E. Brun

Observation of order and chaos in a nuclear spin–flip laser

Experimental observations and computer simulations of the nonlinear response are discussed for a single-mode, solid-state, nuclear spin–flip, ruby nuclear-magnetic-resonance (NMR) laser. A theoretical model is derived that is based on the classical Bloch equations and that demonstrates one-to-one correspondence to a homogeneously broadened, single-mode ring laser. Experimental evidence is presented for limit cycle behavior, sequences of sub-harmonic bifurcations, transitions to chaos, noisy bands, windows of regular behavior, intermittency, abrupt transitions between different basins of attraction, and hysteresis when a physical system parameter of the NMR laser is modulated at a low frequency. First experimental results are shown for a NMR laser with an external, detuned high-frequency signal below the injection-locking threshold. In this region, the output exhibits transitions from regular to chaotic oscillations and phase-locked spiking somewhat of the nature of what has been theoretically proposed for optical systems.

Dimension analysis of a chaotic nuclear magnetic resonance laser

Improved experimental investigations of the parametrically modulated nuclear magnetic resonance laser are discussed with emphasis on the analysis of chaotic states. Phase diagrams of the parameter space are constructed from bifurcation diagrams to display the rich phenomenology of periodic behavior, chaos, and collisions between stable and unstable orbits. Long data strings have been recorded in particularly interesting regions of the parameter space. From the corresponding time series, the attractors have been reconstructed by embedding techniques, and generalized dimensions and entropies have been computed using the kth nearest-neighbor method.

Bistability and Chaos in NMR Systems

In natural systems paths from disorder to order and from simple to chaotic behavior may show an astonishing universality. Models of nontrivial simplicity are helpful for systematic investigations of these remarkable phenomena. An almost ideal system of this sort are the polarized nuclear spins of a solid in a magnetic field and embedded in a resonant structure. There, nuclear magnetic resonance (NMR) becomes feasible for which sophisticated experimental techniques and adequate theoretical models exist.

lnstabilities and Chaos of a Solid State NMR Laser With lnjected Signals

The solid-state ruby nuclear magnetic resonance (NMR) laser shows sequence of instabilities if amplitude or frequency of an external driving signal are swept. With the parametrically modulated NMR laser sequence of period-doubling bifurcations and subsequent transitions to a chotic behaviour were found which are typical of the Feigenbaum scenoario for a route to chaos. In the same system intermittency was observed indicating the presence of the Pomeau-Mannaeville scenario. Chaotic bands were found also along the route to injection-locking where the NMR laser is driven by a stable external oscillator with its frequency slighty detuned from the NMR frequency. Side-products of these investigations of chaotic dynamics are observations with respect to the frequency-pushing of two lasers and the use of a period-doubling laser as small-signal detection.

The NMR-Laser — A Nonlinear Solid State System Showing Chaos

We present experimental observations along the roads to chaos of a tuned low-Q solid state spin-flip NMR laser (raser) which, according to our earlier work , should show the universal Feigenbaum scenario under certain conditions. The free running ruby raser is periodically perturbed by modulating one of its physical parameters. For example, one may modulate the pumping magnetization sinusoidally with the angular frequency Ω close to the eigenfrequency of the linearized raser equations, typically f = Ω/2π ≃ 30 Hz.

Using nuclear spins, radio waves, sodium atoms, and laser light to investigate spatiotemporal nonlinear systems

Within the wide field of nonlinear dynamics we investigate temporal and spatial behavior of electromagnetic systems. A strange type of laser, the nuclear magnetic resonance (NMR) laser, shows truly chaotic behavior and is therefore ideally suited to analyze experimentally and theoretically a variety of temporal nonlinear effects. Of particular interest is the analysis of its strange attractors in terms of unstable periodic orbits. For the extension of our research from the NMR laser (representing a purely temporal system described by the Bloch-Kirchhoff ordinary differential equations) to spatial and spatiotemporal systems, we chose, as a three-dimensional dynamic system, polarized laser beams interacting nonlinearly with sodium atoms. Among other effects, we have observed beam bouncing, beam splitting, and beam switching. This can be well described by partial differential equations for beam propagation derived from the Schrodinger equation and the Maxwell equations. An intuitive explanation is given in terms of intensity and polarization patterns formed by optical-pumping-induced mutual refractive index modifications between polarized resonant laser beams.

Ordered and Chaotic Response of a Modulated or Driven NMR Laser

The Feature Issue on Instabilities in Active Optical Media of the Journal of the Optical Society of America B [1]shows the increasing interest in nonlinear phenomena in laser systems. The ruby nuclear-magnetic-resonance (NMR) laser [2], among others, is an excellent test system with which to study the nature of instabilities and the routes to chaos of lasing systems. In our contribution [3] we reviewed theoretical and experimental investigations of the ruby NMR laser that operates in the rf regime and has its counterpart in the homogeneously broadened single-mode ring laser. Two topics were stressed in particular: the transition from ordered to chaotic response of the parametrically modulated laser (PML), and the transition to injection-locking of a laser with an injected signal (LIS). In both cases a control parameter of the system was slowly swept in time. For the PML it was either the amplitude or the frequency of the parametric modulation signal Apsinωpt; for the LIS it was the amplitude of the injected signal V0sinωt which was detuned by Δωa=ωa−ω from the NMR frequency ωa. In scanning the control parameter we observed in both cases sequences of instabilities leading to either regular or irregular response.