Quantum simulation of a general anti-PT-symmetric Hamiltonian with a trapped ion qubit

TL;DR

This paper demonstrates the first quantum simulation of an anti-PT-symmetric Hamiltonian using a trapped ion qubit, revealing unique dynamics and phase transitions relevant for quantum information processing.

Contribution

It implements and characterizes an anti-PT-symmetric Hamiltonian in a single trapped ion, a significant step in observing anti-PT symmetry in quantum systems.

Findings

Observation of anti-PT phase transition via eigenvalue mapping

Quantum state tomography of the anti-PT system

Implementation of anti-PT Hamiltonian with microwave and optical control

Abstract

Non-Hermitian systems satisfying parity-time (PT) symmetry have aroused considerable interest owing to their exotic features. Anti-PT symmetry is an important counterpart of the PT symmetry, and has been studied in various classical systems. Although a Hamiltonian with anti-PT symmetry only differs from its PT-symmetric counterpart in a global $\pm$ i phase, the ways they change information and energy with the enivronment are completely different, suggesting an essential different dynamics in anti-PT-symmetric systems from their PT -symmetric variants. Moreover, theortical works have shown that qubits with anti-PT-symmetric Hamiltonians (anti-PT-symmetric qubits) have superior decoherence properties over Hermitian qubits, as well as PT-symmetric ones. So far, the observation of anti-PT symmetry in individual quantum systems remains elusive. Here, we implement an anti-PT -symmetric Hamiltonian of a single qubit in a single trapped ion by a designed microwave and optical control-pulse sequence. We characterize the anti-PT phase transition by mapping out the eigenvalues at different dissipation rates. The full inforamtion of the quantum state is also obtained by quantum state tomography. Our work allows quantum simulation of genuine open-system feature of an anti-PT-symmetric system, which paves the way for utilizing non-Hermitian properties for quantum information processing.