Precision measurement

Sensing past the quantum limit

Quantum physics ultimately constrains how well sensors of position, speed and acceleration can perform. A hybrid quantum system that avoids these constraints could give rise to improved sensor technologies. See Letter p.191

In quantum physics, even the act of looking can have dramatic consequences. For instance, it can kill the cat in Schrödinger's classic thought experiment. This feature limits the performance of sensors such as gravitational-wave detectors and high-precision accelerometers. On page 191, Møller et al.1 show that these limits can be avoided in engineered quantum systems that have a 'negative-mass' component — one that, when pushed in a particular direction, counter-intuitively accelerates in the opposite direction. The authors' demonstration paves the way for sensor technologies that perform beyond the usual limits of quantum physics.

Motion sensors are a fundamental technology. They can tell us where we are and how fast we are moving, and they allow us to explore the microscopic world — from the behaviour of biomolecules such as DNA down to atomic and subatomic scales. When applied in gravitational-wave detectors, they even offer glimpses into the dynamics of massive objects such as black holes that are more than a billion light years from Earth2.

Nanomechanical motion sensors consist of a mechanical element that vibrates (oscillates) in response to stimuli — much like a diving board, but reduced in size by a factor of about a million. This response is usually analysed by reflecting an electromagnetic field (such as light, radio waves or microwaves) from the sensor and detecting the field using a position-sensitive detector. In terms of technological applications3,4, nanomechanical sensors are used as clocks, filters and accelerometers in portable electronic devices such as mobile phones, and as a tool for biomedical diagnostics that can identify the presence of even a single biomolecule.

With advances in nanofabrication and measurement science, nanomechanical sensors have reached the point at which their performance can be strongly influenced by quantum effects. When an electromagnetic field reflects from the surface of such a sensor, momentum is transferred through a force called radiation pressure. Although radiation pressure is not appreciable in our everyday lives, it explains, for instance, why comet tails point away from the Sun, and is the basis of proposals to propel spacecraft using solar sails. Quantum physics tells us that the energy of an electromagnetic field is divided into discrete units (photons). As a consequence of this granularity, nanomechanical sensors are subjected to a series of momentum 'kicks' that are randomly distributed in time — one kick for every photon that reflects from the sensor's surface. This introduces a level of uncertainty when analysing the motion of such sensors, termed quantum back-action noise5.

It turns out that back-action noise is a fundamental feature not only of nanomechanical sensing, but also of quantum measurement in general. It is a consequence of the Heisenberg uncertainty principle, which tells us that it is not possible to know both the exact position and the exact momentum of an object at any one time. Given the unbending nature of this principle, one might think that back-action noise is absolute. However, it can be avoided. For instance, carefully designed stroboscopic measurements6 can provide the position of an object without revealing any information about its momentum. In this case, the uncertainty principle does not come into play. Moreover, the principle does not apply directly to measurements performed collectively on more than one object. Therein lies the trick used by Møller and colleagues.

The authors' work can be understood by considering a simple thought experiment in which laser light is reflected from two mechanical oscillators (mirrors attached to springs) in an effort to determine the oscillators' separation (Fig. 1a). Each oscillator receives momentum kicks from the photons in the laser beam, but because every photon that hits the first oscillator also hits the second, the momentum kicks are correlated — they add together, causing fluctuations in the oscillators' separation. However, if it were possible to replace one oscillator with an object that has negative mass, such an object would be pulled, rather than pushed, by the reflected photons (Fig. 1b). The momentum kicks would be anti-correlated, their effect on the separation would cancel, and the back-action noise on the collective measurement would be avoided.

Figure 1: Quantum back-action noise avoided.

a, When laser light is reflected from a pair of mirrors attached to springs, the light exerts a force on the mirrors (blue arrows). The mirrors accelerate (red arrows) in the same direction as the force. The probabilistic nature of photons means that the applied force varies randomly with time. Consequently, when the light is used to determine the separation between the mirrors, the measured separation fluctuates — a phenomenon known as quantum back-action noise. b, When light is reflected from a hypothetical mirror that has negative mass, the mirror accelerates in the opposite direction to the applied force. Therefore, when one of the mirrors in a is replaced by a negative-mass mirror, the separation between the mirrors is unaffected by the measurement process. Møller et al.1 create the equivalent of a negative-mass mirror using a cloud of caesium atoms, and provide experimental proof that such a method allows quantum back-action noise to be avoided.

But this sounds like science fiction. How can one make an object that has negative mass? Although the concept is counter-intuitive, both theory and experiments have shown that oscillators can be engineered to behave as if they have negative mass, without violating any fundamental laws of physics7,8,9.

Møller et al. have provided the experimental proof that such an oscillator allows quantum back-action noise to be avoided. They created the equivalent of a negative-mass oscillator using the angular-momentum properties of a cloud of caesium atoms. Each electron in an atom carries a form of quantum angular momentum known as spin. Much as a spinning top aligns with a gravitational field, an electron's spin aligns with an applied magnetic field. It then acts like an oscillator — displace its orientation and, in attempting to reorient itself, it oscillates. The authors used a method called optical pumping to invert the orientation of the atoms' combined spin. They then demonstrated that this spin behaves like a negative-mass oscillator.

The authors used laser light to interface this spin oscillator with a conventional mechanical oscillator (see Fig. 2a of the paper1). The latter consisted of a silicon nitride membrane, which the authors placed in a device called an optical cavity to enhance the membrane's interaction with light. Just as in our simple thought experiment, observing the light from the real experiment provides a collective measurement of the two oscillators. Møller et al. showed that this measurement allows quantum back-action noise to be suppressed by 34% with respect to an experiment in which only a conventional mechanical oscillator is used.

Similar levels of back-action-noise suppression were reported last year10, also using collective measurements, but in a system of two conventional mechanical oscillators in a superconducting electrical circuit. In both of these quite different experiments, the reduction in back-action noise with respect to standard techniques was relatively modest1,10. Moreover, to achieve any suppression at all, the conventional mechanical oscillators needed to be cooled to temperatures of a few kelvin, limiting potential applications. Nevertheless, these experiments clearly demonstrate that specially engineered collective measurements allow quantum back-action noise to be avoided.

Møller and colleagues' work provides a path towards more-precise sensors of acceleration, force, gravity and any other stimulus that can be coupled to the motion of a mechanical element. In a particularly topical application, their approach could be used in next-generation gravitational-wave interferometers, potentially improving our understanding of the early Universe. The authors' experiments are also a key step towards generating atoms and macroscopic mechanical elements that are entangled (correlated in a non-classical way). Such entangled states could be used for future quantum communication and computation systems.Footnote 1


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Correspondence to Warwick P. Bowen.

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Baker, C., Bowen, W. Sensing past the quantum limit. Nature 547, 164–165 (2017).

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