Poisson noise induced switching in driven micromechanical resonators

We study Poisson-noise induced switching between coexisting vibrational states in driven nonlinear micromechanical resonators. In contrast to Gaussian noise induced switching, the measured logarithm of the switching rate is proportional not to the reciprocal noise intensity, but to its logarithm, for fixed pulse area. We also find that the switching rate logarithm varies as a square root of the distance to the bifurcation point, instead of the conventional scaling with exponent 3/2.Comment: accepted by PR

Spectrum of an oscillator with jumping frequency and the interference of partial susceptibilities

We study an underdamped oscillator with shot-noise frequency fluctuations. The oscillator spectrum is determined by the interference of the susceptibilities for different eigenfrequencies. Depending on the parameters, it has a fine structure or displays a single asymmetric peak. For nano-mechanical resonators with a fluctuating number of attached molecules, the spectrum is found in a simple analytical form. The results bear on various types of systems where the reciprocal correlation time of frequency fluctuations can be comparable to the typical frequency jumps

Scaling in activated escape of underdamped systems

Noise-induced escape from a metastable state of a dynamical system is studied close to a saddle-node bifurcation point, but in the region where the system remains underdamped. The activation energy of escape scales as a power of the distance to the bifurcation point. We find two types of scaling and the corresponding critical exponents.Comment: 9 page

Many-particle confinement by constructed disorder and quantum computing

Many-particle confinement (localization) is studied for a 1D system of spinless fermions with nearest-neighbor hopping and interaction, or equivalently, for an anisotropic Heisenberg spin-1/2 chain. This system is frequently used to model quantum computers with perpetually coupled qubits. We construct a bounded sequence of site energies that leads to strong single-particle confinement of all states on individual sites. We show that this sequence also leads to a confinement of all many-particle states in an infinite system for a time that scales as a high power of the reciprocal hopping integral. The confinement is achieved for strong interaction between the particles while keeping the overall bandwidth of site energies comparatively small. The results show viability of quantum computing with time-independent qubit coupling.Comment: An invited paper for the topical issue of J. Opt. B on quantum contro

Activation barrier scaling and crossover for noise-induced switching in a micromechanical parametric oscillator

We explore fluctuation-induced switching in a parametrically-driven micromechanical torsional oscillator. The oscillator possesses one, two or three stable attractors depending on the modulation frequency. Noise induces transitions between the coexisting attractors. Near the bifurcation points, the activation barriers are found to have a power law dependence on frequency detuning with critical exponents that are in agreement with predicted universal scaling relationships. At large detuning, we observe a crossover to a different power law dependence with an exponent that is device specific.Comment: 5 pages, 5 figure

Dynamical multistability in high-finesse micromechanical optical cavities

We analyze the nonlinear dynamics of a high-finesse optical cavity in which one mirror is mounted on a flexible mechanical element. We find that this system is governed by an array of dynamical attractors, which arise from phase-locking between the mechanical oscillations of the mirror and the ringing of the light intensity in the cavity. We describe an analytical approximation to map out the diagram of attractors in parameter space, derive the slow amplitude dynamics of the system, including thermally activated hopping between different attractors, and suggest a scheme for exploiting the dynamical multistability in the measurement of small displacements.Comment: 5 pages, 4 figure

Theory of Second and Higher Order Stochastic Processes

This paper presents a general approach to linear stochastic processes driven by various random noises. Mathematically, such processes are described by linear stochastic differential equations of arbitrary order (the simplest non-trivial example is $\ddot x = R(t)$, where $R(t)$ is not a Gaussian white noise). The stochastic process is discretized into $n$ time-steps, all possible realizations are summed up and the continuum limit is taken. This procedure often yields closed form formulas for the joint probability distributions. Completely worked out examples include all Gaussian random forces and a large class of Markovian (non-Gaussian) forces. This approach is also useful for deriving Fokker-Planck equations for the probability distribution functions. This is worked out for Gaussian noises and for the Markovian dichotomous noise.Comment: 35 pages, PlainTex, accepted for publication in Phys Rev. E

Universality in escape from a modulated potential well

We show that the rate of activated escape $W$ from a periodically modulated potential displays scaling behavior versus modulation amplitude $A$. For adiabatic modulation of an optically trapped Brownian particle, measurements yield $\ln W\propto (A_{\rm c} - A)^{\mu}$ with $\mu = 1.5$. The theory gives $\mu=3/2$ in the adiabatic limit and predicts a crossover to $\mu=2$ scaling as $A$ approaches the bifurcation point where the metastable state disappears.Comment: 4 pages, 3 figure

Paths of fluctuation induced switching

We demonstrate that the paths followed by a system in fluctuation-activated switching form a narrow tube in phase space. A theory of the path distribution is developed and its direct measurement is performed in a micromechanical oscillator. The experimental and theoretical results are in excellent agreement, with no adjustable parameters. We also demonstrate the lack of time-reversal symmetry in switching of systems far from thermal equilibrium.Comment: Accepted to Phys. Rev. Let