Investigating the origin of time with trapped ions

TL;DR

This paper explores how internal degrees of freedom in trapped ions can serve as a clock to define time, providing a potential experimental test for concepts in quantum cosmology related to the nature of time.

Contribution

It proposes a detailed experimental method to investigate the emergence of time from quantum correlations in a single trapped ion system.

Findings

Demonstrates how internal degrees of freedom can act as a clock

Provides a feasible experimental setup with trapped ions

Links quantum control experiments to foundational questions in quantum cosmology

Abstract

Even though quantum systems in energy eigenstates do not evolve in time, they can exhibit correlations between internal degrees of freedom in such a way that one of the internal degrees of freedom behaves like a clock variable, and thereby defines an internal time, that parametrises the evolution of the other degrees of freedom. This situation is of great interest in quantum cosmology where the invariance under reparametrisation of time implies that the temporal coordinate dissapears and is replaced by the Wheeler-DeWitt constraint. Here we show that this paradox can be investigated experimentally using the exquisite control now available on moderate size quantum systems. We describe in detail how to implement such an experimental demonstration using the spin and motional degrees of freedom of a single trapped ion.