to explain the logic, perhaps not as simply as it might!  It’s all due to using the wrong notation, so that “Not A” (which means getting either no detection at all or one in the “A_bar” channel) is confused with “A_bar” (i.e. actually getting a detection in the A_bar channel).   There was no direct response to my letter but, three years later Hardy wrote:

“ … I do share a concern that the experiments do not demonstrate conclusively this nonlocality.  I have always been keen to point out this.” 

He went on to say, though:

“I disagree with you that nonlocality is illogical or irrational.  For something to be illogical or irrational it has to be impossible to even imagine it happening.  But we can imagine nonlocality.  Anything we can imagine is possible in the widest sense of the word.”

He concluded:

“Even though I disagree with you I think it is good that somebody is putting the local realist cause.  This will encourage experimenters to perform the deciding experiment.”

 

Hardy’s attitude is typical.  Our disagreement is profound:  personally, I cannot imagine nonlocality.

 

·        “Observation of two-photon "ghost" interference and diffraction”, Strekalov, D V et al., Physical Review Letters 74, 3600-3603 (1995)

Is this really a matter of detector 2 somehow being aware of the geometry of slits in front of detector 1?  Though the explanation given has some elements of plausibility, and has led others (see Bennink et al, 2002) to think that it’s all a matter of photons travelling in exact directions, I think this is only part of the story.

 

The actual pattern seen at screen 2 may depend on a feature of the experiment that seems to be ignored – the fact that the beam passes through a small hole – and not as directly as the authors think on interference at the slit or slits in front of detector 1.  From the way in which the light beams are formed, using a prism after downconversion by a nonlinear crystal, direction will inevitably be strongly correlated with frequency, and this may need to be taken into account.  As the authors rightly say, the first order interference beyond the two slits is washed out, but this could be partly due to frequency differences (despite the use of a narrow bandpass filter).  Effectively, the slits mean that the detector beyond them selects one particular frequency, or maybe a limited set of frequencies – those that have peaks at that particular position.  The detector receiving the “ghost” pattern is simply receiving the diffraction pattern (or superposition of a limited set of diffraction patterns) corresponding to the selected frequencies but formed not by the slits but by a pinhole through which the light passes before encountering the beamsplitter.

 

Note [November 2002]: I have not yet got the bottom of this!  Perhaps there is no need to consider variations in frequency.  Possibly there is need to consider phase relationships and phenomena such as interference between successive pulses.  On one matter, though, I am pretty confident: the “ghost” pattern is formed by an interference effect that is purely classical.  A test for this (though unless efficiency’s were exceptionally high it would not be feasible) would be run the whole experiment at “single photon” intensities and put several detectors at different positions along screen 2.  Check whether or not different parts of the ghost pattern can be detected simultaneously.

 

·        Tonomura, Akita, J Endo, T Matsuda and T Kawasaki, “Demonstration of single-electron buildup of an interference pattern”, American Journal of Physics 57, 117 (1989)

Did this experiment really have any particle-like electrons in the beam at all?  This seems questionable.  A field-effect electron microscope was used, the “electron beam” intensity being estimated as so weak that there was only one electron at a time in the instrument.  For all we know, the beam could have been pure wave.  We have only their word for it that what was detected was electrons acting as particles.  What was actually observed was a fluorescence effect.  The “electron” interference pattern was converted to light then analysed in such a way that the result was almost a forgone conclusion: the apparatus would have been hard put to it to register anything but discrete clicks at discrete points on a grid.

 

The Hitachi Web site, I’m told, is even more definite in its claims than the original paper.  “As far as these micrographs show, you can be confident that electrons are particles”, they say.  Sorry, but I am unconvinced.

 

Incidentally, there is an interesting collection of letters in Physics World this month (May, 2003) on the subject of priority.  The first double slit electron experiment that produced the same kind of video picture as Tonomura’s, with points claimed to represent electron detections appearing one at a time, was apparently by Pier Giorgio Merli, GianFranco Missiroli and Giulio Pozzi in Bologna in 1974 (published as P G Merli et al., Am. J. Phys. 44, 306-7 (1976)).  Physics World publishes a letter by these authors and one by Tonomura.  Not to worry about the theory, though.  As Merli et al. point out in their letter, the experiment was a by-product of research into practical applications of electron interferometry.  Which reminds me: in Mark Silverman’s book, And Yet it Moves (Cambridge University Press 1993) he tells the story of the Hitachi (Tonomura) experiment, in which he was involved.  The initial motivation there was publicity.

·         “Experimental evidence for a photon anticorrelation effect on a beam splitter: a new light on single-photon interferences”, Grangier, P, G Roger and A Aspect, Europhysics Letters 1, 173-179 (1986)

It is argued that the low numbers of  “coincidences” observed between detected outputs from a beamsplitter when light intensities are very low (considered by quantum theorists to be at the “single photon” level) are evidence that we are dealing with “photons” that cannot be split.  They must go one way or the other.

 

From the start, the claim has been disputed (see Marshall, T W and Santos, E, Europhysics Letters, 3, 293-6 (1987)), but a computer simulation that has now been done models what I consider the most likely explanation.  See

 

Sulcs, Sue and C F Osborne,  “Computer simulation of photon anticorrelations experiment using additive pre-detection noise and finite instrument bandwidth”, Int. J. Mod. Phys.C 13 (6), 823-828 (2002)

 

Note that, as ever, you need to take into account the true circumstances of the experiment.  Though the talk is of coincidences between the beamsplitter outputs, what is actually counted is the 3-fold coincidences, requiring the “A” photon (from the same atomic cascade source as was used in Aspect’s famous 1981-2 Bell test experiments) and the two outputs produced by the split “B” photon all to fall within a rather small “coincidence window” (9 ns).  Since each actual pulse that they are considering to be a photon is in fact (see my deductions from the observed time-spectrum reported in the Bell test experiments, quant-ph/9711044) a short wave train of duration up to about 20 ns, this definition of “coincidence” has an effect on the logic.

 

Note also that they do not get right down to the “single-photon” level at which there should be no coincidences.  Since the intensity used in the Bell tests fell within the range investigated, one corollary of this is that Aspect’s Bell tests did not fulfil the QT requirment for single photons.

 

 

This is probably Aspect’s most famous experiment.  As explained in my paper on the subtraction of accidentals, the test he used, though logically acceptable (it was the CH74 test, not the CHSH one), was invalidated by the fact that he subtracted accidentals before analysing his data.  The raw data was not made available.  I was fortunate in having a copy of his PhD thesis, where data from a similar experiment (his 1981 one) was presented.  Even here it was not immediately obvious how serious the data adjustment had been, since the data was presented in random order.  The 1982 experiment had even more “accidentals” than the 1981 one, so the bias due to assuming accidentals around the zero point of the time spectrum to be the same as at other points would have been even more serious.

 

The fact that the analyser settings were changed during the flight of the “photons” is irrelevant.  The local realist explanation is simply the standard one for use in optical experiments.

 

 

·        “Experimental realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: A new violation of Bell's inequalities”, A. Aspect, P. Grangier, G. Roger, Phys. Rev. Lett. 49, 91-94 (1982)

This experiment is of historical importance as being the first, so far as I know, to use the so-called CHSH version of the Bell test – the one of form –2 <= S <= 2.  It is well known – and indeed has been known since 1970 or earlier – that this test is valid only so long as you can assume “fair sampling”.  This, unfortunately, is extremely unlikely to be the case (see my papers).  It is not the experimenter who chooses the sample of pairs that will be registered as “coincidences”, but Nature herself, and there are very good reasons to expect her to do this unfairly. 

 

The CHSH test is an adaptation of Bell’s original scheme, designed for experiments in which both ‘+’ and ‘-’ outcomes are counted, modified to allow for the fact that photon counters are not 100% efficient (Bell’s own version of the test was intended for use with spin-1/2 particles, all of which were assumed to be detected).  The test that was used prior to 1982 was the “CH74” test, or variants thereof, intended for experiments in which only the ‘+’ outcomes are measured.  In this test whether or not the ‘+’ and ‘-’ outcomes together represent a fair sample of the emitted particles is not relevant.  The ‘-’ ones are not even counted.

 

Aspect, unfortunately, was (and apparently still is, judging by a talk he gave in 2000) under the impression that the CH74 test is inferior to the CHSH one, being equally dependent on the fair sampling assumption and requiring measurements not needed in the CHSH test: you have to take counts with polarisers absent as well as with them present.  But the derivation given in the Clauser and Horne 1974 paper (reproduced as an appendix to my paper on subtraction of accidentals) shows that the test is, in its own right, a perfectly valid test of QM versus local realism, the only assumption required being the relatively innocuous one of  “no enhancement” (the presence of a polariser does not increase the probability of detection).

 

So Aspect used a biased test.  He also subtracted accidentals.  Although in this experiment the latter was not critical, it did increase the apparent significance of his result.  It is unfortunately not possible from the published facts to find out just how much bias there was.  Observation that the singles rates were constant tells us nothing.  He stated in the paper that his total coincidence counts were also constant, but in his PhD thesis mentions that there were slight variations.  He does not give us the critical information, which is how big the variations were (the fact that they were not “statistically significant” does not interest us, in view of their logical importance) and what angles gave the maximum and minimum.  Did he even look, in this context, at the angles not directly needed for the Bell test?  He does not say.

 

·         “Experimental Tests of Realistic Local Theories via Bell's Theorem”,  Alain Aspect, Phillippe Grangier and Gerard Roger, Physical Review 47,460 (1981)

This experiment was similar in structure to the time-varying one of 1982, with only the ‘+’ detections counted  The polarisers in these two experiments were “pile of plates” polarisers, for which there is only the one output, as against “polarising cubes” which have two.  It is the only experiment out of the three for which some of the raw data is available in Aspect’s PhD thesis, and was used as the source for my papers on subtraction of accidentals.

 

 

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