Emergent non-Hermitian localization phenomena in the synthetic space of zero-dimensional bosonic systems

Abstract

Phase transitions in non-Hermitian systems are at the focus of cutting edge theoretical and experimental research. On the one hand, parity-time- ($\mathcal{P}\mathcal{T}$-) and anti-$\mathcal{P}\mathcal{T}$-symmetric physics have gained ever-growing interest, due to the existence of non-Hermitian spectral singularities called exceptional points (EPs). On the other, topological and localization transitions in non-Hermitian systems reveal new phenomena, e.g., the non-Hermitian skin effect and the absence of conventional bulk-boundary correspondence. The great majority of previous studies exclusively focus on non-Hermitian Hamiltonians, whose realization requires an {\it a priori} fine-tuned extended lattices to exhibit topological and localization transition phenomena.In this work, we show how the non-Hermitian localization phenomena can naturally emerge in the synthetic field moments space of zero-dimensional bosonic systems, e.g., in anti-$\mathcal{P}\mathcal{T}$ and $\mathcal{P}\mathcal{T}$-symmetric quantum dimers. This offers an opportunity to simulate localization transitions in low-dimensional systems, without the need to construct complex arrays of, e.g., coupled cavities or waveguides. Indeed, the field moment equations of motion can describe an equivalent (quasi-)particle moving in a one-dimensional (1D) synthetic lattice. This synthetic field moments space can exhibit a nontrivial localization phenomena, such as non-Hermitian skin effect, induced by the presence of highly-degenerate EPs. We demonstrate our findings on the example of an anti-$\mathcal{P}\mathcal{T}$-symmetric two-mode system, whose higher-order field moments eigenspace is emulated by a synthetic 1D non-Hermitian Hamiltonian having a Sylvester matrix shape. Our results can be directly verified in state-of-the-art optical setups, such as superconducting circuits and toroidal resonators, by measuring photon moments or correlation functions.

arXiv comment18 pages

References in corpus (84)

• Topological Insulators
• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Topological Photonics
• Quantum Simulation
• Classification of topological quantum matter with symmetries
• Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities
• Edge states and topological invariants of non-Hermitian systems
• Unidirectional Invisibility induced by PT-Symmetric Periodic Structures
• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• Localization transitions in non-Hermitian quantum mechanics
• Topological phases of non-Hermitian systems
• Symmetry and Topology in Non-Hermitian Physics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Origin of Non-Hermitian Skin Effects
• Loss-induced suppression and revival of lasing
• Correspondence between winding numbers and skin modes in non-hermitian systems
• Pseudo-Hermitian Representation of Quantum Mechanics
• Non-Hermitian Boundary Modes
• Efficient Light Funneling based on the non-Hermitian Skin Effect
• Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
• Non-Hermitian skin effect and chiral damping in open quantum systems
• Quantum Simulators: Architectures and Opportunities
• Reversing the Pump-Dependence of a Laser at an Exceptional Point
• Synthetic Dimension in Photonics
• Non-Hermitian Topological Invariants in Real Space
• Metrology with $\mathcal{P}\mathcal{T}$-symmetric cavities: Enhanced sensitivity near the $\mathcal{P}\mathcal{T}$-phase transition
• Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps
• Observation of parity-time symmetry breaking in a single spin system
• Quantum state tomography across the exceptional point in a single dissipative qubit
• Spectral theory of Liouvillians for dissipative phase transitions
• Topologically protected defect states in open photonic systems with non-hermitian charge-conjugation and parity-time symmetry
• Non-Hermitian Quantum Sensing: Fundamental Limits and Non-Reciprocal Approaches
• Photonic Topological Insulator in Synthetic Dimensions
• A Universal Operator Growth Hypothesis
• Quantum Noise Theory of Exceptional Point Sensors
• No exceptional precision of exceptional point sensors
• Topological exceptional surfaces in non-Hermitian systems with parity-time and parity-particle-hole symmetries
• Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition
• The Chirality of Exceptional Points
• Observation of a Chiral State in a Microwave Cavity
• Symmetry and Higher-Order Exceptional Points
• Observation of tunable mobility edges in generalized Aubry-André lattices
• Exact steady state of a Kerr resonator with one- and two-photon driving and dissipation: Controllable Wigner-function multimodality and dissipative phase transitions
• Liouvillian Skin Effect: Slowing Down of Relaxation Processes without Gap Closing
• Experimental observation of exceptional surface in synthetic dimensions with magnon polaritons
• Synthetic parity-time symmetry breaking in a single microcavity
• Hybrid-Liouvillian formalism connecting exceptional points of non-Hermitian Hamiltonians and Liouvillians via postselection of quantum trajectories
• Symmetry-protected multifold exceptional points and their topological characterization
• Observation of non-Hermitian topological Anderson insulator in quantum dynamics
• Exact mobility edges, $\mathcal{P}\mathcal{T}$-symmetry breaking and skin effect in one-dimensional non-Hermitian quasicrystals
• Phase transitions in a non-Hermitian Aubry-André-Harper model
• Anderson localization in the Non-Hermitian Aubry-André-Harper model with physical gain and loss
• Exceptional Photon Blockade: Engineering Photon Blockade with Chiral Exceptional Points
• Enhanced sensing of weak anharmonicities through coherences in dissipatively coupled anti-PT symmetric systems
• Non-Hermitian Localization in Biological Networks
• Non-equilibrium stationary states of quantum non-Hermitian lattice models
• Unraveling the Non-Hermitian Skin Effect in Dissipative Systems
• Symmetry-protected zero-mode laser with a tunable spatial profile
• Liouvillian exceptional points of any order in dissipative linear bosonic systems: Coherence functions and switching between $\mathcal{P}\mathcal{T}$ and anti-$\mathcal{P}\mathcal{T}$ symmetries
• Bulk-boundary correspondence in non-Hermitian systems: stability analysis for generalized boundary conditions
• Quantum and semiclassical exceptional points of a linear system of coupled cavities with losses and gain within the Scully-Lamb laser theory
• Light transport in PT-invariant photonic structures with hidden symmetries
• Scully-Lamb quantum laser model for parity-time-symmetric whispering-gallery microcavities: Gain saturation effects and non-reciprocity
• Kaleidoscope of symmetry protected topological phases in one-dimensional periodically modulated lattices
• Dynamics of almost strong edge modes in spin chains away from integrability
• The robust $\mP\mT$-symmetric chain and properties of its Hermitian counterpart
• Non-Dissipative Non-Hermitian Dynamics and Exceptional Points in Coupled Optical Parametric Oscillators
• Exceptional points of any order in a single, lossy, waveguide beamsplitter by photon-number-resolved detection
• Non-Hermitian skin effect as an impurity problem
• Dissipative Topological Phase Transition with Strong System-Environment Coupling
• Generating high-order quantum exceptional points in synthetic dimensions
• Anderson localization transition in a robust $\mathcal{P}\mathcal{T}$-symmetric phase of a generalized Aubry-Andre model
• Quantum theory of multimode fields: Applications to optical resonators
• Experimental demonstration of coherence flow in $\mathcal{P}\mathcal{T}$- and anti-$\mathcal{P}\mathcal{T}$-symmetric systems
• Liouvillian spectral collapse in the Scully-Lamb laser model
• Collectively induced exceptional points of quantum emitters coupled to nanoparticle surface plasmons
• Squeezed lasing
• Generalized Householder Transformations for the Complex Symmetric Eigenvalue Problem
• Lyapunov equation in open quantum systems and non-Hermitian physics
• Eigenvalue Repulsion and Eigenfunction Localization in Sparse Non-Hermitian Random Matrices
• Multi-Photon Synthetic Lattices in Multi-Port Waveguide Arrays: Synthetic Atoms and Fock Graphs
• Rotation-time symmetry in bosonic systems and the existence of exceptional points in the absence of $\mathcal{P}\mathcal{T}$ symmetry
• Simulating two-dimensional dynamics within a large-size atomic spin

Cited by in corpus (7)

• Topological Non-Hermitian skin effect
• Dynamically crossing diabolic points while encircling exceptional curves: A programmable symmetric-asymmetric multimode switch
• Enhancing the sensitivity of nonlinearity sensors through homodyne detection in dissipatively coupled systems
• Fully solvable finite simplex lattices with open boundaries in arbitrary dimensions
• Achieving the Quantum Fisher Information Bound in Pseudo-Hermitian Sensors
• How to realize compact and non-compact localized states in disorder-free hypercube networks
• Multiple quantum exceptional, diabolical, and hybrid points in multimode bosonic systems: II. Nonconventional PT-symmetric dynamics and unidirectional coupling