FRAMEWORK
OF PHYSICS must somehow connect the exotica of quantum mechanics--its
dead-and-alive cats, orbitals, oscillating ions and matter waves--with the more
intuitive counterparts from classical physics: probabilities, planetary
motions, pendulum swinging and double-slit, light-wave interference.
Editor’s
note (10/9/2012): We are making the text of this article freely available for
30 days because the article was cited by the Nobel Committee as a further
reading in the announcement of the 2012 Nobel Prize in Physics. The full
article with images, which originally appeared in the June 1997 issue, is
available for purchase here.
Pritchard
and other experimentalists have begun to peek at the boundary between quantum
and classical realms. By cooling particles with laser beams or by moving them
through special cavities, physicists have in the past year created small-scale
Schrödinger’s cats. These “cats” were individual electrons and atoms made to
reside in two places simultaneously, and electromagnetic fields excited to
vibrate in two different ways at once. Not only do they show how readily the
weird gives way to the familiar, but in dramatic fashion they illustrate a
barrier to quantum computing—a technology, still largely speculative, that some
researchers hope could solve problems that are now impossibly difficult.
The mystery
about the quantum-classical transition stems from a crucial quality of quantum
particles—they can undulate and travel like waves (and vice versa: light can
bounce around as a particle called a photon). As such, they can be described by
a wave function, which Schrödinger devised in 1926. A sort of quantum Social
Security number, the wave function incorporates everything there is to know
about a particle, summing up its range of all possible positions and movements.
Taken at
face value, a wave function indicates that a particle resides in all those
possibilities at once. Invariably, however, an observation reveals only one of
those states. How or even why a particular result emerges after a measurement
is the point of Schrödinger’s thought experiment: in addition to the cat and
the poison, a radioactive atom goes into the box. Within an hour, the atom has
an even chance of decaying; the decay would trigger a hammer that smashes open
the vial of antifeline serum.
The Measurement Problem
According
to quantum mechanics, the unobserved radioactive atom remains in a funny state
of being decayed and not decayed. This state, called a superposition, is
something quantum objects enter quite readily. Electrons can occupy several
energy levels, or orbitals, simultaneously; a single photon, after passing
through a beam splitter, appears to traverse two paths at the same time.
Particles in a well-defined superposition are said to be coherent.
But what
happens when quantum objects are coupled to a macroscopic one, like a cat?
Extending quantum logic, the cat should also remain in a coherent superposition
of states and be dead and alive simultaneously. Obviously, this is patently
absurd: our senses tell us that cats are either dead or alive, not both or
neither. In prosaic terms, the cat is really a measuring device, like a Geiger
counter or a voltmeter. The question is, then, Shouldn’t measuring devices
enter the same indefinite state that the quantum particles they are designed to
detect do?
For the
Danish physicist Niels Bohr, a founder of quantum theory (and to whom
Schrödinger’s regretful comment was directed), the answer was that measurements
must be made with a classical apparatus. In what has come to be called the
standard, or Copenhagen, interpretation of quantum mechanics, Bohr postulated
that macroscopic detectors never achieve any fuzzy superposition, but he did
not explain exactly why not. “He wanted to mandate ‘classical’ by hand,” says
Wojciech Zurek of Los Alamos National Laboratory. “Measurements simply became.”
Bohr also recognized that the boundary between the classical and the quantum
can shift depending on how the experiment is arranged. Furthermore, size
doesn’t necessarily matter: superpositions can persist on scales much larger
than the atomic.
In November
1995 Pritchard and his M.I.T. colleagues crystallized the fuzziness of
measurement. The team sent a narrow stream of sodium atoms through an interferometer,
a device that gives a particle two paths to travel. The paths recombined, and
each atom, acting as a wave, “interfered” with itself, producing a pattern of
light and dark fringes on an observing screen (identical to what is seen when a
laser shines through two slits). The standard formulation of quantum mechanics
states that the atom took both paths simultaneously, so that the atom’s entire
movement from source to screen was a superposition of an atom moving through
two paths.
The team
then directed a laser at one of the paths. This process destroyed the
interference fringes, because a laser photon scattering off the atom would
indicate which path the atom took. (Quantum rules forbid “which-way”
information and interference from coexisting.)
On the
surface, this scattering would seem to constitute a measurement that destroys
the coherence. Yet the team showed that the coherence could be “recovered”—
that is, the interference pattern restored—by changing the separation between
the paths to some quarter multiple of the laser photon’s wavelength. At those
fractions, it was not possible to tell from which path the photon scattered.
“Coherence is not really lost,” Pritchard elucidates. “The atom became
entangled with a larger system.” That is, the quantum state of the atom became
coupled with the measuring device, which in this case was the photon.
Like many
previous experiments, Pritchard’s work, which is a realization of a proposal
made by the late Richard Feynman many years ago, deepens the mysteries
underlying quantum physics rather than resolving them. It demonstrates that the
measuring apparatus can have an ambiguous definition. In the case of
Schrödinger’s cat, then, is the measurement the lifting of the lid? Or when
light reaches the eye and is processed by the mind? Or a discharge of static
from the cat’s fur?
A recent
spate of Schrödinger’s cat experiments have begun to address these questions.
Not all physicists concur that they are looking at bona fide quantum
cats—“kitten” is the term often used, depending on the desired level of
cuteness. In any event, the attempts do indicate that the quantum-classical
changeover— sometimes called the collapse of the wave function or the
state-vector reduction— has finally begun to move out of the realm of thought
experiments and into real-world study.
Here,
Kitty, Kitty
In 1991
Carlos Stroud and John Yeazell of the University of Rochester were
experimenting with what are called Rydberg atoms, after the Swedish
spectroscopist Johannes Rydberg, discoverer of the binding-energy relation
between an electron and a nucleus. Ordinarily, electrons orbit the nucleus at a
distance of less than a nanometer; in Rydberg atoms the outer electron’s orbit
has swollen several 1,000-fold. This bloating can be accomplished with brief
bursts of laser light, which effectively put the electron in many outer
orbitals simultaneously. Physically, the superposition of energy levels
manifests itself as a “wave packet” that circles the nucleus at an atomically
huge distance of about half a micron. The packet represents the probability of
the excited electron’s location.
While
swelling potassium atoms, the Rochester workers noticed that after a few
orbits, the wave packet would disperse, only to come back to life again as two
smaller packets on opposite ends of its large orbit. With his colleague Michael
W. Noel, Stroud showed last September that the two packets constituted a
Schrödinger’s cat state—a single electron in two locations.
An
electron, though, is essentially a mere point. Closer to the macroscopic realm
is an ion (a charged atom), which consists of many elementary particles. In May
1996 Chris Monroe, David J. Wineland and their colleagues at the National Institute
of Standards and Technology (NIST) in Boulder, Colo., created a Schrödinger’s
cat out of a beryllium ion. They first trapped the ion with electromagnetic
fields, then hit it with a laser beam that stifled the ion’s thermal jitters
and thereby cooled it to within a millikelvin of absolute zero. Then the
researchers fired two laser beams, each of a slightly different frequency, at
the ion to manipulate its spin, an intrinsic, quantum feature that points
either up or down. With the lasers, the researchers made the ion take on a
superposition of spin-up and spin-down states.
So much for
the preparations; next came the more macroscopic part. By manipulating the
tuning of the two lasers, the NIST team could swing the spinup state to and fro
in space, and the spin-down state fro and to. A snapshot would show the ion in
the spin-up state at one physical location and simultaneously in the spin-down
state at a second position. The states were 80 nanometers apart—large on the
atomic scale. “We made one ion occupy two places that are very far separated
compared with the size of the original ion,” Monroe says.
Last
December, Michel Brune, Serge Haroche, Jean-Michel Raimond and their colleagues
at the Ecole Normale Supérieure (ENS) in Paris took matters a step further. “We
were able to monitor the washing-out of quantum features,” Haroche explains. To
see how the superposition collapsed to one state or another, they in effect
dangled a quantum mouse in front of their Schrödinger’s cat to check whether it
was alive or dead.
The cat was
a trapped electromagnetic field (a bunch of microwave photons in a cavity). The
researchers sent into the cavity a Rydberg atom that had been excited into a
superposition of two different energy states. The Rydberg atom transferred its
superposed state to the resident electromagnetic field, putting it into a
superposition of two different phase, or vibrational, states. With its two
phases, the field thus resembled the Schrödinger’s cat in its odd superposition
between life and death.
For the
mouse, the ENS team fired another Rydberg atom into the cavity. The
electromagnetic field then transferred information about its superposed phases
to the atom. The physicists compared the second atom with the first to glean
superposition information about the electromagnetic field.
More
interesting, however, was the team’s ability to control crucial variables and
to determine how coherent states become classical ones. By varying the interval
between the two atoms sent into the cavity (from 30 to 250 microseconds), they
could see how the collapse of the superposition varied as a function of time,
and by enlarging the electromagnetic field (by putting more photons in the
cavity), they could see how the collapse changed with size. “This is the first time
we can observe the progressive evolution of quantum to classical behavior,”
Haroche says.
“This is a
breathtaking experiment,” Zurek enthuses. “Seeing a Schrödinger’s cat is always
surprising, but being able to see the cat forced to make a choice between
‘dead’ and ‘alive,’ to observe for the first time quantum weirdness going away,
is the real coup.” Moreover, the ENS results jibed with most theorists’
technical expectations. “What it tells me,” Zurek remarks, “is that the simple
equations we’ve been writing down seem to be a good approximation.”
Losing
Coherence
Zurek is
the leading advocate of a theory called decoherence, which is based on the idea
that the environment destroys quantum coherence. He formulated it in the 1980s
(although some of it harkens back to Bohr and other quantum founders) and with
various collaborators has been investigating its consequences ever since.
The
destabilizing environment essentially refers to anything that could be affected
by—and hence inadvertently “measure”—the state of the quantum system: a single
photon, a vibration of a molecule, particles of air. The environment is not
simply “noise” in this theory; it acts as an apparatus that constantly monitors
the system.
The ENS
experiment makes that effect clear. “The system decoheres because the system
leaks information,” Zurek notes. Some photons can escape the cavity and hence
betray the state of the remaining ones to the rest of the universe. “So in a
sense, Schrödinger’s cat is having kittens crawling out,” Zurek says.
Having the
environment define the quantum-classical boundary has the advantage of removing
some of the mystical aspects of quantum theory that certain authors have
promulgated. It does away with any special need for a consciousness or new
physical forces to effect a classical outcome. It also explains why size per se
is not the cause of decoherence: large systems, like real-life cats, would
never enter a superposition, because all the particles that make up a feline
influence a vast number of environmental parameters that make coherence
impossible. Given a one-gram bob on a pendulum and a few reasonable
assumptions, the interference terms in the system’s wave function drop to about
2.7–1,000 of their original value in a nanosecond—a virtually instantaneous
disappearance of quantum weirdness. “The old intuition going back to Bohr is on
the money,” although now there is a physical mechanism to substantiate his
mandate, Zurek concludes.
Still,
Zurek’s decoherence model is flawed in some eyes. “In my view, decoherence
doesn’t select a particular outcome,” opines Anthony J. Leggett of the
University of Illinois. “In real life, you get definite macroscopic outcomes.”
Zurek
argues that the environment does indeed dictate the quantum possibilities that
end up in the real world. The process, which he refers to as environment-
induced superselection, or einselection, tosses out the unrealistic, quantum
states and retains only those states that can withstand the scrutiny of the
environment and thus might become classical. “The selection is done by the
environment, so you will not be able to predict which of the allowed possibili-
ties will become real,” Zurek observes.
The
explanation feels less than satisfying. Zurek’s approach is “very appealing. It
allows you to calculate things, to see how the interference fringes wash out as
the superposition gets bigger,” NIST’s Monroe says. “But there’s still
something funny about it. He’s sweeping things under the rug, but it’s hard to
say what rug.” The problem is that decoherence—and in fact any theory about the
quantumclassical transition—is necessarily ad hoc. Quantum superpositions must
somehow yield outcomes that conform to our everyday sense of reality. That
leads to circuitous logic: the results seen in the macroscopic world arise out
of the quantum world because those results are the ones we see. A solution of
sorts, advocated by a few prominent cosmologists, is the unwieldy “many worlds”
interpretation, which holds that all possibilities stipulated by the wave
function do in fact happen. They go on to exist in parallel universes. The
idea, however, is untestable, for the parallel universes remain forever
inaccessible to one another.
Radical
Reworkings
The
problems with decoherence and the many-worlds idea have led a sizable minority
to support a view called GRW theory, according to Leggett. The concept was put
forward in 1986 by GianCarlo Ghirardi and Tullio Weber of the University of
Trieste and Alberto Rimini of the University of Pavia.
In the GRW
scheme, the wave function of a particle spreads out over time. But there is a
small probability that the spreading wave “hits” a mysterious “something” in
the background. The wave function suddenly becomes localized. Individual
particles have only a small chance of a hit, about once every 100 million
years. But for a macroscopic cat, the chance that at least one of its roughly
1027 particles makes a hit is high, at least once every 100 picoseconds. The
cat never really has a chance to enter any kind of superposition. Hence, there
is no need for decoherence: the macroscopic state of the cat results from
spontaneous microscopic collapses.
A few
problems plague this model. One is that the timing factor that triggers the hit
is entirely arbitrary; proponents simply choose one that produces reasonable
results. More important, though, is the source of the trigger. “Basically,
[there is] a sort of universal background noise that cannot itself be described
by quantum mechanics,” Leggett explains. The noise is not simply random
processes in the environment; it has a distinct mathematical flavor. Roger
Penrose of the University of Oxford argues in his book Shadows of the Mind that
the trigger may be gravity, which would neatly sidestep certain technical
objections.
Other, more
radical proposals abound. The most well known was put forth by the late David
Bohm, who postulated that “hidden variables” underpin quantum mechanics. These
variables—describing properties that in a way render wave functions as real
forces—would eliminate the notion of superpositions and restore a deterministic
reality. Like the many-worlds idea, Bohm’s theory cannot be verified: the
hidden variables by definition remain, well, hidden.
Given such
choices, many working physicists are subscribing to decoherence, which makes
the fewest leaps of faith even if it arguably fails to resolve the measurement
problem fully. “Decoherence does answer the physical aspects of the questions,”
Zurek says, but does not get to the metaphysical ones, such as how a conscious
mind perceives an outcome. “It’s not clear if you have the right to expect the
answer to all questions, at least until we develop a better understanding of
how brain and mind are related,” he muses.
Bigger
superpositions may enable researchers to start ruling out some theories— GRW
and decoherence predict them on different scales, for instance. “What we would
like to do is to go to more complex systems and entangle more and more
particles” than just the mere 10 trapped before, Haroche of the ENS says.
Future NIST experiments are particularly suited to serve as “decoherence
monitors,” Monroe contends. “We can simulate noise to deliberately cause the
superposition to decay.” Leggett has proposed using sensors made from
superconducting rings (called SQUIDs): it should be possible to set up large
currents flowing in opposite directions around the ring simultaneously.
Still,
there’s a long way to go. “Even in the most spectacular experiments, at most
you’ve shown a superposition for maybe 5,000 particles. That’s a long way from
the 1023 characteristic of the macroscopic world,” says Leggett, who
nonetheless remains supportive. “My own attitude is that one should just try to
do experiments to see if quantum mechanics is still working.”
Shrinking
transistors, now with features less than a micron in size, may also lead to
insights about the quantum-classical changeover. In a few years they may reach
dimensions of tens of nanometers, a realm sometimes called the mesoscopic
scale. Da Hsuan Feng of Drexel University speculates that quantum mechanics
perhaps really doesn’t lead to classical mechanics; rather both descriptions
spring from still undiscovered concepts in the physical realm between them.
Quantum
Computing
Even if
experiments cannot yet tackle the measurement problem fully, they have much to
contribute to a very hot field: quantum computing. A classical computer is
built of transistors that switch between 0 or 1. In a quantum computer,
however, the “transistors” remain in a superposition of 0 and 1 (called a
quantum bit, or qubit); calculations proceed via interactions between
superposed states until a measurement is performed. Then the superpositions
collapse, and the machine delivers a final result. In theory, because it could
process many possible answers simultaneously, a quantum computer would
accomplish in seconds tasks, such as factoring large numbers to break codes,
that would take years for a classical machine.
In December
1995 researchers successfully created quantum two-bit systems. Monroe and his colleagues
crafted a logic element called a controlled- NOT gate out of a beryllium ion.
The ion is trapped and cooled to its lowest vibrational state. This state and
the first excited vibrational state constitute one bit. The second bit is the
spin of one of the ion’s electrons. Laser pulses can force the bits into
superpositions and flip the second bit depending on the state of the first bit.
Other variations of gates couple two photons via an atom in a cavity or
transmit an entangled pair of photons through a network of detectors.
Yet the
creation of a useful quantum computer, relying on superpositions of thousands
of ions performing billions of operations, remains dubious. The problem? Loss
of superposition. The logic gates must be fast enough to work before the qubits
lose coherence. Using data from the NIST gate experiment, Haroche and Raimond
calculated in an August 1996 Physics Today article that given the gate speed of
0.1 millisecond, the bits would have to remain in a superposition for at least a
year to complete a meaningful computation (in this case, factoring a 200-digit
number).
Other
physicists are less pessimistic, since error-correcting codes (which are
indispensable in classical computing) might be the solution. “It gives you
instructions on how to repair the damage,” says David DiVincenzo of the IBM
Thomas J. Watson Research Center in Yorktown Heights, N.Y.
Moreover,
DiVincenzo points out that a new method of quantum computation, making use of
nuclear magnetic resonance (NMR) techniques, could raise coherence times to a
second or more. Say a liquid—a cup of coffee—is placed in a magnetic field;
because of thermal vibration and other forces, only one out of every million
nuclei in the caffeine molecules would line up with the magnetic field. These
standouts can be manipulated with radio waves to put their spins in a
superposition of up and down. Maintaining coherence is easier here than in the
other techniques because the nuclear spins undergoing the superpositions are
well protected from the environment by the surrounding turmoil of seething
molecules, the mad scramble of which averages out to zero. The calculating
caffeine sits effectively in the calm eye of a hurricane. Two groups have
recently demonstrated quantum computing by NMR, using a four-qubit version to
sum 1 and 1. More complex systems, using perhaps 10 qubits, could be had by the
end of the year.
The
drawback is readout. With no way to detect individual spins, researchers must
measure all the molecules’ spins— both qubit and nonqubit ones. Complex
molecules capable of sustaining many spins are therefore “noisier” than simpler
ones. “They’ll be able to do some nice stuff,” Monroe says, “but beyond about
10 bits, they’ll run into fundamental problems.” The output from 10 bits is only
0.001 as strong as that from a single bit; for 20, the output is down by one
million. So the NMR technique may not enter a meaningful computational realm of
at least 50 bits.
There might
be other uses for quantum superpositions, though. Stroud proposes data storage
on an atom, because an electron in a Rydberg atom could be made to inhabit a
superposition of 2,500 different energy levels. “That means that the electron’s
wave function can be quite complex, encoding a great deal of information,”
Stroud expounds. He demonstrated the possibility theoretically by writing
“OPTICS” on an atom. Other uses for quantum superposition, such as in
cryptography, chemistry and even teleportation, have been demonstrated.
Schrödinger’s boxed cat may have outwitted the best philosophical minds so far,
but it seems to have found plenty of technological reasons to stay put.
Jobs for
Quantum Cats
Researchers
have proposed and demonstrated several technologies exploiting entangled and
superposed quantum states, such as quantum computing. A few other schemes
include the following:
Quantum
Chemistry
Using
lasers, researchers can place molecules in a superposition of reaction
pathways; then they can control the chemical process by adjusting the degree of
interference. Last December workers separated isotopes with a similar
technique. Obstacles include less than practical efficiency levels and
difficulty in controlling phase characteristics of the laser.
Quantum Key
Cryptography
A much
better prospect than quantum computing is quantum key cryptography. Legitimate
communicators create shared keys using the polarization of photons.
Eavesdropping on these keys would immediately be noticed, because it would
disrupt the key photons’ states. Quantum cryptography has been shown to
function over several kilometers in optical fibers.
Quantum
Teleportation
The idea
has less to do with Star Trek than with reconstructing destroyed information.
The crux is the Einstein-Podolsky-Rosen effect, which shows that two photons
can remain entangled, no matter how far apart they are, until a measurement is
made (which instantaneously puts both in a definite state). Alice takes one EPR
photon, Bob the other. Later, Alice measures her EPR photon with respect to a
third photon. Bob can use the relational measurement to re-create Alice’s
non-EPR photon. Whether Bob truly rematerialized the photon or just created an
indistinguishable clone is unclear. Researchers at the University of Innsbruck
reportedly demonstrated the phenomenon, which might have use in quantum
cryptography.
Quantum
Laser Optics
Lasers
ordinarily require a population inversion, a condition in which atoms in an
excited state outnumber those in the ground state; the excited atoms emit laser
photons as they drop to the ground state. In 1995 researchers sidestepped this
requirement. In lasing without inversion, two coupling lasers give ground-state
atoms two paths to one higher energy level. Interference between the paths
renders the ground-state atoms invisible, and so fewer excited atoms are
needed. Such lasers do not require as much power and in principle could emit
light in the desirable x-ray region.
By Philip Yam
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