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How can the strange properties of quantum particles be exploited to perform extremely accurate measurements? This question is at the heart of the research field of quantum metrology. One example is the atomic clock, which uses the quantum properties of atoms to measure time much more accurately than would be possible with conventional clocks.

However, the fundamental laws of quantum physics always involve a certain degree of uncertainty. Some randomness or a certain amount of statistical noise has to be accepted. This results in fundamental limits to the accuracy that can be achieved. Until now, it seemed to be an immutable law that a clock twice as accurate requires at least twice as much energy.

Now a team of researchers from TU Wien, Chalmers University of Technology, Sweden, and the University of Malta has demonstrated that special tricks can be used to increase accuracy exponentially. The crucial point is using two different time scales—similar to how a clock has a second hand and a minute hand.

The paper is in the journal Nature Â鶹ÒùÔºics.

What exactly is a clock?

"We have analyzed in principle which clocks could be theoretically possible," says Prof. Marcus Huber from the Atomic Institute at TU Wien. "Every clock needs two components: first, a time base generator, such as a pendulum in a pendulum clock, or even a quantum oscillation. And second, a counter—any element that counts how many time units defined by the time base generator have already passed."

The time base generator can always return to exactly the same state. After one complete oscillation, the pendulum of a pendulum clock is exactly where it was before. After a certain number of oscillations, the cesium atom in an atomic clock returns to exactly the same state it was in before. The counter, on the other hand, must change—otherwise the clock is useless.

"This means that every clock must be connected to an irreversible process," says Florian Meier from TU Wien. "In the language of thermodynamics, this means that every clock increases the entropy in the universe; otherwise, it is not a clock." The pendulum of a pendulum clock generates a little heat and disorder among the air molecules around it, and every laser beam that reads the state of an atomic clock generates heat, radiation and thus entropy.

"We can now consider how much entropy a hypothetical clock with extremely high precision would have to generate—and, accordingly, how much energy such a clock would need," says Prof. Huber. "Until now, there seemed to be a linear relationship: if you want a thousand times the precision, you have to generate at least a thousand times as much entropy and expend a thousand times as much energy."

Quantum time and classical time

However, the research team at TU Wien, together with the Austrian Academy of Sciences (ÖAW) in Vienna and the teams from Chalmers University of Technology, Sweden, and the University of Malta, has now shown that this apparent rule can be circumvented by using two different time scales.

"For example, you can use particles that move from one area to another to measure time, similar to how grains of sand indicate the time by falling from the top of the glass to the bottom," says Meier. You can connect a whole series of such time-measuring devices in series and count how many of them have already passed through—similar to how one clock hand counts how many laps the other clock hand has already completed.

"This way, you can increase accuracy, but not without investing more energy," says Prof. Huber. "Because every time one clock hand completes a full rotation and the other clock hand is measured at a new location—you could also say every time the environment around it notices that this hand has moved to a new location—the entropy increases. This counting process is irreversible."

However, quantum physics also allows for another kind of particle transport: The particles can also travel through the entire structure, i.e. across the entire clock dial, without being measured anywhere. In a sense, the particle is then everywhere at once during this process; it has no clearly defined location until it finally arrives—and only then is it actually measured, in an irreversible process that increases entropy.

Like second and minute clock hands

"So we have a fast process that does not cause entropy—quantum transport—and a slow one, namely the arrival of the particle at the very end," explains Yuri Minoguchi of TU Wien. "The crucial thing about our method is that one hand behaves purely in terms of quantum physics, and only the other, slower hand actually has an entropy-generating effect."

The team has now been able to show that this strategy enables an exponential increase in accuracy per increase in entropy. This means that much higher precision can be achieved than would have been thought possible according to previous theories.

"What's more, the theory could be tested in the real world using superconducting circuits, one of the most advanced quantum technologies currently available," says Simone Gasparinetti, co-author of the study and leader of the experimental team at Chalmers.

"This is an important result for research into high-precision quantum measurements and the suppression of unwanted fluctuations," says Prof. Huber, "and at the same time it helps us to better understand one of the great unsolved mysteries of physics: the connection between quantum physics and thermodynamics."