In a grandfather clock, a pendulum swings back and forth and this periodic motion is maintained using the energy stored in its suspended weights. This is done with the help of the escapement mechanism, which converts the gravitational energy of the weights into impulses that drive the pendulum, which then moves the clock’s gears, which move its hands.
A group of researchers recently designed a quantum version of the pendulum clock. According to their new study, published in Physical Review A, this quantum pendulum clock can operate autonomously and is more accurate than previous quantum clocks.
A quantum analog to the grandfather clock
While the quantum version may not look much like your typical grandfather clock, the mechanism is similar. In the quantum version, a single atom acts as the escapement mechanism. Instead of converting the energy of weights to drive a classical pendulum, the atom cycles through three energy states, absorbing energy from temperature fluctuations and emitting photons at intervals that drive oscillations in the quantum clock.
The atom is placed between two very small mirrors, one of which can move back and forth, therefore acting as a pendulum. The emitted photon bounces between the mirrors, transmitting energy to the oscillating mirror to make it move. Here, the photon plays a part in the weights. The team says the mechanical resonator (the mirror) is driven by the photons, which compensate for the energy loss from friction and sustain the periodic motion.
“Ideally, for a strong enough optomechanical coupling, a single cavity photon can displace the mechanical oscillator enough to bring the cavity out of resonance such that the injection of a second photon is suppressed. Once the photon leaks out of the cavity, the mechanical restoring force brings the cavity back to resonance, favoring the injection of the next photon into the cavity. This autonomous self-regulating mechanism can attain self-sustained mechanical oscillations,” explain the study authors.
Overcoming thermodynamic uncertainty relations
Normally, the thermodynamic uncertainty relation (TUR) sets limits on clock accuracy in classical systems. The TUR creates a fundamental trade-off between the accuracy of a clock and the energetic cost (in terms of entropy production) required to run it. This means that a more accurate clock requires more dissipated heat. However, the study authors say that most clocks that are used for timekeeping actually rely on oscillatory degrees of freedom, and the TUR does not apply to these. But, the TUR can still be used as a benchmark to characterize performance.
The team analyzed the accuracy and performance using both analytical and numerical methods. The accuracy was defined as the average number of ticks before the clock is off by one tick. They found that the pendulum clock violates the TUR and is thus more accurate for a given entropy production than other autonomous clocks.
The study authors write, “As the cold temperature is decreased, we find that both the entropy production as well as the accuracy increase. The accuracy increases faster, resulting in a violation of the TUR, before it plateaus. Once the cold temperature becomes sufficiently small to suppress unwanted transitions, a further decrease only increases dissipation but does not benefit the accuracy.”
Transitions to the classical realm
Interestingly, the team also found that when they add more emitters (atoms), the clock behaves more like a classical pendulum clock, but also becomes more accurate. Noise is reduced and the operation becomes more deterministic. Because increasing the number of emitters coupled to the cavity steadily transitions the system into the classical regime, the TUR limits begin to establish themselves again.
“As expected, the increased accuracy that is obtained by increasing M comes at the cost of an increased entropy production. We anticipate a linear scaling N ∝ M. The accuracy is also anticipated to scale linearly in the number of emitters N ∝ M. We thus expect the TUR violations to persist in the limit of large M, where the clock behaves like a macroscopic, classical pendulum clock. For a number of emitters up to M = 6, this is indeed what we observe,” the study authors write.
This work provides a novel way to study the transition from quantum to classical timekeeping, potentially leading to advances in more efficient quantum timekeeping devices and improved noise engineering for quantum technologies.
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Publication details
Matteo Brunelli et al, Quantum mechanical pendulum clock, Physical Review A (2026). DOI: 10.1103/hb36-7m2r
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Quantum pendulum clock overcomes classical accuracy limits and sheds light on quantum to classical transitions (2026, May 28)
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