Logarithmic quantum time crystal

TL;DR

This paper introduces a many-boson system that forms a quantum time crystal with a period logarithmically proportional to the number of particles, making it experimentally observable even in large systems.

Contribution

It constructs a ground-state-based quantum time crystal with a logarithmic period dependence on particle number, advancing understanding of time crystals in many-boson systems.

Findings

Quantum time crystal with period T~logN

Ground states become infinitely degenerate in the thermodynamic limit

Experimental proposals for observing the time crystal

Abstract

We investigate a time-independent many-boson system, whose ground states are quasi-degenerate and become infinitely degenerate in the thermodynamic limit. Out of these quasi-degenerate ground states we construct a quantum state that evolves in time with a period that is logarithmically proportional to the number of particles, that is, T~logN. This boson system in such a state is a quantum time crystal as it approaches the ground state in the thermodynamic limit. The logarithmic dependence of its period on the total particle number N makes it observable experimentally even for systems with very large number of particles. Possible experimental proposals are discussed.