arXiv subjects

Daniel J. Gauthier

Publications and source records attributed to Daniel J. Gauthier.

86 records · Page 5Linked to original sources

arXiv2008

Transient dynamics and momentum redistribution in cold atoms via recoil-induced resonances

We use an optically dense, anisotropic magneto-optical trap to study recoil-induced resonances (RIRs) in the transient, high-gain regime. We find that two distinct mechanisms govern the atomic dynamics: the finite, frequency-dependent atomic response time, and momentum-space population redistribution. At low input probe intensities, the residual Doppler width of the atoms, combined with the finite atomic response time, result in a linear, transient hysteretic effect that modifies the locations, widths, and magnitudes of the resulting gain spectra depending on the sign of the scan chirp. When larger intensities (\textit{i.e.}, greater than a few $μ$W/cm$^2$) are incident on the atomic sample for several $μ$s, hole-burning in the atomic sample's momentum distribution leads to a coherent population redistribution that persists for approximately 100 $μ$s. We propose using RIRs to engineer the atomic momentum distribution to enhance the nonlinear atom-photon coupling. We present a numerical model, and compare the calculated and experimental results to verify our interpretation.

quant-ph↗

arXiv2007

Cardiac Alternans Arising from an Unfolded Border-Collision Bifurcation

Following an electrical stimulus, the transmembrane voltage of cardiac tissue rises rapidly and remains at a constant value before returning to the resting value, a phenomenon known as an action potential. When the pacing rate of a periodic train of stimuli is increased above a critical value, the action potential undergoes a period-doubling bifurcation, where the resulting alternation of the action potential duration is known as alternans in the medical literature. Existing cardiac models treat alternans either as a smooth or as a border-collision bifurcation. However, recent experiments in paced cardiac tissue reveal that the bifurcation to alternans exhibits hybrid smooth/nonsmooth behaviors, which can be qualitatively described by a model of so-called unfolded border-collision bifurcation. In this paper, we obtain analytical solutions of the unfolded border-collision model and use it to explore the crossover between smooth and nonsmooth behaviors. Our analysis shows that the hybrid smooth/nonsmooth behavior is due to large variations in the system's properties over a small interval of the bifurcation parameter, providing guidance for the development of future models.

physics.bio-ph↗

arXiv2007

All-Optical Switching with Transverse Optical Patterns

We demonstrate an all-optical switch that operates at ultra-low-light levels and exhibits several features necessary for use in optical switching networks. An input switching beam, wavelength $λ$, with an energy density of $10^{-2}$ photons per optical cross section [$σ=λ^2/(2π)$] changes the orientation of a two-spot pattern generated via parametric instability in warm rubidium vapor. The instability is induced with less than 1 mW of total pump power and generates several $μ$Ws of output light. The switch is cascadable: the device output is capable of driving multiple inputs, and exhibits transistor-like signal-level restoration with both saturated and intermediate response regimes. Additionally, the system requires an input power proportional to the inverse of the response time, which suggests thermal dissipation does not necessarily limit the practicality of optical logic devices.

physics.optics↗

arXiv2006

Small-Signal Amplification of Period-Doubling Bifurcations in Smooth Iterated Maps

Various authors have shown that, near the onset of a period-doubling bifurcation, small perturbations in the control parameter may result in much larger disturbances in the response of the dynamical system. Such amplification of small signals can be measured by a gain defined as the magnitude of the disturbance in the response divided by the perturbation amplitude. In this paper, the perturbed response is studied using normal forms based on the most general assumptions of iterated maps. Such an analysis provides a theoretical footing for previous experimental and numerical observations, such as the failure of linear analysis and the saturation of the gain. Qualitative as well as quantitative features of the gain are exhibited using selected models of cardiac dynamics.

nlin.CD↗

arXiv2006

Broadband SBS Slow Light in an Optical Fiber

We investigate slow-light via stimulated Brillouin scattering in a room temperature optical fiber that is pumped by a spectrally broadened laser. Broadening the spectrum of the pump field increases the linewidth $Δω_p$ of the Stokes amplifying resonance, thereby increasing the slow-light bandwidth. One physical bandwidth limitation occurs when the linewidth becomes several times larger than the Brillouin frequency shift $Ω_B$ so that the anti-Stokes absorbing resonance cancels out substantially the Stokes amplifying resonance and hence the slow-light effect. We find that partial overlap of the Stokes and anti-Stokes resonances can actually lead to an enhancement of the slow-light delay - bandwidth product when $Δω_p \simeq 1.3 Ω_B$. Using this general approach, we increase the Brillouin slow-light bandwidth to over 12 GHz from its nominal linewidth of $\sim$30 MHz obtained for monochromatic pumping. We controllably delay 75-ps-long pulses by up to 47 ps and study the data pattern dependence of the broadband SBS slow-light system.

physics.optics↗

arXiv2006

Evidence for an unfolded border-collision bifurcation in paced cardiac tissue

We investigate, both experimentally and theoretically, the bifurcation to alternans in heart tissue. Previously, this phenomenon has been modeled either as a smooth or as border-collision period-doubling bifurcation. Using a new experimental technique, we find a hybrid behavior: very close to the bifurcation point the dynamics are smooth-like, whereas further away they are border-collision-like. This behavior is captured by a new type of model, called an unfolded border-collision bifurcation.

q-bio.TO↗

arXiv2006

Competition between Electromagnetically Induced Transparency and Raman Processes

We present a theoretical formulation of competition among electromagnetically induced transparency (EIT) and Raman processes. The latter become important when the medium can no longer be considered to be dilute. Unlike the standard formulation of EIT, we consider all fields applied and generated as interacting with both the transitions of the $Λ$ scheme. We solve Maxwell equations for the net generated field using a fast-Fourier-transform technique and obtain predictions for the probe, control and Raman fields. We show how the intensity of the probe field is depleted at higher atomic number densities due to the build up of multiple Raman fields.

physics.optics↗

arXiv2005

Hopf bifurcations in time-delay systems with band-limited feedback

We investigate the steady-state solution and its bifurcations in time-delay systems with band-limited feedback. This is a first step in a rigorous study concerning the effects of AC-coupled components in nonlinear devices with time-delayed feedback. We show that the steady state is globally stable for small feedback gain and that local stability is lost, generically, through a Hopf bifurcation for larger feedback gain. We provide simple criteria that determine whether the Hopf bifurcation is supercritical or subcritical based on the knowledge of the first three terms in the Taylor-expansion of the nonlinearity. Furthermore, the presence of double-Hopf bifurcations of the steady state is shown, which indicates possible quasiperiodic and chaotic dynamics in these systems. As a result of this investigation, we find that AC-coupling introduces fundamental differences to systems of Ikeda-type [Ikeda et al., Physica D 29 (1987) 223-235] already at the level of steady-state bifurcations, e.g. bifurcations exist in which limit cycles are created with periods other than the fundamental ``period-2'' mode found in Ikeda-type systems.

nlin.CD↗

arXiv2005

All-optical switching in rubidium vapor

We report on an all-optical switch that operates at low light levels. It consists of laser beams counterpropagating through a warm rubidium vapor that induce an off-axis optical pattern. A switching laser beam causes this pattern to rotate even when the power in the switching beam is much lower than the power in the pattern. The observed switching energy density is very low, suggesting that the switch might operate at the single-photon level with system optimization. This approach opens the possibility of realizing a single-photon switch for quantum information networks and for improving transparent optical telecommunication networks.

nlin.PS↗

arXiv2004

Rate-dependent propagation of cardiac action potentials in a one-dimensional fiber

Action potential duration (APD) restitution, which relates APD to the preceding diastolic interval (DI), is a useful tool for predicting the onset of abnormal cardiac rhythms. However, it is known that different pacing protocols lead to different APD restitution curves (RCs). This phenomenon, known as APD rate-dependence, is a consequence of memory in the tissue. In addition to APD restitution, conduction velocity restitution also plays an important role in the spatiotemporal dynamics of cardiac tissue. We present new results concerning rate-dependent restitution in the velocity of propagating action potentials in a one-dimensional fiber. Our numerical simulations show that, independent of the amount of memory in the tissue, waveback velocity exhibits pronounced rate-dependence and the wavefront velocity does not. Moreover, the discrepancy between waveback velocity RCs is most significant for small DI. We provide an analytical explanation of these results, using a system of coupled maps to relate the wavefront and waveback velocities. Our calculations show that waveback velocity rate-dependence is due to APD restitution, not memory.

q-bio.QM↗

arXiv2004

An ionically based mapping model with memory for cardiac restitution

Many features of the sequence of action potentials produced by repeated stimulation of a cardiac patch can be modeled by a 1D mapping, but not the full behavior observed in the restitution portrait: in particular, not (i) distinct slopes for dynamic and S1-S2 restitution (rate dependence) and not (ii) long transients in the approach to steady state (accomodation). To address these shortcomings, \emph{ad hoc} 2D mappings, where the second variable is a ``memory'' variable, have been proposed; it seems that these models exhibit some, but not all, of the relevant behavior. In this paper we introduce a new 2D mapping and determine a set of parameters for it that gives a rather accurate description of the full restitution portrait found for one animal. The changes in the mapping, compared to previous models, result from requiring that the mapping can be derived as an asymptotic limit of a simple ionic model. Among other benefits, one can interpret the parameters in the mapping in terms of the ionic model. The ionic model is an extension of a two-current model that adds a third dependent variable, a generalized concentration. The simplicity of the ionic model and the physiological basis for the mapping contribute to the usefulness of these ideas for describing restitution data in a variety of contexts. The fitting procedure is straightforward and can easily be applied to obtain a mathematical model for data from other experiments, including experiments on different species. Uniqueness of the parameter choice is also discussed.

q-bio.QM↗

arXiv2003

High Speed Chaos in Optical Feedback System with Flexible Timescales

We describe a new opto-electronic device with time-delayed feedback that uses a Mach-Zehnder interferometer as passive nonlinearity and a semiconductor laser as a current-to-optical-frequency converter. Bandlimited feedback allows tuning of the characteristic time scales of both the periodic and high dimensional chaotic oscillations that can be generated with the device. Our implementation of the device produces oscillations in the frequency range of tens to hundreds of MHz. We develop a model and use it to explore the experimentally observed Andronov-Hopf bifurcation of the steady state and to estimate the dimension of the chaotic attractor.

nlin.CD↗

arXiv2003

Control of cardiac alternans in a mapping model with memory

We investigate a map-based model of paced cardiac muscle in the presence of closed-loop feedback control. The model relates the duration of an action potential to the preceding diastolic interval as well as the preceding action potential duration and thus has some amount of `memory.' We find that the domain of control depends on this memory, independently of the specific functional form of the map. The memory-dependent domain of control can encompass large feedback gains, thus providing the first possible explanation of the recent experimental results of Hall et al. [Phys. Rev. Lett, 88, 198102 (2002)] on controlling alternans in small pieces of rapidly-paced cardiac muscle.

physics.bio-ph↗

arXiv2001

Polarization instabilities in a two-photon laser

We describe the operating characteristics of a new type of quantum oscillator that is based on a two-photon stimulated emission process. This two-photon laser consists of spin-polarized and laser-driven $^{39}$K atoms placed in a high-finesse transverse-mode-degenerate optical resonator, and produces a beam with a power of $\sim $0.2 $μ$W at a wavelength of 770 nm. We observe complex dynamical instabilities of the state of polarization of the two-photon laser, which are made possible by the atomic Zeeman degeneracy. We conjecture that the laser could emit polarization-entangled twin beams if this degeneracy is lifted.

quant-ph↗