Side Stepping Heisenberg’s Uncertainty Principle isn’t easy

Improving the sensitivity of measuring equipment such as LIGO’s massive laser interferometer involves attempting to ‘sidestep’ the uncertainty principle. But, new research shows, that is going to be even harder than we had believed.

Two different quantum optomechanical systems used to demonstrate novel dynamics in backaction-evading measurements. Left (yellow): silicon nanobeam supporting both an optical and a 5 GHz mechanical mode, operated in a helium-3 cryostat at 4 Kelvin and probed using a laser sent in an optical fibre. Right (purple): microwave superconducting circuit coupled to a 6 MHz mechanically-compliant capacitor, operated in a dilution refrigerator at 15 milli-Kelvin. (I. Shomroni, EPFL.)

Recent developments in science such as the detection of gravitation waves by way of the minute displacement of mirrors at LIGO and the development of atomic and magnetic force microscopes to reveal atomic structure and spins of single atoms have pushed the boundaries of what can be defined as measurable.

Yet, as scientists push the limits of mechanical measurements the spectre of Heisenberg’s uncertainty principle remains to remind them that no matter how accurate their equipment and procedures become, nature has an intrinsic, in-built limit to what they can ‘know’.

One of the main results of early investigations in quantum physics, the uncertainty principle says that even as the sensitivity of our measuring equipment improves — these conventional measurements are limited by a “measurement backaction”. The most common and easiest to explain example of the uncertainty principle is the idea that knowledge of a particle’s exact location immediately destroys knowledge of its momentum — and by extension, the ability to predict its location in the future.

Fundamentally, the Heisenberg uncertainty principle arises from the fact that we can define matter as exhibiting both wave-like and particle-like behaviour. Momentum is given by the equation below, where the denominator on the right-hand side is the wavelength of the wave in question.

Thus, momentum is intrinsically tied to wavelength, usually defined as the peak of one crest to another.

A perfect wave description of momentum would look something like the image below where the x-axis is the location and the y-axis is the probability of finding the particle at this location, the graph forms an infinitely long sine wave.

The momentum here is well defined; there is almost zero uncertainty because the wavelength is known. But we can assume from this that because the wavelength is infinitely long, the location could be at any point. The position is not defined at all. To ascertain some information regarding location multiple waves of differing wavelengths are overlaid. This creates an inference pattern as peaks of corresponding waves cancel the troughs of others, and the particle can begin to be localised. Physicists refer to this as a wave packet and it can be seen below.

The more waves that are added, the more the particle’s location resolves. But as these waves are all differing wavelengths (and thus describe different momentum values) the value of that momentum becomes much less clear.

Sense and sensitivity in laser interferometers

Despite this seeming hinderance, researchers are hard at work developing potential methods to help them ‘sidestep’ Heisenberg’s uncertainty principle. These techniques hinge on the careful collection of only certain information about a system, whilst intentionally omitting other aspects.

So, for example, as waves and wavefunctions are of vital importance in quantum mechanics — using this selective method researchers would attempt to take the measurement of the wave’s amplitude, whilst simultaneously ignoring its phase.

These methods could, in principle at least, have unlimited sensitivity with the drawback of only being able to gauge half of the information about a system. That is the aim of Tobias Kippenberg at Ecole Polytechnique Federale De Lausanne (EPFL). In conjunction with scientists at the University of Cambridge and IBM Research, Zurich, Kippenberg has uncovered new dynamics that place further unexpected constraints on such systems and just what levels of sensitivity are achievable.

An aerial view of LIGO. The laser interferometer that runs through these massive kilometre scale arms must be incredibly sensitive to detect gravitational waves. But new research suggests another hindrance to such sensitivity. (LIGO)

The team’s work shows particular interest to the interferometers that are used to measure gravitational waves. The sensitivity of these instruments is of vital importance as gravitational waves are incredibly difficult to detect. As these pieces of equipment use disturbances in laser beams shined down their massive, kilometre-scale arms, improving their sensitivity means trying to avoid backaction in electromagnetic waves.

The team’s study — published in the journal Physical Review X — demonstrates that small deviations optical frequency, coupled with deviations in mechanical frequency can lead to mechanical oscillations being amplified out of control. This mimics the physics displayed in a state physics refer to as “degenerate parametric oscillator”.

This behaviour was found by Kippenberg and his team in two radically different systems — one operating with optical radiation, the other operating with microwave radiation. This is a fairly disastrous discovery as it implies that the dynamics are not unique to any particular system, but rather, are common across many such systems.

The researchers from EPFL investigated these dynamics further — tuning the frequencies and demonstrating a perfect match with pre-existing theories. EPFL scientist Itay Shomroni, the paper’s first author, explains: “Other dynamical instabilities have been known for decades and shown to plague gravitational wave sensors.

“Now, these new results will have to be taken into account in the design of future quantum sensors and in related applications such as backaction-free quantum amplification.”