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.
Highlights
Dirac Hermiticity of a Hamiltonian has been a tenet of quantum theory since its inception
This constraint guarantees real eigenvalues, orthogonal eigenstates, and a unitary time evolution; it reflects the dynamics of an isolated system
Over the past two decades, non-Hermitian Hamiltonians that are symmetric under combined parity (P) and time-reversal (T ) transformations were extensively investigated, first mathematically [1,2] and experimentally in classical wave systems [3,4]
Summary
Dirac Hermiticity of a Hamiltonian has been a tenet of quantum theory since its inception This constraint guarantees real eigenvalues, orthogonal eigenstates, and a unitary time evolution; it reflects the dynamics of an isolated system. The. overall evolution in this model allows single- or many-particle excitations to tunnel between the twin systems, with a probability that scales with the non-Hermiticity of the simulated Hamiltonians. Overall evolution in this model allows single- or many-particle excitations to tunnel between the twin systems, with a probability that scales with the non-Hermiticity of the simulated Hamiltonians This construction permits the experimental investigation of states superposed across opposite directions of time in the context of non-Hermitian Hamiltonians. Combined with the current advances in photonic technologies, these demonstrations point towards the inclusion of nonHermitian simulations in the realm of quantum technologies
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