Output from an atom laser: theory vs. experiment

Atom lasers based on rf-outcoupling can be described by a set of coupled generalized Gross-Pitaevskii equations (GPE). We compare the theoretical predictions obtained by numerically integrating the time-dependent GPE of an effective one-dimensional model with recently measured experimental data for the F=2 and F=1 states of Rb-87. We conclude that the output of a rf-atom laser can be well described by this model.Comment: 4 pages, 5 figures, submitted to App. Phys.

Investigations of a two-mode atom laser model

Atom lasers based on rf-outcoupling from a trapped Bose-Einstein condensate can be described by a set of generalized, coupled Gross-Pitaevskii equations (GPE). If not only one but two radio frequencies are used for outcoupling, the atoms emerging from the trap have two different energies and the total wavefunction of the untrapped spin-state is a coherent superposition which leads to a pulsed atomic beam. We present results for such a situation obtained from a 1D-GPE model for magnetically trapped Rb-87 in the F=1 state. The wavefunction of the atomic beam can be approximated by a sum of two Airy functions. In the limit of weak coupling we calculate the intensity analytically.Comment: 7 pages, 7 figures, submitted to Phys. Rev.

Optical decay from a Fabry-Perot cavity faster than the decay time

The dynamical response of an optical Fabry-Perot cavity is investigated experimentally. We observe oscillations in the transmitted and reflected light intensity if the frequency of the incoupled light field is rapidly changed. In addition, the decay of a cavity-stored light field is accelerated if the phase and intensity of the incoupled light are switched in an appropriate way. The theoretical model by M. J. Lawrence em et al, JOSA B 16, 523 (1999) agrees with our observations.Comment: submitted to Josa

Multiplicative processes and power laws

[Takayasu et al., Phys. Rev.Lett. 79, 966 (1997)] revisited the question of stochastic processes with multiplicative noise, which have been studied in several different contexts over the past decades. We focus on the regime, found for a generic set of control parameters, in which stochastic processes with multiplicative noise produce intermittency of a special kind, characterized by a power law probability density distribution. We briefly explain the physical mechanism leading to a power law pdf and provide a list of references for these results dating back from a quarter of century. We explain how the formulation in terms of the characteristic function developed by Takayasu et al. can be extended to exponents $\mu >2$, which explains the ``reason of the lucky coincidence''. The multidimensional generalization of (\ref{eq1}) and the available results are briefly summarized. The discovery of stretched exponential tails in the presence of the cut-off introduced in \cite{Taka} is explained theoretically. We end by briefly listing applications.Comment: Extended version (7 pages). Phys. Rev. E (to appear April 1998

Electromagnetically-Induced-Transparency-Like Effect in the Degenerate Triple-Resonant Optical Parametric Amplifier

We investigate experimentally the absorptive and dispersive properties of triple-resonant optical parametric amplifier OPA for the degenerate subharmonic field. In the experiment, the subharmonic field is utilized as the probe field and the harmonic wave as the pump field. We demonstrate that EIT-like effect can be simulated in the triple-resonant OPA when the cavity line-width for the harmonic wave is narrower than that for the subharmonic field. However, this phenomenon can not be observed in a double-resonant OPA. The narrow transparency window appears in the reflected field. Especially, in the measured dispersive spectra of triple-resonant OPA, a very steep variation of the dispersive profile of the subharmonic field is observed, which can result in a slow light as that observed in atomic EIT medium.Comment: 10 pages, 4 figures, appear in Opt. Let

Systems with Multiplicative Noise: Critical Behavior from KPZ Equation and Numerics

We show that certain critical exponents of systems with multiplicative noise can be obtained from exponents of the KPZ equation. Numerical simulations in 1d confirm this prediction, and yield other exponents of the multiplicative noise problem. The numerics also verify an earlier prediction of the divergence of the susceptibility over an entire range of control parameter values, and show that the exponent governing the divergence in this range varies continuously with control parameter.Comment: Four pages (In Revtex format) with 4 figures (in Postcript

Adiabatic reduction near a bifurcation in stochastically modulated systems

We re-examine the procedure of adiabatic elimination of fast relaxing variables near a bifurcation point when some of the parameters of the system are stochastically modulated. Approximate stationary solutions of the Fokker-Planck equation are obtained near threshold for the pitchfork and transcritical bifurcations. Stochastic resonance between fast variables and random modulation may shift the effective bifurcation point by an amount proportional to the intensity of the fluctuations. We also find that fluctuations of the fast variables above threshold are not always Gaussian and centered around the (deterministic) center manifold as was previously believed. Numerical solutions obtained for a few illustrative examples support these conclusions.Comment: RevTeX, 19 pages and 16 figure

Universal Scaling Properties in Large Assemblies of Simple Dynamical Units Driven by Long-Wave Random Forcing

Large assemblies of nonlinear dynamical units driven by a long-wave fluctuating external field are found to generate strong turbulence with scaling properties. This type of turbulence is so robust that it persists over a finite parameter range with parameter-dependent exponents of singularity, and is insensitive to the specific nature of the dynamical units involved. Whether or not the units are coupled with their neighborhood is also unimportant. It is discovered numerically that the derivative of the field exhibits strong spatial intermittency with multifractal structure.Comment: 10 pages, 7 figures, submitted to PR

Asymptotic power law of moments in a random multiplicative process with weak additive noise

It is well known that a random multiplicative process with weak additive noise generates a power-law probability distribution. It has recently been recognized that this process exhibits another type of power law: the moment of the stochastic variable scales as a function of the additive noise strength. We clarify the mechanism for this power-law behavior of moments by treating a simple Langevin-type model both approximately and exactly, and argue this mechanism is universal. We also discuss the relevance of our findings to noisy on-off intermittency and to singular spatio-temporal chaos recently observed in systems of non-locally coupled elements.Comment: 11 pages, 9 figures, submitted to Phys. Rev.

Brownian motion approach to the ideal gas of relativistic particles

The relativistic generalization of a free Brownian motion theory is presented. The global characteristics of the relaxation are {\it explicitly} found for the velocity and momentum (stochastic) kinetics. It is shown that the thermal corrections, to the both relaxation times $T$ (of stationary autocorrelations) and transient relaxation time of momentum, appear slowing down the processes. The transient relaxation time of the velocity does not depend {\it explicitly} on temperature, $T(v_0)= m(v_0)/\gamma \equiv \epsilon_0/\gamma c^2$, and it is proportional to the initial energy of a relativistic Brownian particle.Comment: 4 fig