Time in Quantum Mechanics and Thermodynamics

Precise and stable clock technology underwrites economic growth and security. Synchronising telecommunication networks and power grids and time-stamping of transactions and data transmissions is critical national infrastruture. Precise timekeeping is crucial for satellite navigation and communication systems. The physical systems we engineer as clocks are are driven dissiaptive systems. necessarily irreversible and thus subject to uncertainty. In the classical case the uncertainty arises from thermal noise. In the quantum case the uncertainty arises from the nature of quantum measurement. Periodic clocks exhibit self-sustained oscillations known as limit cycles, which are ubiquitous in open, driven, stable, dissipative systems.  We present a number of examples of classical quantum clocks and highlight the key role played by measurement.  

We address the physical limits to clocks using stochastic thermoynamics and kinetic uncertainty relations derived from the quantum trajectories of  continuous readout of a driven quantum system.  As examples we discuss artomic clocks, superconducting circuit clocks   and superradiant clocks.  We introduce a novel, fully quantum clock using a driven superconducting oscillator in the quantum regime and coherent quantum feedback.  We show  that the accuracy of this clock is higher compared to the clock implemented with the classical measurement feedback. An experiement using two superconducting cavities with incorporated Josephson junctions and microwave circulators for the realisation of the quantum feedback will be described.  

It is the prevailing paradigm in contemporary physics to model the dynamical evolution of physical systems in terms of a real parameter conventionally denoted as `t  ' (ittle tee). We typically call such dynamical models `laws of nature' and t  we call `physical time'. The  examples discussed here illustrate  that physical time  is  better defined in terms of physical clock events that coordinate local coincidences.