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A group of physicists in Spain has shown how to make a quantum = measurement=20 that overcomes a limit related to Werner Heisenberg's uncertainty = principle. The=20 researchers confirmed a theoretical prediction of how to beat the = Heisenberg=20 limit by using interacting photons to measure atomic spin, and they say = that=20 their approach could lead to more sensitive searches for the ripples in=20 space=E2=80=93time known as gravitational waves and perhaps also to = improved brain=20 imaging.
The standard limit on the precision with which a quantum measurement = can be=20 carried out is due to the statistical error associated with counting = discrete=20 particles rather than continuous quantities. So, for example, when = measuring the=20 phase difference between the waves sent down two arms of an = interferometer, the=20 error in this quantity will scale with the square root of the total = number of=20 photons measured, N. Since the signal scales with N, the=20 signal-to-noise ratio also scales in the same way. Or, put another way, = the=20 sensitivity of the measurement, which is the minimum signal that can be = measured=20 with a given level of noise, will scale with = 1/N1/2.
It is possible to improve on this scaling, however, by entangling the = photons, because this correlates what would otherwise be independent = sources of=20 noise from the individual particles. Such entanglement allows = measurements to=20 approach the so-called Heisenberg limit, which means that sensitivity = scales=20 with 1/N. Until recently it was thought that this scaling = represented an=20 absolute limit on the sensitivity of quantum measurements.
Caught in a trap
However, in 2007 a group led by Carlton Caves at the University of = New Mexico=20 in the US predicted that the Heisenberg limit could be beaten by = introducing=20 nonlinear interactions between the measuring particles. That prediction = has now=20 been shown to be true, thanks to an experiment carried out by Morgan = Mitchell=20 and colleagues at the Institute of Photonic Sciences at Barcelona. = Mitchell's=20 group fired laser pulses into a sample of ultracold rubidium atoms held = in an=20 optical trap and measured how the atoms' spin angular momentum caused = the=20 polarization axis of the photons to rotate.
In a linear measurement, each photon would interact separately with = the=20 atoms, resulting in a relatively weak signal. But what the researchers = did was=20 to carry out nonlinear measurements, ramping up the intensity of the = laser=20 pulses enough so that each photon, as well as registering the magnetic = state of=20 an atom also altered the electronic structure of that atom. This in turn = left=20 its mark on the polarization of the next photon, so amplifying the = signal. "We=20 have a signal that is not dependent just on the thing we are aiming at, = but also=20 on what we send in," explains team member Mario Napolitano.
According to Napolitano, it wasn't clear that a signal could in = practice be=20 amplified in this way because it was reckoned that the nonlinearity = would=20 increase the noise as well as the signal. But his team was able to = tailor the=20 nonlinearity accordingly, by concentrating the interaction between atoms = and=20 photons to a very tiny region of space and by very precisely tuning the=20 frequency of the laser so that it was very well matched to the = atoms=E2=80=99 electronic=20 structure. Then by measuring the rotation in the photons' polarization = using an=20 interferometer, measuring the noise and measuring the number of photons, = then=20 repeating this process for different photon numbers, the researchers = were able=20 to show that the sensitivity scales with photon number better than the = scaling=20 of the Heisenberg limit. In fact, they achieved a sensitivity that = scaled with=20 1/N3/2.
Clocks and brains could benefit
Napolitano is keen to point out that this result does not imply that = the=20 Heisenberg uncertainty principle is wrong, but rather it shows that we = do not=20 properly understand how to scale that principle up to multiple-particle = systems.=20 He also believes that the work could ultimately have significant = practical=20 applications, such as improving atomic clocks, given that such devices = rely on=20 interferometers. What's more, several research groups are investigating = the=20 possibility of measuring electrical changes in the brain by using light = to probe=20 the magnetic properties of atoms placed close to the brain, and the = lastest work=20 could enhance this technique.
Jonathan Dowling, a theoretical physicist at Louisiana State = University in=20 the US, says that the latest work could also help in the search for=20 gravitational waves. Researchers hope to register gravitational waves'=20 distortion of space time by measuring the difference in path length = experienced=20 by laser beams travelling in the two orthogonal pipes of an = interferometer.=20 Dowling says that if the American LIGO detector could operate with a = sensitivity=20 that scales as 1/N3/2 rather than as = 1/N1/2=20 then either its sensitivity could be greatly increased or its laser = power=20 enormously reduced, which would avoid potential heating and deformation = of the=20 facilities' optics. "This opens up a whole new ball game in nonlinear=20 interferometry," he adds.
However, Barry Sanders, a quantum physicist at the University of = Calgary in=20 Canada, urges caution. "The experiment demonstrates that the Heisenberg = limit=20 can be beaten in the real world," he says. "But practical applications = are not=20 likely in the near future because of the technical challenges that need = to be=20 overcome, especially noise. We are still exploring the basic physics of = using=20 quantum resources for precise measurements."
The research is published in Nature.
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Transcending uncertainty