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Random resonant media being one of the possible realizations of disordered metamaterials open a room of opportunities for achieving new fundamental effects and designing advanced nanophotonic devices. Strongly nonlinear optical properties…
Nonlinear spectroscopy employs a series of laser pulses to interrogate dynamics in large interacting many-body systems, and has become a highly successful method for experiments in chemical physics. Current quantum optical experiments…
We study the inhibition of pattern formation in nonlinear optical systems using intracavity photonic crystals. We consider mean field models for single and doubly degenerate optical parametric oscillators. Analytical expressions for the new…
We have observed nonlinear transduction of the thermomechanical motion of a nanomechanical resonator when detected as laser transmission through a sideband unresolved optomechanical cavity. Nonlinear detection mechanisms are of considerable…
Open dynamical systems are mathematical models of machines that take input, change their internal state, and produce output. For example, one may model anything from neurons to robots in this way. Several open dynamical systems can be…
Recent theoretical studies of statistical mechanical properties of systems with long range interactions are briefly reviewed. In these systems the interaction potential decays with a rate slower than 1/r^d at large distances r in d…
We study an optomechanical system for the purpose of generating a nonclassical mechanical state when a mechanical oscillator is quadratically coupled to a single-mode cavity field driven by a squeezed optical field. The system corresponds…
Stable limit cycle as a stabilized mechanical oscillation is the primary result of the dynamical evolution of an optomechanical system under sufficiently powerful pump. Because this dynamical process is highly nonlinear, it was not clear…
The micromechanics of a variety of systems experiencing a structural arrest due to their high density could be unified by a thermodynamic framework governing their approach to 'jammed' configurations. The mechanism of supporting an applied…
This paper explores the connection between dynamical system properties and statistical physics of ensembles of such systems. Simple models are used to give novel phase transitions; particularly for finite N particle systems with many…
Linear mechanical oscillators have been applied to measure very small forces, mostly with the help of noise suppression. In contrast, adding noise to non-linear oscillators can improve the measurement conditions. Here, this effect of…
The propagation of compressional MHD waves is studied for an externally driven system. It is assumed that the combined action of the external sources and sinks of the entropy results in the harmonic oscillation of the entropy (and…
We present a novel geometric approach for determining the unique structure of a Hamiltonian and establishing an instability criterion for quantum quadratic systems. Our geometric criterion provides insights into the underlying geometric…
The study of collective nonlinear dynamics of coupled mechanical resonators is regaining attention in recent years thanks to rapid developments in the fields of microelectromechanical and nanoelectromechanical systems (MEMS and NEMS). We…
Cavity optomechanical systems in the quantum regime consist of a cavity mode and mechanical element coupled together through radiation pressure. In the nonlinear optomechanical regime, open-system dynamics is generally challenging to treat…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…
Atom and nanoparticle arrays trapped in optical lattices are shown to be capable of sustaining collective oscillations of frequency proportional to the strength of the external light field. The spectrum of these oscillations determines the…
Observing few-photon optomechanical effects remains a significant challenge in optomechanical systems. To investigate intrinsic radiation-pressure-induced nonlinear effects in the few-photon regime, it is essential to strengthen the…
The non-linear relations between polarization strength and electric field strength for ferroelectrics, as well as magnetization strength and magnetic field strength for ferromagnetics, can be achieved by introducing retarded electromagnetic…
We examine the general question of statistical changes experienced by ensembles of nonlinear random waves propagating in systems ruled by integrable equations. In our study that enters within the framework of integrable turbulence, we…