Quantum advantages in timekeeping: dimensional advantage, entropic advantage and how to realise them via Berry phases and ultra-regular spontaneous emission

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Quantum advantages in timekeeping: dimensional advantage, entropic advantage and how to realise them via Berry phases and ultra-regular spontaneous emission

Authors

Arman Pour Tak Dost, Mischa P. Woods

Abstract

When an atom is in an excited state, after some amount of time, it will decay to a lower energy state emitting a photon in the process. This is known as spontaneous emission. It is one of the three elementary light-matter interactions. If it has not decayed at time $t$, then the probability that it does so in the next infinitesimal time step $[t, t+\delta t]$, is $t$-independent. So there is no preferred time at which to decay -- in this sense it is a random process. Here we show, by carefully engineering this light-matter interaction, that we can associate it with a clock, where the matter constitutes the clockwork and the spontaneous emission constitutes the ticking of the clock. In particular, we show how to realise the quasi-ideal clock. Said clock has been proven -- in an abstract and theoretic sense -- to be the most accurate clock permissible by quantum theory, with a polynomial enhancement in precision over the best stochastic clock of the same size. Our results thus demonstrate that the seemingly random process of spontaneous emission can in actual fact, under the right circumstances, be the most regular one permissible by quantum theory. To achieve this we use geometric features and flux-loop insertions to induce symmetry and Berry phases into the light-matter coupling. We also study the entropy the clock produces per tick and show that it also possesses a quantum advantage over that generated from the previously known semi-classical clocks in the literature.

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Thank you for your submission. Can you elaborate at the layman/intuitive level why spontaneous emission would be more accurate than conventional atomic clocks, which operate  based on the consistent oscillation of atoms, such as cesium or rubidium, when they are exposed to a specific frequency of microwave radiation. At a layman level, they are exceptionally precise because the frequency of these atomic oscillations is an inherent property of the atom and is largely unaffected by external conditions.

Spontaneous emission on the other hand is due to the inherent random process of photon emission. While it can be predicted statistically, the exact moment when a specific atom will undergo spontaneous emission is fundamentally unpredictable, making it a counter-intuitive platform for the precise timekeeping required in a clock.
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mischa-woods

The errors in atomic clocks come from 2 contributions: the act of measuring the oscillating atomic state and the linewidth and drift of the laser. Given the total number of degrees of freedom actively used in the dynamics, the precision of the photonic decay in our paper will in principle be more accurate. In practice noise will make both atomic clocks and our approach less precise, so which is better depends on your experimental abilities to implement them with minimal noise.    You are correct in saying that textbook spontaneous emission is an inherent random process, but the derivation assumes conventional states of matter. What we show, is that if unconventional states are used, involving induced Berry phases, that it can in fact, be the most precise process possible.   Another important difference between our spontaneous emission process and an atomic clock is that our process just decays once, i.e. produces one "tick", where as an atomic clock produces many ticks in a sequential and continuous fashion.   The connection between our spontaneous emission process and that of nature is explained in the paper in more detail.

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scicastboard

Thanks for your explanation. It sounds like if indeed Berry phase physics makes spontaneous emission less spontaneous, there could be other applications of it, apart from clocks. Say, take Gamow's  alpha-decay - a textbook example of tunneling of a metastable state experiencing radioactive decay. If you can lift the problem  to higher dimensions, add proper spin-orbit terms to enrich it with Berry phase physics, perhaps this textbook problem can take a new interesting form? 

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