Abstract
In the last decade, there have been tremendous technological advances in the fabrication and control of microelectromechanical and nanoelectromechanical systems (MEMS & NEMS). Micromechanical systems play a significant role in many research fields due to their high frequency stabilization and sensitivity. Consequently, MEMS & NEMS have paved the way for studying systems of nonlinear micromechanical and nanomechanical oscillators and resonators. Among these, parametrically pumped resonators play an important role in many areas of science and technology.
A parametric oscillator with two coexisting states of identical amplitude but opposite phases can be used to represent a classical bit or an Ising spin for logic or computation applications. We investigate multiple near-identical parametric oscillators. The introduction of weak coupling that favors vibrations of opposite phases among multiple parametric oscillators enables mapping onto the Ising model of interacting spins. Coupled parametric oscillators have been used to build Ising machines that are considered in the context of inferring the ground state of these systems. So far, Ising machines have been analyzed using symmetric Ising models where the energy of the system is invariant to interchanging two spins. We will show that in the presence of weak disorder, coupled parametric oscillators map instead onto asymmetric Ising models in which the symmetry of interchanging two spins is broken, and serves as a building block for asymmetric Ising models.
For two identical parametric oscillators with the same eigenfrequency, with noise voltage introduced the modification ratio of transition rates is identical, in a manner similar to Ising spins in equilibrium, and detailed balance is maintained. On the other hand, when the eigenfrequencies are tuned to be mismatched, the coupling between parametric oscillators displays incommensurate. The system resembles two Ising spins with asymmetric interactions. Detailed balances are broken here and a probability current in discrete state space is generated.
We design three micro-resonators adjacent to each other arranged in a triangular array. In the absence of coupling, we induce the phase transition by applying artificial noise, the vibration phase transitions of the oscillators are independent. While introduced with weak coupling that favors vibrations of opposite phases, oscillator’s vibration phase transitions are modified by their neighbor resonators. We theoretically and experimentally demonstrate the existence of degenerate ground states satisfying local minimum energy, mapping onto three frustrated Ising spin models. Investigating the annealing states, we can also implement the results for the states occupation distribution. By controlling the detune of the eigenfrequencies of three oscillators, we perform the measurement of all possible vibration phases vs frequency with and without coupling.
Besides investigating coupled parametric oscillators, I also carry out researching exceptional points of coupled two-mode electromechanical systems. EP is one of the important characteristics of non-Hermitian physics, characterized by a singularity of the spectrum and eigenfunctions where two energy levels coalesce. By applying dynamical back-action in a two-mode electromechanical system, we can control system parameters of damping coefficient. We can also control the coupling strength between two oscillators determined by electric potential difference. We have implemented theory and measurement of the existence of EP in the coupled micro-electromechanical oscillators.