Bryan Galdrikian

Testing for nonlinearity in time series: the method of surrogate data

We describe a statistical approach for identifying nonlinearity in time series. The method first specifies some linear process as a null hypothesis, then generates surrogate data sets which are consistent with this null hypothesis, and finally computes a discriminating statistic for the original and for each of the surrogate data sets. If the value computed for the original data is significantly different than the ensemble of values computed for the surrogate data, then the null hypothesis is rejected and nonlinearity is detected. We discuss various null hypotheses and discriminating statistics. The method is demonstrated for numerical data generated by known chaotic systems, and applied to a number of experimental time series which arise in the measurement of superfluids, brain waves, and sunspots; we evaluate the statistical significance of the evidence for nonlinear structure in each case, and illustrate aspects of the data which this approach identifies.

Nonlinear quantum dynamics in semiconductor quantum wells

Abstract We discuss recent measurements of the nonlinear response of electrons in wide quantum wells driven by intense electromagnetic radiation at terahertz frequencies. The theme is the interplay of quantum mechanics, strong periodic driving, the electron-electron interaction and dissipation. We discuss harmonic generation from an asymmetric double quantum well in which the effects of dynamic screening are important. Measurements and theory are found to be in good agreement. We also discuss intensity-dependent absorption in a 400A square quantum well. A new nonlinear quantum effect occurs, in which the frequency at which electromagnetic radiation is absorbed shifts to the red with increasing intensity. The preliminary experimental results are in agreement with a theory by Zaluzny, in which the source of the nonlinearity is the self-consistent potential in the Hartree approximation for the electron dynamics.

Materials science in the far-IR with electrostatic based FELs

Abstract A technology gap exists between ∼ 100 GHz and ∼ 10 THz. Free-electron lasers (FELs), driven by high quality, relatively low energy electron beams from electrostatic accelerators, and capable of generating kilowatts of coherent, tunable radiation, are ideally suited to explore the enabling science for future technology in this spectral range. We describe two experiments that use terahertz “optical rectification” to measure i) the intensity and temperature dependent energy relaxation in quantum wells and ii) the intrinsic relaxation of resonant tunneling diodes. Both benefit from the power and tunablilty of the UCSB FELs.

Intersubband dynamics of asymmetric quantum wells studied by THz `optical rectification'

We have measured the rectification of far-infrared radiation resonant with the lowest intersubband transition of an AlGaAs/GaAs asymmetric coupled double-quantum well in which the subband spacing is 11 meV. From these measurements we can extract an intersubband lifetime of at low excitation intensity and T = 10 K, which appears promising for devices such as FIR detectors or mixers which can operate at low excitation and temperature. In order to investigate the effect of carrier concentration on the relaxation time we have performed the same experiments in a logarithmically graded quantum well.

Nonlinear multiphoton resonances in quantum wells

Abstract The periodically driven particle in a box serves as a starting point for the qualitative analysis of nonintegrable systems, and as a simple model of semiconductor quantum wells exposed to intense far-infrared radiation. Classically, the phase space contains chaotic low-momentum trajectories, bounded by a sharp transition to regular motion for high momenta. The quantized system contains invariant states which localize upon classical invariant surfaces. We model the time evolution of the ground state (in the classical system, an ensemble of low-momentum trajectories) under various driving amplitudes and frequencies. Whereas the dynamics of the classical system are governed by the presence of KAM tori, the quantized system also displays sharp, nonperturbative resonances at particular driving parameters. These resonances correspond to the mixing of Floquet states at avoided crossings in the quasienergy spectrum. This form of transport should survive when many-body effects, dissipation, and the continuum are taken into account.

Nonlinear resonant optical rectification in a coupled quantum well

Abstract We have measured the rectification of far-infrared radiation resonant with the lowest intersubband transition of an AlGa/AsGaAs asymmetric coupled double-quantum well in which the subband spacing is 11 meV. From these measurements we can extract an intersubband lifetime of 1.2 ± 0.4 ns at low excitation intensity and T = 10K, which appears promising for devices which can operate at low excitation and temperature, such as FIR detectors or mixers. From simultaneous measurements of the optical rectification and of the intersubband absorption coefficient we can determine the intensity-dependent intersubband lifetime, which shows a strong decrease for increasing intensities.

Far-Infrared nonlinear response of electrons in semiconductor nanostructures

Electrons in semiconductor nanostructures such as quantum wells can exhibit a highly nonlinear response to far-infrared radiation of sufficient intensity, such as can be supplied by the free-electron lasers (FELs) at UCSB. Several different physical mechanisms can cause nonlinear behavior in nanostructures. Experimental results at UCSB demonstrate that transport, absorption, and harmonic generation can be used as probes of nonlinear response. In the future, it may be possible to use the UCSB-FELs to observe completely new nonlinear phenomena, such as non-perturbative quantum resonances in quantum wells driven by intense far-infrared radiation.