Quantum chaos, thermalization and tunneling in an exactly solvable few body system

TL;DR

This paper investigates exactly solvable few-qubit quantum systems modeled as kicked tops, revealing signatures of chaos, ergodicity, and thermalization, and comparing analytical results with experimental data.

Contribution

It provides exact solutions for 3 and 4 qubit kicked top models, showing their ability to exhibit quantum chaos and thermalization signatures.

Findings

Analytical expressions for entanglement entropy and concurrence match ensemble averages.

Agreement with experimental data for short-time correlations.

Identification of a precursor to dynamical tunneling in 4-qubit systems.

Abstract

Exactly solvable models that exhibit quantum signatures of classical chaos are both rare as well as important - more so in view of the fact that the mechanisms for ergodic behavior and thermalization in isolated quantum systems and its connections to non-integrability are under active investigation. In this work, we study quantum systems of few qubits collectively modeled as a kicked top, a textbook example of quantum chaos. In particular, we show that the 3 and 4 qubit cases are exactly solvable and yet, interestingly, can display signatures of ergodicity and thermalization. Deriving analytical expressions for entanglement entropy and concurrence, we see agreement in certain parameter regimes between long-time average values and ensemble averages of random states with permutation symmetry. Comparing with results using the data of a recent transmons based experiment realizing the 3-qubit case, we find agreement for short times, including a peculiar step-like behaviour in correlations of some states. In the case of 4-qubits we point to a precursor of dynamical tunneling between what in the classical limit would be two stable islands. Numerical results for larger number of qubits show the emergence of the classical limit including signatures of a bifurcation.