SUPERFLUID helium is to liquids what Salvador Dali is to artists—full
of surreal surprises. Put some in a bowl, set the bowl spinning, and the liquid
inside will remain stationary. Draw a cupful out of the bowl, suspend it a few
centimetres above the remaining liquid, then stand back and rub your
eyes—the fluid in the cup will cheat common sense by pouring itself, drop
by drop, back into the bowl. A drop climbs up the inside of the cup, then runs
down the outside. When it falls, another begins climbing, and the magic
continues until the cup is dry.
When you have spent most of your life working with a liquid which brings the
weirdness of the quantum world into our own, you would think nothing could
surprise you. You’d think that once you had seen it defy gravity and climb the
walls of its container, you would have seen it all. And that’s just what
physicists Richard Packard and Seamus Davis thought—until the liquid in
their lab started whistling.
Last year, Packard, Davis and their colleagues at the University of
California at Berkeley linked two pools of superfluid by a tiny hole, and out
came an eerie sound like a falling bomb, a whistling that gradually decreased in
pitch. They had discovered the quantum whistle.
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In the days that followed, the two researchers couldn’t stop playing with its
strange sounds, but now things are becoming a bit more serious. For behind the
light-entertainment value of this whistle lies a host of exotic applications.
The group has already used the phenomenon to fashion a gyroscope that harnesses
a superfluid’s weirdness to measure how fast the Earth is spinning. They are
hard at work on other devices too, some of which could be used to put Einstein’s
relativity theories through more demanding tests than ever before.
Conceptually, a superfluid is little more than a liquid that lives by quantum
rather than classical rules. To make one, you need to cool a substance down to
extremely cold temperatures so that its particles move very slowly. According to
quantum theory, this causes the waves associated with the particles to stretch
out and become more influential—the quantum nature of one can affect the
behaviour of others. But most liquids turn to solids long before this can
happen.
What makes helium special is that it remains a liquid at all temperatures.
Near absolute zero, when the quantum waves associated with its atoms begin to
overlap, a superfluid is born: the atoms suddenly lose their individuality and
the liquid collapses into a Bose-Einstein condensate, a quantum substance in
which the atoms move in lockstep. It’s a strange and super-slippery stuff that
can flow through pipes with no friction at all, and perform all sorts of other
stunts.
In 1963, physicist Brian Josephson of Cambridge University predicted that
merely linking together two tiny pools of superfluid would cause a natural
quantum oscillation, in which the liquid would rush back and forth through the
link. Packard and his colleagues were searching for these oscillations in early
1997, but, like others before them, they weren’t finding anything. The screens
of their oscilloscopes—used to detect and display rapid
oscillations—showed nothing interesting, and Packard’s frustrated graduate
students were ready to give up. Their sophisticated research equipment was
getting them nowhere.
Quantum dance
When Packard suggested that they take a pair of headphones and listen for the
signal, the students were less than enthusiastic. “They kept arguing that there
was no point because there was nothing there,” he says. He kept at them to try
it, but they resisted. “They really didn’t want to do it—in the end they
simply argued that they couldn’t do it because they didn’t have any headphones
in the lab.”
So Packard went to a local electronics store, bought a $50 pair of
headphones out of his own pocket, and presented them to his students. “The
connector’s wrong,” they said. He went back to the shop and bought an adaptor.
Graduate student Sergey Pereverzev reluctantly plugged in the headphones and
flicked a switch to start up the experiment. His jaw dropped. What he heard was
just what the theory had predicted: a high-pitched whistle that gradually became
lower in tone, like the sound of a falling bomb.
People got so excited, Packard recalls, that the headphones only lasted four
days. “Pulling them on and off, they tore them apart.” But not before they were
able to do the tests and measurements that pinned down the discovery, which they
reported last year in Nature (vol 388, p 449).
So what makes the whistle? According to Josephson’s calculations,
oscillations should occur in any two pools of superfluid connected by a tiny
hole. All you need is a small pressure difference between them. In an ordinary
liquid, the fluid would simply flow from one side to the other. But a superfluid
has other ideas.
Since each fluid is a quantum substance, it has a “wave function”—an
undulating wave-like form that describes its properties. This wave function
depends on, among other things, a superfluid’s pressure, which means that the
wave functions of the two superfluid pools differ. This leads to a kind of
confusion involving the atoms at the boundary between the pools. Roughly
speaking, these atoms try to occupy both regions at once and end up doing a
rapid quantum dance back and forth between the two.
The idea is simple enough. And yet it took ten years to detect the
oscillations. To do it, Packard and his colleagues had to create what is known
as a “weak link”. This is a hole just large enough to allow the superfluids’
wave functions to overlap, yet small enough to prevent the liquids from merging
into one.
Making the perfect weak link relies on creating a connection with a diameter
roughly equal to the “healing length” of the superfluid—the length over
which the wave function remains more or less constant. For the most common form
of helium—helium-4, which has two neutrons and two protons in its
nucleus—that would mean punching a hole between the reservoirs that was
only 0.1 nanometres in diameter, which for now is technically impossible. But
helium-3, a less common isotope having only one neutron in its nucleus, has a
far larger healing length, so a weak link can be 500 times larger.
Even with helium-3, however, there is a problem. A good, weak link would
produce a whistling so tiny as to be undetectable. So Packard’s team linked
their superfluid baths with a grid of 4225 identical perforations in a tiny
silicon wafer (see Diagram).
They were hoping that the apertures would
together produce oscillations large enough to be detected. As it turns out, they
were lucky.
Superfluid pools
They started by embedding the silicon wafer in a stiff membrane, which they
glued to the bottom of an aluminium washer. A chamber filled with superfluid was
made by gluing a flexible, metal-coated membrane to the top of the washer. The
object was then immersed in superfluid to create two pools—one inside and
one outside—connected by the tiny holes in the silicon wafer.
To apply a pressure difference, the team momentarily deformed the flexible
membrane with a voltage, so compressing the helium-3 trapped within the
structure. This caused an oscillation across the weak links, just as Josephson
had predicted in 1963. An ultra-sensitive motion sensor placed next to the
washer detected the movement and sent the signal up to an oscilloscope, or the
headphones.
As the membrane slowly returned to its original shape, the pressure
difference slowly decreased. Consequently, the oscillation
frequency—proportional to the pressure difference—also fell off
slowly. This explains why it was so hard to see the signal on the oscilloscope.
In sweeping over a range of frequencies, it left no single “spike” on the
screen. But the human ear is adept at hearing sounds with changing
pitches—so the falling bomb sound was clear through the headphones.
The group is still working out a complete theoretical model for its whistling
superfluid, but that hasn’t stopped them seeking applications. Eventually, they
hope to incorporate it into the world’s most sensitive gyroscope.
Gyroscopes use rotating bodies to sense shifts in the direction of movement.
They are essential for navigation on board ships and aeroplanes, providing an
absolute reference for their orientation and movement. Using helium-4, the
Berkeley team has already produced a superfluid gyroscope that can detect
changes in the Earth’s rotation speed with an accuracy of 0.5 per cent. Using
helium-3 and “whistling links”, they believe they can do much better.
The design of a superfluid gyroscope is based on the fact that these quantum
liquids like to remain perfectly motionless. More specifically, they prefer to
remain in a state of zero angular momentum. This can happen if the fluid remains
completely motionless, or, if the “amount” of rotation clockwise and
anticlockwise compensate one another. If you push one part of a superfluid one
way, another part will move in the opposite direction to compensate. But if the
flow velocity at any point gets too high, the superfluid can save energy by
allowing a “phase slip”, the sudden creation of a vortex-like tornado in the
superfluid. This removes excess energy from the fluid by pinching all the
rotation down into a tiny tube.
Packard and his team have exploited this effect to build a highly sensitive
device for measuring rotation. Their apparatus lives on a 1-centimetre-square
silicon chip. An etched channel spirals around the edge of the chip. At one
outer end of the spiral is a relatively large (1 millimetre in diameter) hole,
and at the other end is a tiny 1 micrometre hole. When immersed in a superfluid,
there is a circular path around which the fluid can flow. Essentially, the
device forms a ring of superfluid with a weak link fixed inside it
(see Diagram).
As the Earth spins, so does the chip. And this is enough to cause a
compensating flow in the superfluid—a small backflow through the tiny
aperture. This is too small to measure, so Packard’s team has had to develop an
ingenious means of watching the superfluid’s motion. They covered one side of
the chip with a plastic membrane. When set vibrating, this membrane pumps
superfluid back and forth in the channel, so inducing a corresponding flow
through the tiny aperture.
At a certain point in the cycle of this alternating flow, the fluid reaches a
critical velocity, which forces a vortex through the aperture. This causes a
jump in the position of the membrane, and a glitch on a nearby position sensor.
The glitches would happen at a fixed rate even if the device wasn’t rotating.
But rotation changes how the glitches occur.
By slowly turning the cryostat containing the silicon chip from an east-west
orientation through to north-south, Packard and his team could watch as the
effect of the Earth’s rotation was gradually added to the oscillating flow
velocity of the superfluid, changing the glitch’s position in the cycle. This
change gave them a way to measure the effect of the Earth’s rotation.
By adding more turns and increasing the loop area, Packard believes it may be
possible to improve the gyroscope’s sensitivity by up to 10 000 times. But they
are currently working at the limits of their laboratory, and conducting
experiments in the dead of night, when no one is around to ruin the results by,
for example, flushing a distant toilet. Further improvements will mean quitting
the Berkeley campus to escape such vibrations. Eventually, the gyroscope may
even have to be calibrated in space.
One of the possible applications of the instrument is in geodesy, which is
concerned with surveying and mapping the Earth. Studying the vibrations and
rotation of the planet can reveal what is happening in its interior. The signals
involved are exceedingly tiny, and the only way the team will be able to tell if
the gyroscope is up to the task is to detach it from terrestrial
vibrations—by putting it in a satellite and letting it float.
If it isn’t up to the task, that would probably be due to the noise
introduced by the vortices as they pass through the aperture. A gyroscope made
to a different design, using the whistling helium-3 weak links, doesn’t rely on
creating vortices. Instead, it uses quantum interference effects to detect
rotation. “Our belief is that the noise is going to be a good deal smaller in
this system,” Packard says.
Helium-3 might make the ultimate gyroscope, but it has its own problems,
Packard admits. “It would need to be a thousand times colder than the helium-4,
so it’s technologically more difficult. Whether one would want to do it depends
on whether there’s a scientific problem that justifies the effort.”
Modern aircraft and submarines employ ring laser gyroscopes, in which
revolving beams of light detect changes in orientation and position. Packard
concedes that they are already as good as they need to be. Who wants to make a
gyroscope that needs cooling to near absolute zero? “It’s clear,” he says, “that
nobody’s going to put this in an aeroplane when laser gyroscopes are already
good enough to get you from New York to London.”
But superfluid gyroscopes could be put to work in other fields. Their quantum
sensitivity may, for example, be sufficient to finally settle a century-old
argument about Einstein’s general theory of relativity. That’s because
superfluids on Earth pick out what physicists call an “absolute inertial
frame”—they have an unnerving ability to keep still while their containers
revolve around them. But what constitutes true “stillness”, and to what does the
helium anchor itself so as not to rotate?
In an absolute inertial frame, the laws of physics are just what Einstein’s
special theory of relativity says they are. In particular, a body at rest should
remain that way. We rotate as the Earth spins, so we clearly don’t live in such
a frame. The superfluid shows us how much we’re rotating with respect to the
ultimate state of no rotation. “The question,” says Packard, “is whether this is
the same frame in which the distant stars are at rest. General relativity would
say that it is not.”
Einstein’s general theory of relativity deals with gravity, and says that the
proximity of the spinning Earth should change the inertial frame of anything
near it. To test this, you could make a highly sensitive superfluid gyroscope,
move it around, and work out what it considers to be the absolute inertial frame
near the Earth. Then you can couple the superfluid gyroscope to a telescope that
points at a distant star. The aim is to find out if that distant star is moving
with respect to the inertial frame as detected by the gyroscope on the
Earth.
The measurements involved would have to be more accurate than anything
currently possible, and Packard is not sure they will ever get the required
accuracy. “We’ll continue the development and see what happens,” he says.
Whatever the future holds, he is confident that his team will discover more
about superfluids. This laid-back, optimistic approach exemplifies Packard’s
philosophy of science. He sees his research as more of a leisure pursuit than a
career. Some make model aeroplanes, some people make superfluids whistle. In a
world where liquids climb walls, who’s to say what’s strange?