Coexistence of stable and unstable population dynamics in a nonlinear non-Hermitian mechanical dimer

Abstract

Non-Hermitian two-site ``dimers'' serve as minimal models in which to explore the interplay of gain and loss in dynamical systems. In this paper, we experimentally and theoretically investigate the dynamics of non-Hermitian dimer models with non-reciprocal hoppings between the two sites. We investigate two types of non-Hermitian couplings; one is when asymmetric hoppings are externally introduced, and the other is when the non-reciprocal hoppings depend on the population imbalance between the two sites, thus introducing the non-Hermiticity in a dynamical manner. We engineer the models in our synthetic mechanical set-up comprised of two classical harmonic oscillators coupled by measurement-based feedback. For fixed non-reciprocal hoppings, we observe that, when the strength of these hoppings is increased, there is an expected transition from a $\mathcal{P}\mathcal{T}$-symmetric regime, where oscillations in the population are stable and bounded, to a $\mathcal{P}\mathcal{T}$-broken regime, where the oscillations are unstable and the population grows/decays exponentially. However, when the non-Hermiticity is dynamically introduced, we also find a third intermediate regime in which these two behaviors coexist, meaning that we can tune from stable to unstable population dynamics by simply changing the initial phase difference between the two sites. As we explain, this behavior can be understood by theoretically exploring the emergent fixed points of a related dimer model in which the non-reciprocal hoppings depends on the normalized population imbalance. Our study opens the way for the future exploration of non-Hermitian dynamics and exotic lattice models in synthetic mechanical networks.

16 pages, 9 figures -- added references

References in corpus (17)

• Making Sense of Non-Hermitian Hamiltonians
• The physics of exceptional points
• Efficient Light Funneling based on the non-Hermitian Skin Effect
• Unidirectional Nonlinear PT-symmetric Optical Structures
• Nonreciprocity and magnetic-free isolation based on optomechanical interactions
• Observation of Non-Hermitian Skin Effect and Topology in Ultracold Atoms
• Topological quantum matter in synthetic dimensions
• Topological invariance and global Berry phase in non-Hermitian systems
• A non-Hermitian $PT-$symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
• Mean-field dynamics of a non-Hermitian Bose-Hubbard dimer
• Tunable non-reciprocal quantum transport through a dissipative Aharonov-Bohm ring in ultracold atoms
• Quantum Classical Correspondence for a non-Hermitian Bose-Hubbard Dimer
• Josephson Oscillation and Transition to Self-Trapping for Bose-Einstein-Condensates in a Triple-Well Trap
• Stationary states of a PT-symmetric two-mode Bose-Einstein condensate
• Topological theory of non-Hermitian photonic systems
• Interaction-induced non-Hermitian topological phases from a dynamical gauge field
• Interplay of nonreciprocity and nonlinearity on mean-field energy and dynamics of a Bose-Einstein condensate in a double-well potential

Cited by in corpus (5)

• Quantum theory of non-Hermitian optical binding between nanoparticles
• Hopf Bifurcation of Nonlinear Non-Hermitian Skin Effect
• Quantum metric dependent anomalous velocity in systems subject to complex electric fields
• Manipulation of Weyl Points in Reciprocal and Nonreciprocal Mechanical Lattices
• Trails of clouds in binary black holes