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One of the most intriguing consequences of quantum mechanics is that
empty space is not really empty at all. The Heisenberg uncertainty principle
predicts that it is never possible to be absolutely precise about the energy
of a system, including even that of empty space, or more correctly, the
vacuum. This fuzziness manifests itself as what are called vacuum fluctuations
– a sort of background quantum noise. Vacuum fluctuations have real effects
on forms of energy such as light.

A light beam consists of an oscillating electromagnetic field. In the
classical, or wave description of light, these oscillations may be pictured
as a smooth wave with a well-defined amplitude (the height of the wave crest,
which relates to the intensity of the light) and a definite phase (which
relates to the position of the wave and the wavelength).

If we apply quantum mechanics to light, we can then visualise light
as a stream of ‘wave packets’ called photons. These wave packets obey the
uncertainty principle, so a well-defined wave is not permitted. There are
fluctuations in the amplitude and phase of the wave which are basically
the result of the vacuum fluctuations, as defined by the uncertainty principle.
These fluctuations can be a nuisance because they impose a limit on the
precision of optical measurements. For example, some optical measurements
depend on detecting the interference patterns produced when two light waves
meet – a technique called optical inter-ferometry. Fluctuations in the phase
produce optical ‘noise’, smearing out the patterns and so making any sensitive
measurement difficult.

Recently, physicists working on optical systems have succeeded in generating
light with fewer fluctuations than the complete darkness of the vacuum.
This is called ‘squeezed’ light. Though at first sight the uncertainty principle
seems to make this impossible, there are, in fact, several ways of manipulating,
or squeezing, the quantum fluctuations in a light wave.

One way is to redistribute the fluctuations between different parts
of the optical wave. This works because what Heisenberg’s uncertainty principle
actually refers to is the contributing uncertainties in the amplitude and
the phase of the wave multiplied together. Although this product of the
uncertainties cannot be less than a certain value, the same does not apply
to the individual amplitude and phase uncertainties. For light of a definite
wavelength, the fluctuations in amplitude and phase are equal. Increasing
the fluctuations in the amplitude part of the wave will allow you to reduce
those in the phase part to produce phase-squeezed light, and vice versa;
neither procedure violates the uncertainty principle. In theory this would
allow you to send a signal at a very low power via the squeezed part of
the light with little interference from quantum noise.

Squeezed light is just one example of nonclassical light – that is,
light with properties that are not predicted by the classical wave theory
of light. It is a uniquely quantum phenomenon. The possibility of nonclassical
light was first proposed in the 1960s by Roy Glauber of Harvard University.
Many physicists, however, were doubtful that nonclassical light could be
created.

It was not until 1975 that my student Howard Carmichael and I, then
at the University of Waikato in Hamilton, New Zealand, identified a system
that shows nonclassical behaviour. According to quantum mechanics, electrons
in atoms can only occupy certain energy levels. An electron can jump from
its lowest energy level – the ground state – to a second and higher energy
level by absorbing light of definite frequency, from, say, a laser. Eventually
the electrons fall back to the ground state, emitting a photon of light
– a process called resonant fluorescence. We predicted from the statistics
of quantum theory that once the electron had returned to the ground state,
there would be a delay before the electron would be re-excited by the laser
light and emit another photon. This delay would result in an intermittent
emission of fluorescence called photon anti-bunching. The classical theory
of electromagnetic radiation, which does not quantise energy, does not predict
antibunching.

The following year, Leonard Mandel and his students Jeff Kimble and
Mario Dagenais at the Rochester Institute of Technology in New York State,
observed photon antibunching in fluorescing sodium atoms. This was the first
nonclassical effect observed in optics. It ushered in a new era in quantum
optics.

During 1976, Horace Yuen, a theorist then at the Massachusetts Institute
of Technology, wrote a comprehensive article predicting the possibility
of another nonclassical phenomenon, squeezed light. Because this does not,
as far as anyone knows, occur in nature, we decided to look at all the possible
ways of generating squeezed states of light. We were particularly excited
about the idea because of its potential for improving the sensitivity of
measurements affected by quantum noise, such as optical interferometry.

But it was not until 1985 that Dick Slusher and Bernard Yurke at AT&T
Bell Laboratories in Murray Hill, New Jersey, generated squeezed light.
They used a method which involves what is called a nonlinear process; the
simplest version of which (although not the one they used) works as follows.
If you shine light of one frequency (from a ‘driving’ or pump laser) onto
certain kinds of materials, such as lithium niobate, they emit light of
a different frequency. For instance, two red photons impinging on the crystal
can combine to emit one blue photon of twice the frequency – a process called
second harmonic generation (see ‘Materials with a bent for light’, New ÐÓ°ÉÔ­´´,
1 July 1989). Naturally, this is much more likely to happen when there is
a greater probability of finding two red photons together – in other words,
when the intensity is large. The subtle trick is that blue photons are therefore
more likely to be emitted when the quantum fluctuations make the amplitude
large. This has the effect of flattening the peaks in the intensity fluctuations
of the red light at the expense of phase fluctuations.

There is also the reverse nonlinear process, which happens when a photon
splits into two photons, each with half the original frequency – a process
called parametric down-conversion, or parametric amplification. The incoming
electric field may be split into its sine and cosine components. When the
crystal is pumped at twice the frequency, it behaves as a phase-sensitive
amplifier with the cosine component amplified and the sine component weakened.

By mixing the output light with another laser whose phase can be varied,
you can select the amplified and reduced noise. The light outputs are, after
mixing, converted to electrical signals using a photodetector. With a balanced
detection scheme (shown in Figure 1), the coherent signal from the laser
can be subtracted to leave behind the noise either amplified or reduced.

The nonlinear interactions used in these experiments are rather weak
and happen very quickly. To allow more time for the process to take place,
short mirrors are placed on either side of the crystal, so that the light
is reflected back through it. The two mirrors form an optical resonator,
or cavity. The mirrors are also partially transmitting, one mirror allowing
the original beam of light into the cavity and the other allowing frequency-doubled
(or para-metrically down-converted) light to pass out. In some experiments
the surfaces of the nonlinear crystal are coated with a mirror to form an
optical resonator.

Several research groups have been successful in producing squeezed light.
In an experiment by Kimble, then at the University of Texas at Austin, and
his colleagues, light was produced with the minimum fluctuations allowed
by the uncertainty principle. The team used parametric down-conversion inside
an optical cavity. The actual quantum noise observed in their detector was
one-third of the vacuum noise level. Taking into account the inefficiencies
of their detector, they estimated that the light emerging from the cavity
had its quantum noise reduced to one-tenth of the vacuum noise level.

At the Max Planck Institute for Quantum Optics in Munich, Andreas Sizman
and colleagues have achieved amplitude squeezing in second harmonic generation.
They succeeded in reaching a 40 per cent reduction in quantum noise.

Squeezed light can also be generated by another nonlinear process called
four-wave mixing. With this technique, two laser photons of a certain frequency
combine in a nonlinear material, such as a beam of sodium ions or a glass
fibre, to form two new photons with frequencies that are different but add
up to twice the original frequency. This approach was, in fact, the one
originally suggested by Yuen and his colleague Jeffrey Shapiro and tried
by Slusher, Yurke and colleagues. The origin of the squeezing in this experiment
is similar to that in parametric down-conversion. Slusher’s group succeeded
in squeezing fluctuations to about 40 per cent of their natural level. Marc
Levenson and Bob Shelby at IBM Almaden Research Laboratories in California
pioneered the use of an optical fibre as a nonlinear medium to generate
squeezed light. The laser can be focused through the entire length of the
fibre, which allows a large interaction time for the process to take place.
More recently, both the IBM group and Herman Haus and Karen Bergmann of
the Massachusetts Institute of Technology obtained significant squeezing
in this way.

Quiet light from correlated photons

Another way of reducing quantum noise is to exploit the two beams of
light produced by parametric down-conversion. The important thing here is
that the corresponding photons in each beam come in pairs which are ‘correlated’,
meaning that their behaviour at the quantum level is interlinked. Each beam
will therefore have exactly the same number of photons. The beams are directed
at photodetectors and converted into electric currents. But, because of
quantum fluctuations which in effect drive the parametric down-conversion
process, the number of photons arriving at a detector will fluctuate, to
give a noisy current.

This can be corrected. When we detect the fluctuations in one beam (called
the idler) we can use this information to correct the fluctuations in the
other (called the signal beam) by altering the power of the pump laser to
adjust the rate at which photon pairs are produced by parametric down-conversion.
John Rarity and Paul Tapster at the Royal Signals and Radar Establishment
in Malvern obtained 30 per cent squeezing using this feedback approach.
Elizabeth Giacobino and her colleagues at the Pierre and Marie Curie University
in Paris have seen similar noise reductions using a feed-forward technique
directly to correct the signal. Alternatively, both beams can be detected
and compared by electronic subtraction. Both the Paris group and Prem Kumar
at Northwestern University in Illinois have seen residual noise reduced
by 90 per cent after electronic subtraction.

Lasers themselves have intensity fluctuations due to ‘shot’ noise caused
by fluctuations in the emission times of individual photons. A novel method
of obtaining squeezed light is to reduce the intensity fluctuations in the
laser output directly, by suppressing the quantum noise in the pumping mechanism
of the laser. Yoshi Yamomoto and colleagues at the NTT research laboratories
in Tokyo have developed semiconductor lasers with intensity fluctuations
reduced by 95 per cent below the shot noise of usual lasers.

What practical use has squeezed light? One is in making very sensitive
measurements. Squeezed light may be useful in detecting gravitational waves
which astronomers think might be generated in catastrophic cosmic events,
such as explosions of supernovae. This would require a very sensitive detector
such as an optical interferometer.

In an optical interferometer, the light from a laser may travel along
two different paths before being reflected by a pair of mirrors and then
recombined at a photodetector. The difference in length of the two paths
may be determined by measuring the interference pattern of the combined
waves. If the paths are identical in length, the light will interfere constructively,
giving a high intensity at the detector. If, however, the waves are exactly
out of phase, they will give a null intensity.

In the gravitational wave experiment the end mirrors are freely suspended
and both optical arms are contained in an evacuated tube. The effect of
the gravitational wave is to produce a tiny change in length in one of the
arms. The interferometer is operated with a path length differing by half
a wavelength, so that there is a null intensity at the detector. Any change
in length due to a gravity wave will then produce an increase in light intensity.
Obviously, these changes in intensity will be very small and may well be
swamped by vacuum fluctuations. Carl Caves, currently at the University
of Southern California, has suggested that using phase-squeezed laser light
would reduce the quantum noise.

Squeezed light could be useful in optical communications where it might
be important to cut down noise. Researchers have suggested that you could
encode information on the quiet component of light – say, the amplitude
of the light wave – and then use detectors that are insensitive to the noisy
component, in this case the phase. At the moment, the losses present in
current optical fibres, which degrade the squeezing, mean that squeezed
light could not be used to transmit information over long distances. For
example, the loss of 0.2 decibels per kilometre would, over a distance of
50 kilometres, drown any advantage gained from squeezing quantum noise.
It might be possible, however, to take advantage of squeezed light in local
area networks to link computers.

One curious potential use of squeezed light is in espionage. It might
be possible to tap off information from a carrier signal without depleting
it noticeably. Normally, to detect any information, the amount of signal
tapped off must be greater than the vacuum fluctuations. Squeezing the vacuum
fluctuations would allow a spy to detect the signal without it being significantly
depleted. Because the squeezed signal does not have to travel far, dissipation
is not a limiting factor. Figure 2 shows a sketch of such an optical tap.

Squeezed light may also be used to make sensitive spectroscopic measurements,
for example in biological samples. Many biological molecules will absorb
weakly when exposed to light of a characteristic frequency. This absorption
could be used to identify the molecules in a material. Normally, you need
high intensity light of the kind obtained with a laser to detect the molecules’
absorption spectra, because any absorption signal obtained using low intensity
light would be drowned out by optical noise. The problem is that biological
molecules can be damaged by high intensities of light. One way around this
would be to use low intensity light containing little quantum noise.

Squeezed light for delicate molecules

This can be done by exploiting the twin beams obtained by parametric
down-conversion. First, you place the sample in one of the beams, and use
the other as a reference beam. Then you tune the driving laser so that the
frequency of the twin beams matches the frequency at which the molecules
absorb. The two beams are detected and the resulting electrical currents
are subtracted as in the experiments described above to remove the noise.
This then reveals the presence of the absorbing molecules.

Twin beams of photons obtained from parametric down-conversion also
provide a way of testing the subtleties of quantum mechanics. The pairs
of photons emitted from the nonlinear process are ‘correlated’. In quantum
terms, this means that they have ‘matching’ properties such as polarisation
or orientation of phase. The odd thing is that quantum theory predicts that
these properties are indeterminate until actually measured. But the photons
maintain their initial quantum correlation even after they have been spatially
separated. Measuring the properties of one photon, therefore, instantaneously
defines the properties of the other photon, even though they do not appear
to communicate – a weird phenomenon called nonlocality, or action at a distance
(‘The man who proved Einstein was wrong’, New ÐÓ°ÉÔ­´´, 24 November 1990).

The famous quantum theorist John Bell designed a test which Alain Aspect
at the University of Paris at Orsay carried out using correlated photon
pairs to reveal the effect of nonlocality. The correlated photon pairs he
used were produced from certain kinds of quantum transitions in atoms. Parametric
down-conversion provides a better method of creating correlated photon pairs
for carrying out Bell’s test because the beams of photons involved have
a definite direction. This makes it easier to collect all the statistical
data that this experiment relies on to work.

The discovery of new quantum sources of light, such as antibunched and
squeezed light from nonlinear processes such as parametric down-conversion,
has opened up a new window in optics. Until very recently, all optical experiments
could adequately be explained by a classical theory of light. The experiments
described here are outside the domain of classical optics, being characteristic
of the uniquely quantum nature of light. These studies are not only fundamentally
important to increasing our understanding of light, they may also open the
door to new technologies.

Dan Walls is professor of physics at the University of Auckland in New
Zealand.