Measurement of time by quantum clocks

A clock is a dynamical system which passes through a succession of states at constant time intervals. If coupled to another system, it can measure the duration of a physical process and even keep a permanent record of it, such as in a time-of-flight experiment or in observing the lifetime of an unstable atom. A clock can also be used to control the duration of a process, e.g., the precession of a spin in a magnetic field which is turned on and off at prescribed times. This article shows how to construct time-independent Hamiltonians describing these possible uses of a quantum clock. As expected, a good time resolution entails a large energy exchange between the clock and the other system, thereby modifying the evolution of the latter. This evolution may even be halted by using a clock which is too precise (this is the quantum analog of Zeno’s paradox).