by Ewan Munro, CTO and Co-Founder of Entropica Labs

Measurement is at the heart of scientific and technological progress. When we can detect and quantify a signal or variable more accurately, new discoveries about nature and how She works often follow. Galileo leveraged the magnifying power of the telescope to study celestial bodies and how they move, paving the way for his successors to write the laws of classical physics. Later, biologists would use the microscope to peek into the workings of living things, leading to the formulation of cell theory.

Measurement devices are physical objects: the laws of physics determine how they work, as well as the accuracy we can achieve with them. Transformative improvements in measurement technologies often happen because a new physical effect is discovered. Just think how electricity dramatically changed how well we could measure temperature. Our previous articles have focused on the second quantum revolution, a game-changing shift in science and technology fuelled by the strange laws of quantum mechanics. Today, we tell the tale of quantum sensing, also known as quantum metrology. As the name suggests, the goal of this trade is to exploit the peculiarities of the quantum world to build new and improved sensors and measuring devices.

Nowadays you don’t have to look far to find news stories about quantum communication or quantum computing. Articles on quantum sensing typically don’t grace the papers as commonly, but this certainly doesn’t mean the technologies are any less groundbreaking. Imagine a world where super-sensitive magnetometers detect tiny electrical signals in the body; where ultra-accurate compasses greatly improve navigation, even underwater; where small local changes in gravity can be detected, revealing information about possible earthquakes or volcanic activity; and where we can measure fundamental physical constants to much greater precision, allowing scientific theories to be tested, and new ones to be discovered.

We’ll introduce three important types of quantum sensor in the sections below. Each is an example of a technology that exploits a different characteristic of quantum mechanics. We’ll first see how quantised energy levels (see our previous article for a more detailed explanation) are used in atomic clocks. Then, we’ll describe how wave interference underpins the workings of atomic interferometers. Finally, we’ll look at how quantum entanglement can be exploited to make ultra-precise measurements.


Legend has it that Galileo — quite the protagonist of this article! — once used his own pulse to measure the back-and-forth swinging of a pendulum at Pisa cathedral. Each successive heartbeat marked the passing of a unit of time, and he was able to make certain observations about the pendulum oscillations thanks to his makeshift ‘clock’. “What’s good enough for science is good enough for me”, you might say. Would you set your agenda by the heartbeat of our dear Tuscan friend?

Let’s think about the defining features of a good clock. Most obviously, you want a clock to “keep time”. Its tick rate should be constant, so that it doesn’t drift and start telling the wrong time. Presumably, when he climbed to the top of the Pisa tower to perform another of his famous experiments, Galileo would have worked up a bit of a sweat. His heart rate would have increased, and — oh dear — your clock just lost time!

But let’s suppose Galileo’s pulse is somehow perfectly constant. As a healthy adult, his heart would beat around once every second. But what do you do if you want to measure milliseconds, or microseconds? You’d need something that ticks much ‘faster’ — something with a much higher frequency.

Finally — and most obviously — Galileo’s heart is not exactly accessible to you. Even if he were still alive, you’d need to set another clock — maybe your own heart — to his pulse, and then use your clock to tell the time. But your heart and his have different sizes, shapes, and contractilities. Even if they appear to be well synchronised at any given instant, they will progressively fall out of harmony because they are not 100% identical ‘devices’.

Alright, so we’ve established that Galileo’s heart isn’t quite as spectacular as his mind. At the same time, we’ve also brought to light some of the important properties of a good clock. As the title of this section suggests, atoms are an excellent ‘device’ for addressing this issues. Let’s explore why.

To begin, what do we mean by the tick rate of an atom? As we explained in our previous article, in the quantum mechanical picture of an atom, an electron can only orbit the nucleus in a discrete set of ways. Each of these motions — which we often call states — has a characteristic energy. To make the electron change its state, you need to give it a photon whose energy is equal to difference between the initial and final state energies. This energy corresponds to a certain photon frequency, and since frequency is simply the number of oscillations in a certain time interval, we can use transitions between two electronic states in an atom as a clock.

More precisely, these atomic transitions are used as frequency standards or frequency references: they are used to synchronise other, more practical clocks that are easier to use or move around with us. To explain why atoms are so suitable for this, let’s address the desirable criteria we highlighted above in reverse order.

All atoms of a given element and isotope are 100% identical. Nature made them that way. In contrast, man-made frequency standards, such as the quartz crystals in your wrist watch, all differ very slightly from one another: we simply don’t have the manufacturing precision to make them absolutely identical.

Secondly, atomic transitions have extremely high frequencies, meaning that their tick rate is very fast. For several decades, the world frequency standard has been a specific transition in the Caesium 133 isotope. Labs in different countries across the globe use this atom to synchronise their clocks. The Caesium reference clock ticks over 9 billion times per second — a frequency in the microwave domain of the electromagnetic spectrum — allowing it to easily resolve very tiny fractions of a second.

Remarkably, researchers are now able to use optical frequency transitions in atoms, which can tick more than 10¹⁵ times per second (that’s a 1 followed by 15 zeros!). This has been enabled by important advances in atomic physics over the years. At the end of our previous article, we explained how quantum systems are highly susceptible to disturbances from their environment. Isolating atoms more effectively from the degrading effects of collisions, heating, and interactions with background radiation, has been a major focus for atomic clock technologies.

Atomic clocks are an essential part of the global positioning system (GPS).

The same isolation and cooling techniques are also key to addressing the first issue we mentioned above. As long as an atom is undisturbed, in a completely clean environment, its tick rate will be perfectly constant. Cutting-edge optical frequency clocks would not drift by more than a tenth of a second over a time interval of over 13 billion years, which is the age of the universe itself!

Optical atomic clocks are still under development, but promise much more precise measurements of time.

So, after all this science, what are atomic clocks actually useful for? For one thing, navigation. Atomic clocks are central to the functioning of GPS. Thanks to their rapid tick rate, very precise time measurements can be made that allow accurate determination of the distance between the satellites and a ground receiver.

In a world increasingly dependent on complex networks, accurate time coordination and time stamping is essential for synchronising, sequencing, and registering the pattern of operations or transactions. Power grids, supercomputers, telecommunications networks, and financial systems are examples whose functionality depends on a high degree of orchestration among their different parts. Atomic clocks can provide this.

And last but not least, atomic clocks are proving useful for fundamental science, such as in the search for elusive dark matter. When scientists have fancy toys, they will invariably use them to go after the deepest questions!


While atomic clocks are based on the existence of quantised energy levels of electrons within atoms, a second approach to quantum sensing exploits the quantum mechanical nature of the atom as a whole — protons and neutrons included. To explain this, we’ll need to take you on a short detour into some of the basic physics of waves.

The defining feature of a wave is that it can exhibit the phenomenon of interference, as illustrated in the figure below. On the left, the two waves shown have their peak amplitudes perfectly lined up. As a result, the net effect is to give a wave of twice the size as the two individual components. Meanwhile, on the right the peaks of one wave are perfectly aligned with the troughs of another wave, and the net result is a cancellation. We refer to the two cases as constructive and destructive interference, respectively.

If you look at the figure for a moment, you’ll realise that we can easily turn constructive interference into destructive interference. Suppose we displace the upper wave in (a) to the left, giving it what we refer to as a “phase shift”. If this phase shift is of the right size, we can align the peaks of the top wave with the troughs of the bottom wave, and we get precisely the situation shown in (b).

Well, it’s not exactly very interesting if we create the phase shift ourselves! Instead, suppose there is some physical effect beyond our control — perhaps a force — that causes the phase shift. Typically, the size of the shift will depend on how strongly the force acts. By observing the interference pattern of a shifted and unshifted wave, we can obtain information about the strength of the force.

What we have just described is the notion of interferometry — literally, using wave interference as a measurement technique. Interferometry is extensively used for technologies in domains as broad as telecommunications, medical imaging, navigation, and construction. “Fine, but what does this have to do with quantum technologies?”, we hear you ask. After all, waves are a central part of classical physics too.

To explain this, we invite you to make the acquaintance of one of quantum theory’s major tenets: wave-particle duality. As the name implies, at the microscopic level of nature the distinction between waves and particles becomes blurred. Light — which we usually think of as a wave — actually comes in small bundles of energy known as photons, as Planck and Einstein famously taught us. Similarly, electrons — which we naively assume to be particles — can behave like waves, as was first postulated by Louis de Broglie in 1924. Remarkably, experiments have shown that even ‘particles’ as large as molecules of 60 atoms of Carbon can display wave interference.

You can probably now appreciate what we mean by atom interferometry. The wave behaviour of atoms — a fundamentally quantum phenomenon — is exploited to make measurements of a particular physical quantity. To give a concrete example that is relevant to real-world applications being pursued now, let’s suppose we want to measure gravity. Atoms are particularly good for this because they have physical mass, and therefore experience the gravitational force. In contrast, photons are massless, and are not suitable for sensing gravity.

The key idea is that gravity imparts a phase shift on an atomic matter wave, and this phase shift is manifest in the modification of an interference pattern. Our measuring apparatus quantifies this phase shift. Provided we then have a theory connecting the shift to the underlying gravitational pull on the atom, we are indirectly measuring gravity itself.

Of course, as the figure above illustrates, we need two beams to create an interference pattern that reflects the phase differences in the paths they take. To achieve this, we can illuminate the atoms with laser light. If an atom absorbs a photon from the laser, it will experience a small ‘kick’ in its momentum, and it will follow a different path from an atom that does not absorb a photon. When they recombine, the interference pattern of the atoms that followed the upper and lower paths reflects the difference in the gravitational strength along the two trajectories. This is illustrated in the figure below.

Besides the fact that they experience gravity, atoms offer another key advantage over photons for sensing. The wavelength (the distance between two consecutive wave peaks) of an atom is typically several orders of magnitude smaller than that of light. When performing interferometry, it is the wavelength that sets the basic limit on how finely we can resolve the difference in two path lengths (i.e., the phase difference). Since atoms have very small wavelengths, they can be used to measure with a far greater level of precision that light.

Atom interferometers have always attracted military interest, since they could facilitate underwater navigation for submarines, where GPS does not work. Likewise, the technology could be used in underwater oil and gas exploration, or in studying the seafloor.

Similarly, there is significant interest in using atom interferometry for underground mapping. Civil engineering and infrastructure works could be made cheaper and less disruptive by improved planning, with atom interferometry furnishing accurate information on the location of pipes, cables, and defects in the ground.


Erwin Schrodinger — one of the founding fathers of quantum mechanics, and famously a cat lover — once said “I would not call [entanglement] one but rather the characteristic trait of quantum mechanics”. Strong words indeed. We introduced the basic idea of quantum entanglement in a previous article. In a nutshell, entanglement is a form of correlation between different parts of a many-body quantum system (a system with — for example — multiple atoms or qubits). These correlations can be stronger than classical physics would allow, as was shown in seminal work by John Bell.

Atomic clocks and atomic interferometers do not necessarily rely on quantum entanglement. But if entanglement is so central to quantum physics, surely it must also bring something to the table for quantum sensing? Indeed it does. Here we’ll simply give the high-level intuition, and describe a few important examples.

Commonly, when we are studying a variable of interest, we make several repeated measurements of it to get an average value. This average has some associated uncertainty, or standard deviation. If we make N measurements, this standard deviation is typically reduced by a factor of √N. The more times you measure the quantity, the better your statistics become.

But if you use entanglement, you might be able to do better still. With an entangled state of N particles (as opposed to a set of N independent particles), the uncertainty can theoretically be reduced by a factor of N, not √N. This fact — which has been observed in experiment for a small number of entangled particles — has been the source of much excitement. What could we do with such precise sensors?

If you have a supersensitive detector, its killer app is surely in measuring the smallest effects you could possibly imagine. This might mean be the tiny disturbances in space as a gravitational wave goes by; or a small change in a magnetic field, perhaps that of the Earth itself; or even overcoming the shortcomings of conventional radar systems, to build a quantum radar for detecting stealth planes.

To date, entanglement-based sensing technologies are not at the level of commercial readiness as atomic clocks or atom interferometers. The challenge is in producing and maintaining entanglement in large quantum systems for long enough to perform the measurements of interest. Highly entangled systems are very susceptible to disturbances from the environment: any theoretical increase in precision might quickly be overwhelmed by noise from the surroundings.

This article completes our introductory series to the second quantum revolution,and its three major strands: quantum communication, quantum computing, and quantum sensing. The following articles will take a closer look at some of the applications of these technologies, and how they are set to disrupt a number of important industries.

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