Conserved quantities in parity-time symmetric systems

Abstract

Conserved quantities such as energy or the electric charge of a closed system, or the Runge-Lenz vector in Kepler dynamics are determined by its global, local, or accidental symmetries. They were instrumental to advances such as the prediction of neutrinos in the (inverse) beta decay process and the development of self-consistent approximate methods for isolated or thermal many-body systems. In contrast, little is known about conservation laws and their consequences in open systems. Recently, a special class of these systems, called parity-time ($\mathcal{P}\mathcal{T}$) symmetric systems, has been intensely explored for their remarkable properties that are absent in their closed counterparts. A complete characterization and observation of conserved quantities in these systems and their consequences is still lacking. Here we present a complete set of conserved observables for a broad class of $\mathcal{P}\mathcal{T}$-symmetric Hamiltonians and experimentally demonstrate their properties using single-photon linear optical circuit. By simulating the dynamics of a four-site system across a fourth-order exceptional point, we measure its four conserved quantities and demonstrate their consequences. Our results spell out non-local conservation laws in non-unitary dynamics and provide key elements that will underpin self-consistent analysis of non-Hermitian quantum many-body systems that are forthcoming.

arXiv comment7 pages, 3 figures

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Cited by in corpus (23)

• Non-Hermitian Topology and Exceptional-Point Geometries
• Experimental demonstration of coherence flow in $\mathcal{P}\mathcal{T}$- and anti-$\mathcal{P}\mathcal{T}$-symmetric systems
• Quantum information dynamics in a high-dimensional parity-time-symmetric system
• Anomalous-order exceptional point and non-Markovian Purcell effect at threshold in one-dimensional continuum systems
• Reservoir-assisted symmetry breaking and coalesced zero-energy modes in an open PT-symmetric Su-Schrieffer-Heeger model
• Pseudo-Hermiticity protects the energy-difference conservation in the scattering
• Conserved quantities, exceptional points, and antilinear symmetries in non-Hermitian systems
• Observation of two PT transitions in an electric circuit with balanced gain and loss
• On-demand Parity-Time symmetry in a lone oscillator through complex, synthetic gauge fields
• Extension of Noether's theorem in PT-symmetric systems and its experimental demonstration in an optical setup
• Connecting active and passive $\mathcal{P}\mathcal{T}$-symmetric Floquet modulation models
• Unitary Scattering Protected by Pseudo-Hermiticity
• The effect of thermal photons on exceptional points in coupled resonators
• Formation of Exceptional Points in pseudo-Hermitian Systems
• Feasibility and method of multi-step Hermitization of crypto-Hermitian quantum Hamiltonians
• Generating high-order exceptional points in coupled electronic oscillators using complex synthetic gauge fields
• Linear Response for pseudo-Hermitian Hamiltonian Systems: Application to PT-Symmetric Qubits
• Bose-Einstein condensation processes with nontrivial geometric multiplicites realized via $\mathcal{P}\mathcal{T}-$symmetric and exactly solvable linear-Bose-Hubbard building blocks
• Non-Hermitian-Hamiltonian-induced unitarity and optional physical inner products in Hilbert space
• Stability of time-periodic $\mathcal{P}\mathcal{T}$ and anti-$\mathcal{P}\mathcal{T}$-symmetric Hamiltonians with different periodicities
• Quantum phase transitions mediated by clustered non-Hermitian degeneracies
• Emergent non-Hermitian conservation laws at exceptional points
• $\mathcal{P}\mathcal{T}$-like phase transitions from square roots of supersymmetric Hamiltonians