Photonic quantum simulations of coupled $PT$-symmetric Hamiltonians

Abstract

Parity-time ($PT$) symmetric Hamiltonians are generally non-Hermitian and give rise to exotic behaviour in quantum systems at exceptional points, where eigenvectors coalesce. The recent realisation of $PT$-symmetric Hamiltonians in quantum systems has ignited efforts to simulate and investigate many-particle quantum systems across exceptional points. Here we use a programmable integrated photonic chip to simulate a model comprised of twin pairs of $PT$-symmetric Hamiltonians, with each the time reverse of its twin. We simulate quantum dynamics across exceptional points including two- and three-particle interference, and a particle-trembling behaviour that arises due to interference between subsystems undergoing time-reversed evolutions. These results show how programmable quantum simulators can be used to investigate foundational questions in quantum mechanics.

arXiv comment15 pages, 7 figures

References in corpus (28)

• Making Sense of Non-Hermitian Hamiltonians
• Complex Extension of Quantum Mechanics
• Microwave photonics with superconducting quantum circuits
• Universal Linear Optics
• Dynamically encircling exceptional points in a waveguide: asymmetric mode switching from the breakdown of adiabaticity
• Topological energy transfer in an optomechanical system with exceptional points
• Pseudo-Hermitian Representation of Quantum Mechanics
• Quantum simulation of the Dirac equation
• Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms
• Enhanced sensitivity operation of an optical gyroscope near an exceptional point
• Anti-Parity-Time Symmetric Optics via Flying Atoms
• Observation of parity-time symmetry breaking in a single spin system
• Quantum state tomography across the exceptional point in a single dissipative qubit
• Non-Hermitian Ring Laser Gyroscopes with Enhanced Sagnac Sensitivity
• Parity-time-symmetric quantum critical phenomena
• Petermann-factor limited sensing near an exceptional point
• Information Retrieval and Criticality in Parity-Time-Symmetric Systems
• Observation of critical phenomena in parity-time-symmetric quantum dynamics
• The Naimark dilated PT-symmetric brachistochrone
• Direct observation of zitterbewegung in a Bose-Einstein condensate
• Observation of PT-symmetric quantum interference
• Solutions of PT symmetric tight-binding chain and its equivalent Hermitian counterpart
• Local PT symmetry violates the no-signaling principle
• Robust and fragile PT-symmetric phases in a tight-binding chain
• Scalable Implementation of Boson Sampling with Trapped Ions
• PT-symmetric photonic quantum systems with gain and loss do not exist
• A proposal for a scalable universal bosonic simulator using individually trapped ions
• Quantum quench in PT-symmetric Luttinger liquid

Cited by in corpus (8)

• Crossing exceptional points in non-Hermitian quantum systems
• Constraining work fluctuations of non-Hermitian dynamics across the exceptional point of a superconducting qubit
• Non-Hermiticity in quantum nonlinear optics through symplectic transformations
• Operator correlations in a quenched non-Hermitian Luttinger liquid
• Transfer learning from Hermitian to non-Hermitian quantum many-body physics
• $\mathcal{P}\mathcal{T}$-Symmetry breaking in quantum spin chains with exceptional non-Hermiticities
• Order-invariant two-photon quantum correlations in PT-symmetric interferometers
• Necessary condition for information transfer under simulated parity-time-symmetric evolution