Experimental simulation of the parity-time symmetric dynamics using photonic qubits

Wei-Chao Gao,Lu Liu,Tie-Jun Wang,Chuan Wang,Chao Zheng

doi:10.1364/oe.405815

Abstract

The concept of parity-time (PT) symmetry originates from the framework of quantum mechanics, where if the Hamiltonian operator satisfies the commutation relation with the parity and time operators, it shows real energy spectrum. Recently, PT symmetry was introduced into various systems, such as optics, electronic circuits, acoustics, and other classical fields to further study the dynamical behaviors of the Hamiltonian and the energies. To focus on the dynamical evolution of the quantum state, here we experimentally studied the dynamical evolution of a two-level quantum system under the PT symmetric Hamiltonian using single-photon system. By enlarging the system using ancillary qubit and encoding the subsystem under the non-Hermitian Hamiltonian with post-selection, the evolution of the state can be characterized with a high fidelity. Owing to the effectively operation of the dilation method, our work provides a route for further exploiting the exotic properties of PT symmetric Hamiltonian for quantum simulation and quantum information processing.

Highlights

The Hermiticity of the operators is considered as one of the fundamental axioms of quantum mechanics, of which guarantees the real energy spectra of the quantum system and the unitary evolution with conserved probability [1, 2]
The concept of PT symmetry was first experimentally observed in electrical circuits system [7, 8], and extended to other systems which usually consists of balanced gain and loss, such as the optical waveguides [9,10,11,12,13], mechanical systems [14], optical microcavities [15, 16], and optical systems with atomic media [17,18,19]
Considering the practical condition in our experiment, the successfully evolved subspace is only a simulation of the PT -symmetric system as a part of the full Hermitian system on account of: 1) Observing the evolution of the broken -PT -symmetry zone is poor at our optical system; 2) Most quantum computation and quantum simulation problems can be implemented in the unbroken -symmetry zone, such as no-signalling principle [26]

Summary

INTRODUCTION

The Hermiticity of the operators is considered as one of the fundamental axioms of quantum mechanics, of which guarantees the real energy spectra of the quantum system and the unitary evolution with conserved probability [1, 2]. The concept of PT symmetry was first experimentally observed in electrical circuits system [7, 8], and extended to other systems which usually consists of balanced gain and loss, such as the optical waveguides [9,10,11,12,13], mechanical systems [14], optical microcavities [15, 16], and optical systems with atomic media [17,18,19] These systems exhibit the properties of conservative systems. Unambiguously observing the evolution of a quantum state (qubit) under the the PT -symmetric Hamiltonian has not been realized which is critical for further applications of PT -symmetric theory and providing great insight for the fundamentals of quantum physics [3]. Our results show that the evolution of high fidelity of the qubit (quantum state) governed by PT -symmetric system reveals the exotic properties of the PT theory and provides a route for further exploiting PT -theory framework to investigate the fundamental problems

METHODS

SUMMARY