Implementation of a coherent feedback clock using superconducting resonators

Clocks play an integral part in a variety of applications but have recently drawn interest in the context of fundamental questions such as the connection between time and thermodynamics and the limits of time keeping. From a thermodynamic point of view, a clock is a nonlinear dissipative system that relies on the increase in entropy to keep track of time. It was recently shown that the resolution of a periodic clock is directly proportional to the energy dissipated per cycle. A good clock, both classical and quantum, therefore, necessitates a high rate of energy dissipation.

Here, we present the realisation of a new type of periodic quantum clock, based on coherent feedback in a system of coupled resonators. The absence of measurement-induced noise allows investigating the inherent quantum noise of the system and its effects on the clock properties.

We implement the coherent feedback clock on a superconducting circuit consisting of two coupled high-Q coplanar resonators, where one is rendered nonlinear by a Josephson junction embedded in the centre conductor. This provides the nonlinearity necessary for a periodic clock. We show the existence of limit cycles in the quantum regime, where quantum fluctuations become the dominant source of noise, and demonstrate the applicability of the system as a new type of quantum clock. Specifically, we show the relation between dissipated energy and clock resolution, and how quantum fluctuations in the feedback cycle affect the clock tick accuracy.

In addition, our clock is a natural candidate for the implementation of spiking neural networks, a novel deep learning model that mimics the behaviour of biological neurons and shows promising advantages in dynamic learning tasks compared to conventional perceptron models.