Baggott J. The Quantum Story: A History in 40 Moments

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the quantum story

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scale and energy between the initial interaction required for measure-

ment and the measured object itself. To make the kinds of measurements

that Feynman believed were impossible, we would need to probe a quan-

tum system in a way that does not impart to it what we might refer to

simply as a classical ‘kick’, an uncontrollable transfer of momentum in

the classical sense.

In 1982 theorists Marlan Scully and Kai Drühl, at the Max Planck

Institute for Quantum Optics near Munich and the Institute for Mod-

ern Optics at the University of New Mexico, believed they had found a

way.

They conceived a thought experiment involving the interference of

photons emitted from two different atoms. The atoms act as distinct

sources of light in much the same way as the two slits in the classic

Young experiment act as sources of waves that expand beyond the

slits, going on to overlap and interfere. We will call these atoms A

and B.

In this thought experiment, each atom is irradiated with a pulse of

laser light and an electron is excited to a higher-energy orbit. In the

situation where both atoms subsequently emit a photon and return

directly to the ground state, the photons cannot be distinguished and

we have no way of knowing which photon has come from which

atom. In other words, we cannot gain which-way information and we

would therefore anticipate that the photons should exhibit an inter-

ference pattern. Scully and Drühl showed that this is, indeed, what

quantum theory predicts: terms appear in the equations characteris-

tic of interference effects.

Now suppose that there is an alternative way in which the excited

atoms can decay, perhaps via an intermediate electron orbit lower

in energy than the initial excited orbit created by the laser pulse, but

higher in energy than the ground state. We arrange the experiment so

that we detect only photons derived from the transition from the ini-

tial excited state to the intermediate state. At ﬁ rst sight, this looks no

different to the situation we considered above, and we might therefore

be tempted to conclude that the interference pattern should remain.

Observation of interference would be behaviour characteristic of the

wave description.

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331

But it seems that we can now also gather which-way information char-

acteristic of the particle description. By discovering whether the atoms

are in the ground or intermediate states after emission of the photons,

we can in principle tell which atom the detected photon came from. For

example, if we ﬁ nd that atom A is in the intermediate state and atom B

is in the ground state, we know immediately that the photon came from

atom A and we therefore know its trajectory from atom A to the detector

(let’s call this path A).

This gives us which-way information, equivalent in Feynman’s version of

the two-slit experiment to discovering which slit the electron went through.

And as we can do this without in any way disturbing the photons after they

have been emitted, it really does seem as though we can measure both the

wave-like and particle-like behaviours of the photons simultaneously.

The Copenhagen interpretation categorically denies that we can do

this. So, if we cannot invoke the ‘clumsiness’ defence, what is it in this

experiment that prevents us from observing both particle-like and wave-

like behaviour simultaneously? How, we might wonder, would Bohr

have responded to such a challenge? Commenting on a different (though

entirely equivalent) thought experiment almost ten years later, Scully

laser pulse

path A

path B

fig 24 Scully and Drühl replaced the two slits of the classic Young’s experiment

with two atoms, A and B. The atoms are irradiated with a pulse of laser light and an

electron in one or other is, with equal probability, excited to a higher-energy orbit.

The excited atom subsequently emits light and the emitted photon goes on to be

detected. As both atoms may absorb and emit light with equal probability, the emit-

ted photons from both atoms should produce an interference pattern, characteristic

of wave behaviour. However, if the emission of a photon leaves the atom in an inter-

mediate state, it may be possible to discover which of the two atoms is left in this state

and therefore which atom emitted the photon. This gives ‘which way’ information

characteristic of particles.

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332

and his colleagues Berthold-Georg Englert and Herbert Walther at the

Max Planck Institute for Quantum Optics and the University of Munich

observed that:

. . . Bohr would not have been distressed by the outcome of these con-

siderations, as the wave-like (interference) phenomenon is lost as soon

as one is able to tell which path the [photon] traversed. Quantum

mechanics contains a built-in safeguard such that the loss of coher-

ence in measurements on quantum systems can always be traced to

correlations between the measuring apparatus and the system being

observed.

The safeguard these physicists refer to arises when the entire system

is considered from the perspective of quantum theory. Even though

the photons are left to propagate towards the detector unaffected by a

‘clumsy’ measurement, they have become inexorably entangled with

the tell-tale quantum states of the atoms they have left behind. It is this

entanglement that destroys the interference.

By introducing the ﬁ nal quantum states of the atoms into the equation,

the terms responsible for wave interference disappear.

Simple mathe-

matics demonstrates that we can’t have it both ways. If we can discover

which-way information—even in principle—the interference terms dis-

appear and we are denied the possibility of observing interference effects.

If we are prevented from discovering which atom the photon came from,

then the interference terms are preserved but we can obviously no longer

gain which-way information.

If we force the photon to reveal which path it followed or which slit

it went through, quantum theory denies us the possibility of observing

interference effects through a mechanism that has nothing whatsoever to

do with the clumsiness of the measurement. If wave–particle duality is the

central mystery at the heart of quantum theory, then complementarity—

not the uncertainty principle—is the mechanism by which it operates.

The interference terms are multiplied by the ‘overlap integrals’ of the ﬁ nal quantum states

of the two atoms, and as these integrals are zero the terms disappear. See Scully and Drühl,

Physical Review A, 25, 1982, p. 2209.

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And, perhaps for the ﬁ rst time, we have here a basis from which we

can begin to understand how complementarity actually works.

But now here’s another thought. What if we set up the experiment in a

way which gives us the opportunity to gain which-way information, but

we choose not to look? By choosing not to look, can we expect the inter-

ference pattern to be restored? What if we wait until the photons have

passed through the apparatus and have been detected and then choose

whether or not we want to look to see which way they had gone? Is it

really possible that we can switch the interference pattern on and off by

choosing whether to look or not after the photons have been detected?

The answers to these questions are quite sophisticated. According to

Scully and Drühl’s original analysis of this hypothetical quantum ‘eraser’

experiment, the interference pattern does indeed come back if we choose

not to look, but the mechanism by which it returns is very subtle.

In the situation where the atoms possess an intermediate electron orbit,

we saw that this gives us the possibility of discovering which-way infor-

mation just by looking to see which state the atom was in after emission

of a photon. But now instead of looking to see what ﬁ nal state each atom

is in, we hit the atoms with another pulse of laser light which excites any

atom present in the intermediate state to another, higher-energy state.

This decays rapidly back to the ground state with the emission of another

photon, which we will call a f-photon to distinguish it from the photons

that go on to interfere (or not). By doing this we lose any opportunity

to measure the ﬁ nal states of the atoms and so we erase the which-way

information from the quantum system.

The interference pattern does not (yet) come back.

To see the interference pattern we must look closely at the f-photons.

Suppose we trap these in elliptically shaped optical cavities, one with

atom A at one of its focal points and the second with atom B at one of its

focal points. The cavity material allows the laser light and the interference

photons to pass through unhindered. The cavities are joined together at

their second focal points by material designed to detect a f-photon and

this detector is isolated by means of a mechanical shutter.

So, what happens now? Let’s assume that the ﬁ rst laser pulse excites

both atoms A and B. One of the atoms decays to the intermediate state,

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334

emitting a photon which goes on to be detected. The second atom decays

directly to the ground state. We now excite both atoms using a second

laser pulse, erasing the information about their ﬁ nal states and leaving

a f-photon in one of the optical cavities. We have no way of knowing

which atom has emitted the f-photon and so we have no way of knowing

which cavity the f-photon is in.

The correct quantum-theoretical description of this situation is in

terms of two ‘partial waves’, one in each cavity, representing a 50:50

chance of ﬁ nding the f-photon in one or the other.

We wait until the interference photon has been detected and open the

mechanical shutter. The f-photon partial waves are reﬂ ected by the cav-

ity walls towards the detector. The partial waves now combine. If they

combine constructively at the point where we have placed the detector,

we expect to record detection of a single f-photon. Alternatively, if the

partial waves combine destructively, the f-photon goes undetected. The

probability of detecting the f-photon and not detecting it is again 50:50.

Of course, by opening the shutters we have denied ourselves the pos-

sibility of ﬁ nding out which cavity the f-photon was in and so gaining

which-way information. The interference pattern does indeed return,

but to see it we must correlate detection of the interference photon with

detection (or non-detection) of the f-photon.

Assume we could in some way code each spot recorded by detection

of an interference photon. If the spot is produced by a photon which is

correlated with detection of a f-photon we code it red. If the spot is pro-

duced by a photon which is correlated by non-detection of a f-photon,

we code it blue. If we then look at the resulting pattern of spots through

different coloured ﬁ lters, we would see an interference pattern formed by

the red spots and a second interference pattern formed by the blue spots

with one displaced from the other.

If we describe the pattern formed by the red spots as interference fringes,

then the pattern formed by the blue spots are ‘anti-fringes’, where the peak

of a fringe coincides with the trough of an anti-fringe. If we do not look at the

pattern through coloured ﬁ lters and therefore do not differentiate between

red and blue, we cannot see any interference pattern at all (in fact, we get a

scatter pattern comparable to that associated with which-way detection).

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These ideas are fascinating, and quantum theory again seems to have

all the answers. But can these ideas be transformed into real experi-

ments? Recognizing the enormity of the challenge to experimentalists,

Scully raised the stakes: ‘Realizing quantum erasure in an experiment,

however, has been difﬁ cult for many reasons (even though Scully offered

a pizza for a convincing demonstration).’

The experiments were tricky, but they were done some years later. The

thought experiment outlined by Scully and Drühl was judged to be too

difﬁ cult. But Thomas Herzog, Paul Kwiat, Harald Wienfurter, and Anton

Zeilinger at the University of Innsbruck in Austria used more familiar

sources of pairs of entangled photons in an entirely analogous quantum

(a)

(b)

(c)

fig 25 By coding photons that

are detected coincidently with

f-photons as red, we recover an

interference pattern that looks

something like (a). Coding

photons detected coincidentally

with non-detection of

f-photons as blue yields an

interference pattern given by

( b). If we do not discriminate

between red and blue photons

we get the sum of interference

fringes and anti-fringes, which

yields what looks like a scatter

pattern, (c).

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336

eraser experiment. They reported their results in a paper submitted to

Physical Review Letters in July 1995.

In fact, the physicists produced two pairs of vertically polarized

photons using type-I parametric down-conversion. One pair, consist-

ing of photons with wavelengths in the red and near-infrared regions

of the spectrum, was produced in a ﬁ rst pass of laser light through the

crystalline material. We will call this path A. The second photon pair,

with identical wavelengths, was produced by reﬂ ecting the laser light

back through the crystal for a second pass. We call this path B. The

pair generated by the ﬁ rst pass was also reﬂ ected back into the crystal,

with the end result that the photon pairs created by direct (ﬁ rst pass) or

reﬂ ected (second pass) laser beams could no longer be distinguished.

The result was interference, detectable as ‘fringes’ in the rates of

detection both the red and near-infrared photons as a function of the

differences in the paths they had taken through the apparatus. In effect,

the two sources of photon pairs (ﬁ rst pass and second pass) acted like

two slits in the classical interference experiment.

With this arrangement, interference could be observed so long as no

attempt was made to identify which path the photons were following,

and hence identifying their source—ﬁ rst pass or second pass (and, by

analogy, identifying which ‘slit’ they had passed through).

However, which-way information could be simply obtained by, for

example, changing the polarization of the ﬁ rst-pass near-infrared

photons from vertical to horizontal and placing a polarizing analyser

in front of the detector. The nature of the photon polarization then

revealed what kind of photon it was—ﬁ rst pass or second pass—and

therefore what path it had taken—path A or path B. Obtaining such

which-way information for the near-infrared photons implied equiva-

lent which-way information for the red photons, too. The end result was

that interference in both red and near-infrared photon detection rates

disappeared.

This which-way information could then be erased simply by rotat-

ing the analyser to an angle of 45°, preventing the possibility of learn-

ing the polarization orientation of the near-infrared photons and hence

identifying which path they had taken. This arrangement was sufﬁ cient

to restore interference in the near-infrared photon detection rate and in

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337

the rate of red and near-infrared photon coincidences, but not the red

photon detection rate.

The physicists now rotated the polarization of the ﬁ rst-pass red

photons from vertical to horizontal and introduced an analyser which

could be used to tell whether the red photons were ﬁ rst or second pass.

This allowed the possibility of regaining which-way information for the

near infrared photons, too. The interference duly disappeared.

But now, the physicists could play the same game once more. Rotating

the analyser through 45° again erased the which-way information. But

this time interference was not restored in the detection rates of either

the red or near-infrared photons. Interference did return if detection of a

near-infrared photon was correlated with detection of a red photon with

the polarizer orientated at either +45° or −45°, analogous to correlation

with red or blue spots in the original thought experiment. This inter-

ference was revealed in the coincidence detection rates, which formed

fringes (+45°) and anti-fringes (−45°).

The physicists concluded:

The use of mutually exclusive settings of the experimental apparatus

implies the complementarity between complete path information and the

occurrence of interference. In conclusion, our results corroborate Bohr’s

view that the whole experimental setup determines the possible experi-

mental predictions.

History does not record if Herzog, Kwiat, Weinfurter, and Zeilinger

claimed their free pizza.

In truth, the Innsbruck physicists had not quite replicated all the fac-

ets of the original thought experiment. Most importantly, they had not

demonstrated the possibility of delaying the choice between observing

which-way and interference phenomena until after the measurements

had been made. Such a delayed-choice quantum eraser experiment was

demonstrated by Scully and Yoon-Ho Kim, Rong Yu, Sergei Kulik, and

Yanhua Shih at the University of Maryland in Baltimore. They submitted

a paper describing their results to Physical Review Letters in January 1999. It

was published in 2000. Their results conﬁ rmed the bizarre nature of the

quantum world. The interference pattern can indeed be switched on and

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338

off by choosing whether or not to look at the which-way information

after the experiment is over.

Further experiments reported in 2002 used a real-life two-slit arrange-

ment to perform both quantum eraser and delayed-choice quantum

eraser experiments. Quantum eraser experiments with kaons were

reported in 2004.

There is of course a direct relationship between complementarity and

quantum non-locality. Interference effects characteristic of waves are the

direct manifestation of non-local behaviour. These effects appear in the

mathematical structure of quantum entanglement—in this case entan-

glement of the states responsible for interference with the states used

to register which-way information. It is simply not possible to design

an apparatus to reveal which-way information which does not result

in entanglement of this kind. And these states cannot be disentangled

without forcing the system to reveal one type of behaviour or the other.

They cannot be disentangled to reveal both types of behaviour simulta-

neously.

This has nothing to do with our ability to conceive an apparatus which

avoids ‘clumsy’ measurements. An apparatus which simultaneously

reveals both wave-like and particle-like behaviour is simply inconceiv-

able. This is the essence of complementarity.

339

The experiments designed to test Bell’s inequality and to explore the nature of comple-

mentarity served only to demonstrate the extraordinarily counter-intuitive behaviour of

the quantum world. There was now much experimental evidence to make the realist feel

distinctly uncomfortable. And there was more discomfort yet to come.

Bohr had insisted on a clear distinction between the microscopic world of quantum par-

ticles and the macroscopic world of classical measuring devices. In the context of von Neu-

mann’s collapse postulate, it is at this boundary between the microscopic and macroscopic

that we might expect to ﬁ nd the elusive collapse of the wavefunction. But Bohr was never

clear about where this distinction should be drawn. Under Einstein’s inﬂ uence, Schrödinger

had used his cat paradox to turn this lack of distinction into a reductio ad absurdum.

Many years later, John Bell wrote about the ‘shifty split’ between the measured quan-

tum object and classical perceiving subject:

What exactly qualiﬁ es some physical systems to play the role of ‘measurer’? Was the

wavefunction of the world waiting to jump for thousands of years until a single-celled

living creature appeared? Or did it have to wait a little longer, for some better qualiﬁ ed

system . . . with a PhD?

Bohr believed that the answer lay in the irreversibility of the act of measurement and John

Wheeler subsequently wrote more speciﬁ cally about an ‘irreversible act of ampliﬁ cation’.

We gain information about the quantum world only when we can amplify elementary

Lab Cats

Stony Brook/Delft, July 2000