Nonlinear dynamics and chaos in two coupled nanomechanical resonators

Nonlinear Dynamics of Nanomechanical Resonators

In the last decade we have witnessed exciting technological advances in the fabrication and control of microelectromechanical and nanoelectromechanical systems (MEMS&NEMS) [16, 19, 26, 54, 55]. Such systems are being developed for a host of nanotechnological applications, such as highly sensitive mass [25, 34, 67], spin [56], and charge detectors [17, 18], as well as for basic research in the m...

Arbitrary distribution and nonlinear modal interaction in coupled nanomechanical resonators

We propose a general one-dimensional continuous formulation to analyze the vibrational modes of antennalike nanomechanical resonators consisting of two symmetric arrays of cantilevers affixed to a central nanobeam. The cantilever arrays can have arbitrary density and length profile along the beam. We obtain the secular equation that allows for the determination of their frequency spectrum and i...

Quantum chaos in an ultrastrongly coupled bosonic junction.

The semiclassical and quantum dynamics of two ultrastrongly coupled nonlinear resonators cannot be explained using the discrete nonlinear Schrödinger equation or the Bose-Hubbard model, respectively. Instead, a model beyond the rotating wave approximation must be studied. In the semiclassical limit this model is not integrable and becomes chaotic for a finite window of parameters. For the quant...

Nonlinear Dynamics of Nanomechanical and Micromechanical Resonators

Kerr nonlinearities and nonclassical states with superconducting qubits and nanomechanical resonators

We propose the use of a superconducting charge qubit capacitively coupled to two resonant nanomechanical resonators to generate Yurke-Stoler states, i.e., quantum superpositions of pairs of distinguishable coherent states 180° out of phase with each other. This is achieved by effectively implementing Kerr nonlinearities induced through the application of a strong external driving field in one o...