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

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the quantum story

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quantum events, like the absorption of photons, and turn them into perceptible signals,

such as the deﬂ ection of a pointer on a scale or the appearance of a visible spot on a piece

of photographic ﬁ lm.

In 1970 the physicist Dieter Zeh noted that the interaction of a wavefunction with a meas-

uring apparatus and its environment might lead to rapid, irreversible decoupling or ‘dephas-

ing’ of its components.

This ‘decoherence’, as it came to be known, would work in such a way

that any interference terms in the superposition are destroyed and we are consequently pre-

vented from observing interference ampliﬁ ed to the level of macroscopic objects. Schrödinger’s

cat is spared at least the discomfort of being both dead and alive because decoherence destroys

the superposition long before it can be ampliﬁ ed to macroscopic dimensions.

Decoherence is a kind of quantum ‘friction’. The wavefunction does not collapse (or

decohere) instantaneously but over a ﬁ nite—if very short—time. Clearly, for individual

photons, electrons, and atoms moving through the vacuum, the decoherence times are

long. But when large numbers of particles are involved, as in the interaction of photons,

electrons, and atoms with a macroscopic measuring apparatus, the decoherence time

becomes extremely short. For all practical purposes the collapse can be assumed to be

essentially instantaneous.

But, as the saying goes, there is no such thing as a free lunch. Whilst this is all intui-

tively appealing, decoherence cannot explain why the wavefunction decoheres only into

components that will be recognized as measurement outcomes, and not as awkward and

embarrassing superposition states. Nor can it be used to predict speciﬁ c measurement

outcomes. Decoherence changes the basis of the prediction from a superposition state

consisting of ‘this’ and ‘that’ to distinct components: ‘this’ or ‘that’, but leaves us dealing

with the same quantum probabilities. As Bell complained:

The idea that elimination of coherence, in one way or another, implies the replacement

of ‘and’ by ‘or’, is a very common one among solvers of the ‘measurement problem’. It

has always puzzled me.

Of course, in the 75 years since Schrödinger published details of his cat paradox, nobody

has ever reported seeing a cat in any kind of superposition state. Decoherence theory sug-

gests that such superpositions are suppressed in a kind of ‘quantum censorship’. But this

just begs another question.

We can think of the term ‘dephasing’ as implying a loss of the alignment between the peaks

and the troughs (the phase) of all the components of the wavefunction under measurement.

Note that the idea of decoherence predates Zeh’s important contributions.

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If cats are indeed too large to sustain quantum superpositions, is it nevertheless pos-

sible to ﬁ nd other kinds of macroscopic objects that can? Is it possible to create laboratory

analogues of Schrödinger’s infamous cat?

Such considerations lead directly to the notion of macroscopic quantum

states and the possibility of their superposition, entanglement, and inter-

ference. It helps to begin with some deﬁ nitions.

In the early 1980s British-born physicist Tony Leggett sought to deﬁ ne

what is meant by ‘macroscopic realism’. We can think of this simply in

terms of a macroscopic object (such as a cat) which can be found in at

least two distinct states (dead/alive). To be macroscopically real, it must

be possible to determine through a measurement that, at any particular

time, the object is in one or other of these states. By deﬁ nition, the meas-

urement must have no effect on the state itself.

Leggett deﬁ ned ‘distinctness’ based on the difference of one or more

‘extensive’ physical properties of the object in question, such as its total

charge, magnetic moment, position, momentum, etc. He called this the

extensive difference.

But extensive difference alone is not sufﬁ cient to deﬁ ne distinctness.

The experiments described in previous chapters involving measure-

ments on correlated particles can be considered ‘macroscopic’ if the

particles are separated by a large distance at the time of measurement.

Clearly, such experiments do not reﬂ ect a Schrödinger cat-type situation.

It is therefore necessary to introduce a further parameter, which Leggett

called ‘disconnectivity’.

The disconnectivity is not well deﬁ ned in a quantitative sense, but can

be thought of as a measure of the degree of quantum entanglement of the

systems. If the systems consist of just one particle each, as in the original

Einstein, Podolsky, and Rosen thought experiment, then their disconnec-

tivity is correspondingly small. If, however, the systems consist of many

particles (dust grains, water drops, golf balls, or cats) then the discon-

nectivity is correspondingly large. Complex systems with large extensive

difference can be expected to possess disconnectivity of the order of the

number of constituents in the systems.

Armed with these deﬁ nitions, it is possible to search for systems exhib-

iting both high extensive difference and disconnectivity, and discover

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what kind of reality prevails: a quantum reality of superpositions of mac-

roscopic states or macroscopic realism?

One major step in this direction was taken by Anton Zeilinger and his

team at the University of Vienna in 1999. These physicists reported the

diffraction and interference of a beam of buckminsterfullerene molecules,

each consisting of 60 carbon atoms in a soccer-ball structure, in an elabo-

rate version of the classic Young experiment.

These experiments were

subsequently repeated with fullerene molecules consisting of 70 carbon

atoms. By Leggett’s reckoning, the extensive difference in these experi-

ments was about a million, and the disconnectivity over a thousand.

These are fascinating experiments, begging all kinds of questions about

what happens to the mass of these molecules as they undergo wave-like

behaviour. But they still take us only a relatively small step towards the

macroscopic world of everyday objects. To go further down this path, we

need to return to the properties of superconductors.

Electrons are fermions and obey the Pauli exclusion principle. How-

ever, when considered as though they are a single entity, two electrons

of opposite spin and momentum have no net spin and, under the right

conditions, they can collectively form a boson. Like other bosons (such

as photons), these pairs of electrons can ‘condense’ into a single quantum

state. When a large number of pairs so condense in a superconductor,

the result is a macroscopic quantum state extending over large distances.

We can think of a macroscopic quantum state as a state with some prop-

erty of macroscopic dimensions, such as electrical conductivity, whose

behaviour is governed by quantum, rather than classical, mechanics.

As described in Chapter 23, this condensed state lies lower in energy than

the normal electrical conduction band of the superconducting material and

For more details on the discovery of buckminsterfullerene and its aftermath, see Jim Bag-

gott, Perfect Symmetry: The Accidental Discovery of Buckminsterfullerene, Oxford University Press,

1992.

Actually the disconnectivity for C

is 60 carbon atoms multiplied by 18 (six protons plus

six neutrons plus six electrons) = 1080.

Another example of a macroscopic quantum state is superﬂ uid helium. Because helium

consists of an even number of fermions it can act like a boson. It also undergoes ‘Bose con-

densation’ at very low temperatures. At temperatures below about −270 °C, liquid helium loses

virtually all of its viscosity and can ‘creep’ as a thin ﬁ lm up the sides of a beaker.

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the paired electrons experience no resistance. The distance between each

electron in a pair is quite large, and so many such pairs overlap within the

metal lattice. The wavefunctions of the pairs likewise overlap and their peaks

and troughs line up just like light waves in a laser beam. The result can be a

macroscopic number of electrons (about 100 billion billion) moving through

a metal lattice with their individual wavefunctions locked in step.

Imagine that an external magnetic ﬁ eld is applied to a superconducting

ring, which is then cooled to its superconducting temperature. The current

which ﬂ ows in the surface of the ring forces the magnetic ﬁ eld to ﬂ ow out-

side the body of the material.

The total ﬁ eld is just the sum of the applied

ﬁ eld and the ﬁ eld induced by the current ﬂ owing in the surface of the ring. If

the applied ﬁ eld is removed, the current continues to circulate ( because the

electrons feel no resistance) and an amount of magnetic ﬂ ux is ‘trapped’.

According to the quantum theory of superconductivity, this trapped

ﬂ ux is quantized: only integer multiples of the so-called superconducting

ﬂ ux quantum are allowed.

These different ﬂ ux states therefore represent

the quantum states of an object of macroscopic dimensions. Such super-

conducting rings are usually about a centimetre or so in diameter. The

existence of these states has been conﬁ rmed by experiment.

In a superconducting ring of uniform thickness, the quantized mag-

netic ﬂ ux states do not interact. The quantum state of the ring can only be

changed by warming it up, changing the applied external ﬁ eld, and then

cooling it down to its superconducting temperature once more. How-

ever, the mixing of the ﬂ ux states becomes possible if the ring contains a

Josephson junction. This is essentially a small region of the ring in which an

insulator has been inserted but which is narrow enough to allow quantum

tunnelling of pairs of electrons from one side to the other.

This is the Meissner effect. See Chapter 23, p. 230.

The ﬂ ux quantum is given by h/2e, where h is Planck’s constant and e is the charge of the

electron.

In quantum tunnelling the wavefunction of a quantum particle can pass through a nar-

row energy barrier, allowing a small proportion of its amplitude to appear on the other side.

Although this is often referred to as ‘quantum’ tunnelling, it is actually a wave phenomenon

which can be exhibited by classical waves (such as sound waves). Quantum tunnelling bog-

gles the mind when we use the wave amplitude as a measure of the probability of ﬁ nding the

associated particle, as it means that an electron (for example) has a ﬁ nite probability of passing

through a barrier in a way that would be classically impossible.

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A variety of quantum interference effects then becomes possible and

the rings are generally called superconducting quantum interference

devices (SQUIDs, for short), ﬁ rst invented in 1964. These devices are

incredibly sensitive, and are used to measure magnetic ﬁ eld strengths in

a variety of medical applications. The smallest change in magnetic ﬂ ux

that can be detected in one second using a typical SQUID ring corre-

sponds roughly to the energy required to raise a single electron one mil-

limetre in the earth’s gravitational ﬁ eld. More sensitive devices approach

the limits imposed by the uncertainty principle.

Interestingly, this sensitivity is a feature of the Josephson junction,

not the ring. This means that a macroscopic variable (such as a measur-

able ﬂ ux of electrons travelling around the ring) can be controlled by a

microscopic amount of energy in a manner that has little to do with the

physical size of the ring itself. The question then becomes: is it possible

to create superpositions of distinct macroscopic states of such devices—

for example, states in which large numbers of electrons are ﬂ owing in

opposite directions around the ring?

How would interference between such macroscopic states be manifested?

Clearly this is not going to be as simple as observing visible interference

fringes. This is a bit like trying to imagine how interference would be

manifested between the macroscopic states of alive and dead cats.

Let’s think instead about the macroscopic quantum states created

in a superconducting ring in which electrons ﬂ ow anticlockwise and

clockwise around the ring. These states sit in separate, distinct, potential

energy ‘wells’. The bottom of each well represents the lowest energy con-

ﬁ guration of each state. To cross from one well to another (i.e. to reverse

the direction of ﬂ ow of the electrons around the ring) we would have to

raise the energy of the ring by warming it up, change the applied ﬁ eld,

and then cool it back down to its superconducting temperature.

Now suppose that we insert a Josephson junction. The effect of the

junction is to allow the anticlockwise and the clockwise states to com-

bine in a superposition. In fact, where the energies of the two states

are equal or near-equal, the states mix together to form a slightly lower

energy anticlockwise + clockwise combination, and a slightly higher

energy anticlockwise − clockwise combination. Spectroscopists refer to

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this kind of effect as an ‘avoided crossing’. Instead of crossing, two new

states are formed in this energy region with characteristics of mixtures

of the original states.

The amount of splitting between these mixed states is given by the

so-called tunnel splitting which is a characteristic of the Josephson junc-

tion. This kind of splitting between quantum states is fairly common in

atomic and molecular spectroscopy, but it is perhaps novel to consider its

effects in quantum states involving large numbers of electrons moving in

a metal ring of macroscopic dimensions.

The experimental demonstration of the possibility of superpositions of

distinct macroscopic states—laboratory versions of Schrödinger cat states—

then comes down to this: what happens in the energy region where the

anticlockwise and the clockwise states are of equal or near-equal energy?

In practice, the experiments require the application of a bias to the junc-

tion in the form of an externally applied magnetic ﬂ ux through the ring. As

the bias is varied, microwave radiation is used to probe the size of the split-

ting between the states, and hence the extent of the interference between

them. A splitting of the order of magnitude of the bias itself implies that

the anticlockwise and clockwise states remain distinct macroscopic states

and there is no interference. A splitting of the order of the square-root of

the sum of the squares of the bias and the tunnel splitting implies that a

superposition of macroscopic quantum states has been created.

The results of two kinds of experiments were reported in 2000 by

two groups of researchers. Jonathan Friedman, Vijay Patel, W. Chen,

S.K. Tolpygo, and J.E. Lukens at the State University of New York, Stony

Brook, used a SQUID ring measuring 140 microns in diameter.

In a

paper submitted to the journal Nature in April 2000 they reported results

conﬁ rming the formation of macroscopic superpositions:

The quantum dynamics of the SQUID is determined by the ﬂ ux through

the loop, a collective coordinate representing the motion of approximately

[a billion] Cooper pairs acting in tandem.

This is the same kind of mixing that produces the kaon states K

and K

from K

and K

see p. 248.

A micron is a millionth of a metre.

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The paper was published in July. That same month, a second group based

at the Delft Institute for Micro Electronics and Submicron Technology

and at MIT submitted a similar paper to the American journal Science.

The approaches of the two groups were somewhat different. The Stony

Brook group used a SQUID ring with a single Josephson junction and

performed measurements on excited levels of the anticlockwise and

clockwise states. The Delft/MIT group used a 5-micron diameter SQUID

ring with three Josephson junctions and measured the splitting between

superpositions of the ground levels of the macroscopic quantum states.

But the results were very similar. The Delft/MIT group claimed their

results indicated:

. . . symmetric [anticlockwise + clockwise] and anti-symmetric [anticlock-

wise − clockwise] quantum superpositions of macroscopic states. The

two classical states have persistent currents of 0.5 microampere and cor-

respond to the center-of-mass motion of millions of Cooper pairs.

Just stop and think for a moment. In a quantum superposition consisting

of a symmetric combination of a macroscopic state in which a billion

electron pairs are moving anticlockwise around the ring and another

macroscopic state in which a billion electron pairs are moving clockwise

around the ring, in just what direction are the electrons actually moving?

Leggett estimated that in these experiments both the extensive difference

and disconnectivity are of the order of 10 billion.

Of course, millions or even billions of pairs of electrons do not repre-

sent a cat-sized object. But this was never quite the point. The Copenhagen

interpretation of quantum theory had always been stubbornly silent on

the question of where the distinction between the microscopic and mac-

roscopic worlds should be drawn. Whilst experiments showing non-local

behaviour between pairs of correlated photons, electrons, atoms, or ions

might be disconcerting, they leave the quantum weirdness ﬁ rmly in the

Leggett now feels this ﬁ gure is somewhat overstated, and suggests instead a ﬁ gure of 1 to 10

million. Tony Leggett, personal communication to the author, 4 August 2009.

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quantum realm. Quantum superpositions involving billions of particles

start to bring the weirdness into a realm we can see with the naked eye.

Writing about these experiments some years later, Leggett saw no rea-

son to suppose that they represented fundamental limits to the size of

macroscopic quantum superpositions that could in principle be created

in the laboratory:

. . . we can say that on a logarithmic scale we have come about 40% of the

way from the atomic level to that of the everyday world . . . there seems no

obvious a priori objection to extending the SQUID experiments from rings

of the size of these used in the existing experiments (a few microns) to

much larger sizes, perhaps of the order of 1 [centimetre].

In a recent review article published in the journal Nature, Vlatko Vedral at

the Univeristy of Leeds notes:

There are many open questions regarding entanglement. Here I have

stated that, in theory, entanglement can exist in arbitrarily large and hot

systems. But how true is this in practice? Another question is whether the

entanglement of massless bodies fundamentally differs from that of mas-

sive ones. Furthermore, does macroscopic entanglement also occur in liv-

ing systems and, if so, is it used by these systems?

This remains a very active area of research. In May 2008 Markus

Aspelmeyer and Zeilinger commented brieﬂ y on research that was

on going in Vienna with the aim to demonstrate quantum interference

effects in heavier and larger systems. The main goal of this work is to

demonstrate interference for small viruses or bacteria with nanometre

( billionth of a metre) dimensions.

There is more to this search for macroscopic quantum phenomena than

questions concerning the nature of reality and the transition from the

quantum to classical realms. Quantum states that represent opposites,

such as spin-up and spin-down, vertical and horizontal, clockwise and

anticlockwise, can in principle represent information in the form of

See Markus Aspelmeyer and Anton Zeilinger, Physics World, July 2008.

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quantum binary digits, or qubits. A computer constructed from macro-

scopic qubits which makes use of quantum entanglement between these

qubits can in theory perform operations much faster than a classical

computer.

Aside from quantum computers based on SQUIDs, other possibili-

ties include computers based on entangled trapped ions, so-called qubit

‘clusters’ involving four-photon GHZ states, quantum ‘dots’, and many

others.

When Einstein and Schrödinger developed their now infamous

thought experiments, they had sought to use entanglement and ‘spooky’

action at a distance to undermine the foundations of the interpretation

of quantum theory laid down by the Copenhagen school. It would have

been quite impossible to imagine that their arguments would become the

basis of an entire new quantum technology.

Those realists intent on standing ﬁ rm in the face of the onslaught from

experiments proving quantum non-locality and macroscopic quantum

superpositions could still ﬁ nd some solace. Reality might indeed be

non-local, they now had to admit, but that doesn’t necessarily mean

that quantum particles do not possess deﬁ ned properties until they are

measured.

Does it?

This means that a quantum computer could in principle be used to crack the encryption

systems used for most Internet transactions, which are based on factoring large prime numbers.

Not to worry, though, as Internet security could perhaps be restored using cryptographic sys-

tems based on quantum entanglement!

349

In their 1935 paper, Einstein, Podolsky, and Rosen had set forth what they judged to be

a ‘reasonable’ deﬁ nition of reality. At its heart was the entirely commonsense assump-

tion that quantum particles have the properties we ascribe to them independent of their

measurement. An electron has a spin-up orientation: the nature of its interaction with a

Stern–Gerlach magnet is determined by this property and its subsequent path through

the apparatus reveals what this property is. Likewise, a photon has a vertical polarization:

its passage through a polarization analyser simply tells us what it is.

We have to accept that this simplistic local realism must give way in quantum mechan-

ics to something rather ‘spookier’. The experimental tests of Bell’s theorem demonstrate

quite unequivocally that the spin orientation of an electron or the polarization state of a

photon can be affected by what happens to another particle an arbitrarily long distance

away. We have no idea how this kind of non-local inﬂ uence might be propagated, or even

if ‘propagated’ is the right word to use. But there is now plenty of evidence to suggest that,

however it works, such non-local inﬂ uences cannot be used to transmit meaningful infor-

mation (messages) faster than the speed of light. In this sense, at least, quantum theory

and special relativity coexist, if not peacefully then with only the grumbling characteristic

of two old but venerable theories that don’t quite get along.

In the face of the repeated and consistent experimental violation of Bell’s inequality, we

trade off the assumption of locality so that we may preserve some semblance of realism.

But realism—the assumption that particles have the properties we assign to them even

when we don’t look—is also an assumption. It is an assumption that has been challenged

The Persistent Illusion

Vienna, December 2006