# Exploring quantum chaos with a single nuclear spin

## TL;DR

This paper proposes using a single nuclear spin in silicon to experimentally observe quantum chaos, enabling detailed study of the quantum-classical boundary and dynamical tunneling with long coherence times.

## Contribution

It introduces a realistic method to realize a quantum chaotic system using a nuclear spin in silicon, facilitating direct observation of quantum chaos phenomena.

## Key findings

- Signatures of chaos are expected with feasible parameters.
- The system allows exploration of quantum decoherence and classical chaos.
- Potential to observe dynamical tunneling in a single-particle quantum system.

## Abstract

Most classical dynamical systems are chaotic. The trajectories of two identical systems prepared in infinitesimally different initial conditions diverge exponentially with time. Quantum systems, instead, exhibit quasi-periodicity due to their discrete spectrum. Nonetheless, the dynamics of quantum systems whose classical counterparts are chaotic are expected to show some features that resemble chaotic motion. Among the many controversial aspects of the quantum-classical boundary, the emergence of chaos remains among the least experimentally verified. Time-resolved observations of quantum chaotic dynamics are particularly rare, and as yet unachieved in a single particle, where the subtle interplay between chaos and quantum measurement could be explored at its deepest levels. We present here a realistic proposal to construct a chaotic driven top from the nuclear spin of a single donor atom in silicon, in the presence of a nuclear quadrupole interaction. This system is exquisitely measurable and controllable, and possesses extremely long intrinsic quantum coherence times, allowing for the observation of subtle dynamical behavior over extended periods. We show that signatures of chaos are expected to arise for experimentally realizable parameters of the system, allowing the study of the relation between quantum decoherence and classical chaos, and the observation of dynamical tunneling.