Anharmonic parametric excitation in optical lattices

We study both experimentally and theoretically the losses induced by parametric excitation in far-off-resonance optical lattices. The atoms confined in a 1D sinusoidal lattice present an excitation spectrum and dynamics substantially different from those expected for a harmonic potential. We develop a model based on the actual atomic Hamiltonian in the lattice and we introduce semiempirically a broadening of the width of lattice energy bands which can physically arise from inhomogeneities and fluctuations of the lattice, and also from atomic collisions. The position and strength of the parametric resonances and the evolution of the number of trapped atoms are satisfactorily described by our model.Comment: 7 pages, 5 figure

Parametric Excitation in a Self-excited Three-degrees of Freedom Problem

The efect of parametric excitation in self-excited has been investigated in two-degrees of freedom problems. The possibility of suppressing self-excited vibrationsby using parametric excitation and the dynamic behavior of those kind systems were discussed. In the this paper, we consider a system in three-degrees of freedom problem which by using a linear transformation the system becomes an Autoparametric. The system consists of a central mass and two external masses where those masses are conectedby springs with the same constant stiffness. The flow-generated self-excited force is actingon the external masses, it is represented by Rayleigh force. The variable stiffness isperiodically varying in time, represents a parametric excitation. It turns out that forcertain parameter ranges full vibration cancellation is possible. The analysis of linearcase of system shows that there are two conditions in order to obtain an interval ofthe parametric excitation. Using the averaging method the fully non-linear system is investigated producing as non-trivial solutions unstable periodic solutions. The behaviorof this unstable solution is studied in the full system.DOI : http://dx.doi.org/10.22342/jims.15.2.48.97-10

Localized Faraday patterns under heterogeneous parametric excitation

Faraday waves are a classic example of a system in which an extended pattern emerges under spatially uniform forcing. Motivated by systems in which uniform excitation is not plausible, we study both experimentally and theoretically the effect of heterogeneous forcing on Faraday waves. Our experiments show that vibrations restricted to finite regions lead to the formation of localized subharmonic wave patterns and change the onset of the instability. The prototype model used for the theoretical calculations is the parametrically driven and damped nonlinear Schr\"odinger equation, which is known to describe well Faraday-instability regimes. For an energy injection with a Gaussian spatial profile, we show that the evolution of the envelope of the wave pattern can be reduced to a Weber-equation eigenvalue problem. Our theoretical results provide very good predictions of our experimental observations provided that the decay length scale of the Gaussian profile is much larger than the pattern wavelength.Comment: 10 pages, 9 figures, Accepte

Parametric excitation of plasma waves by gravitational radiation

We consider the parametric excitation of a Langmuir wave and an electromagnetic wave by gravitational radiation, in a thin plasma on a Minkowski background. We calculate the coupling coefficients starting from a kinetic description, and the growth rate of the instability is found. The Manley-Rowe relations are fulfilled only in the limit of a cold plasma. As a consequence, it is generally difficult to view the process quantum mechanically, i.e. as the decay of a graviton into a photon and a plasmon. Finally we discuss the relevance of our investigation to realistic physical situations.Comment: 5 pages, REVTe

Parametric excitation of multiple resonant radiations from localized wavepackets

Fundamental physical phenomena such as laser-induced ionization, driven quantum tunneling, Faraday waves, Bogoliubov quasiparticle excitations, and the control of new states of matter rely on time-periodic driving of the system. A remarkable property of such driving is that it can induce the localized (bound) states to resonantly couple to the continuum. Therefore experiments that allow for enlightening and controlling the mechanisms underlying such coupling are of paramount importance. We implement such an experiment in a special fiber optics system characterized by a dispersion oscillating along the propagation coordinate, which mimics "time". The quasi-momentum associated with such periodic perturbation is responsible for the efficient coupling of energy from the localized wave-packets sustained by the fiber nonlinearity into free-running linear dispersive waves (continuum), at multiple resonant frequencies. Remarkably, the observed resonances can be explained by means of a unified approach, regardless of the fact that the localized state is a soliton-like pulse or a shock front