Generating Multiparticle Entangled States by Self-Organization of Driven Ultracold Atoms.

We describe a mechanism for guiding the dynamical evolution of ultracold atomic motional degrees of freedom toward multiparticle entangled Dicke-squeezed states, via nonlinear self-organization under external driving. Two examples of many-body models are investigated. In the first model, the external drive is a temporally oscillating magnetic field leading to self-organization by interatomic scattering. In the second model, the drive is a pump laser leading to transverse self-organization by photon-atom scattering in a ring cavity. We numerically demonstrate the generation of multiparticle entangled states of atomic motion and discuss prospective experimental realizations of the models. For the cavity case, the calculations with adiabatically eliminated photonic sidebands show significant momentum entanglement generation can occur even in the "bad cavity" regime. The results highlight the potential for using self-organization of atomic motion in quantum technological applications.

Multiple Self-Organized Phases and Spatial Solitons in Cold Atoms Mediated by Optical Feedback.

We study the transverse self-structuring of cold atomic clouds with effective atomic interactions mediated by a coherent driving beam retroreflected by means of a single mirror. The resulting self-structuring due to optomechanical forces is much richer than that of an effective-Kerr medium, displaying hexagonal, stripe and honeycomb phases depending on the interaction strength parametrized by the linear susceptibility. Phase domains are described by Ginzburg-Landau amplitude equations with real coefficients. In the stripe phase the system recovers inversion symmetry. Moreover, the subcritical character of the honeycomb phase allows for light-density feedback solitons functioning as self-sustained dark atomic traps with motion controlled by phase gradients in the driving beam.

Mapping the dynamical regimes of a SESAM mode-locked VECSEL with a long cavity using time series analysis.

The different dynamical regions of an optically-pumped SESAM mode-locked, long-cavity VECSEL system with a fundamental pulse repetition frequency of ~200 MHz are investigated. The output power, captured as 250 µs long time series using a sampling rate of 200 GSa/s, for each operating condition of the system, is analyzed to determine the dynamical state. A wavelength range of 985-995 nm and optical pump powers of 10 W-16.3 W is studied. The system produces high quality fundamental passive mode-locking (FML) over an extensive part of the parameter space, but the different dynamical regions outside of FML are the primary focus of this study. We report five types of output: CW emission, FML, mode-locking of a few modes, double pulsing, and, semi-stable 4th harmonic mode-locking. The high sampling rate of the oscilloscope, combined with the long duration of the time series analyzed, enables insight into how the structure and substructure of pulses vary systematically over thousands of round trips of the laser cavity. Higher average output power is obtained in regions characterized by semi-stable 4th harmonic mode-locking than observed for FML, raising whether such average powers might be achieved for FML. The observed dynamic transitions from fundamental mode-locking provide insights into instability challenges in developing a stable, widely tunable, low repetition rate, turn-key system; and to inform future modelling of the system.

Complexity in pulsed nonlinear laser systems interrogated by permutation entropy.

Permutation entropy (PE) has a growing significance as a relative measure of complexity in nonlinear systems. It has been applied successfully to measuring complexity in nonlinear laser systems. Here, PE and weighted permutation entropy (WPE) are discovered to show an unexpected inversion to higher values, when characterizing the complexity at the characteristic frequencies of nonlinear drivers in laser systems, for output power sequences which are pulsed. The cause of this inversion is explained and its presence can be used to identify when irregular dynamics transform into a fairly regular pulsed signal (with amplitude and timing jitter). When WPE is calculated from experimental output power time series from various nonlinear laser systems as a function of delay time, both the minimum value of WPE, and the width of the peak in the WPE plot are shown to be indicative of the level of amplitude variation and timing jitter present in the pulsed output. Links are made with analysis using simulated time series data with systematic variation in timing jitter and/or amplitude variations.

Experimental observation of localized structures in medium size VCSELs.

We report experimental evidence of spontaneous formation of localized structures in a 80 µm diameter Vertical-Cavity Surface-Emitting Laser (VCSEL) biased above the lasing threshold and under optical injection. Such localized structures are bistable with the injected beam power and the VCSEL current. We experimentally investigate the formation of localized structures for different detunings between the injected beam and the VCSEL, and different injection beam waists.

Compensation of spatial inhomogeneities in a cavity soliton laser using a spatial light modulator.

Dissipative solitons are self-localized states which can exist anywhere in a system with translational symmetry, but in real systems this translational symmetry is usually broken due to parasitic inhomogeneities leading to spatial disorder, pinning the soliton positions. We discuss the effects of semiconductor growth induced spatial disorder on the operation of a cavity soliton laser based on a vertical-cavity surface-emitting laser (VCSEL). We show that a refractive index variation induced by an external, suitably spatially modulated laser beam can be used to counteract the inherent disorder. In particular, it is demonstrated experimentally that the threshold of one cavity soliton can be lowered without influencing other cavity solitons making two solitons simultaneously bistable which were not without control. This proof of principle paves the way to achieve full control of large numbers of cavity solitons at the same time.

Femtosecond synchronously in-well pumped vertical-external-cavity surface-emitting laser.

We demonstrate the first synchronously in-well pumped vertical-external-cavity surface-emitting laser (VECSEL). Depending on the cavity mismatch, laser pulses with a duration from 1 ps to 7 ps at a repetition rate of 76 MHz were generated directly from the laser at 860 nm. The application of extra-cavity pulse compression further shortened the pulse to a duration of 210 fs providing a peak power of 226 W.

Externally-Triggered Activation and Inhibition of Optical Pulsating Regimes in Quantum-Dot Mode-locked Lasers.

Controlled generation and inhibition of externally-triggered picosecond optical pulsating regimes are demonstrated experimentally in a quantum dot mode locked laser (QDMLL) subject to external injection of an amplitude modulated optical signal. This approach also allows full control and repeatability of the time windows of generated picosecond optical pulses; hence permitting to define precisely their temporal duration (from <1 ns spans) and repetition frequency (from sub-Hz to at least hundreds of MHz). The use of a monolithic QDMLL, operating at 1300 nm, provides a system with a very small footprint that is fully compatible with optical telecommunication networks. This offers excellent prospects for use in applications requiring the delivery of ultrashort optical pulses at precise time instants and at tunable rates, such as optical imaging, time-of-flight diagnostics and optical communication systems.

Femtosecond synchronously mode-locked vertical-external cavity surface-emitting laser.

The behavior of a room temperature synchronously mode-locked vertical-external cavity surface-emitting laser (VECSEL) operating at 980 nm is reported. The laser performance was found to be qualitatively the same for different pump pulse duration (3.6 ps and 70 fs). The pulse duration of the laser is limited by strong self-phase modulation to around 10-40 ps. By compressing the strongly chirped pulses generated directly from the laser, ultrashort pulses with duration of around 200 fs with maximum peak powers of 1.3 kW at 80 MHz were obtained. Multiple pulsing of the laser was observed and the effects of cavity length detuning on pulse width and spectral bandwidth have been investigated.

Vector cavity solitons in broad area Vertical-Cavity Surface-Emitting Lasers.

We report the experimental observation of two-dimensional vector cavity solitons in a Vertical-Cavity Surface-Emitting Laser (VCSEL) under linearly polarized optical injection when varying optical injection linear polarization direction. The polarization of the cavity soliton is not the one of the optical injection as it acquires a distinct ellipticity. These experimental results are qualitatively reproduced by the spin-flip VCSEL model. Our findings open the road to polarization multiplexing when using cavity solitons in broad-area lasers as pixels in information technology.

Correlation properties and drift phenomena in the dynamics of vertical-cavity surface-emitting lasers with optical feedback.

We investigate experimentally the polarization dynamics of vertical-cavity surface-emitting lasers with isotropic optical feedback operating in the long-cavity regime. By means of an analysis of the correlation properties in the time domain and in the frequency domain a connection between a drift phenomenon and frequency components that deviate from the harmonics of the external cavity round-trip frequency is revealed. The latter frequency components are shown to result from an interaction of external cavity dynamics and relaxation oscillations. An analogy to the carrier-envelope effect in mode-locked lasers is drawn. Similar drift phenomena are observed also for other laser systems with delay.

Secondary bifurcations of hexagonal patterns in a nonlinear optical system: alkali metal vapor in a single-mirror arrangement.

Secondary bifurcations of hexagonal patterns are analyzed in a model of a single-mirror arrangement with an alkali metal vapor as the nonlinear medium. A stability analysis of the hexagonal structures is performed numerically. Different instabilities are predicted in dependency on the wave number of the hexagons. Some of the instabilities take place at a finite wave number and result in the formation of structures with 12 spatial modes. These structures are compared with those observed experimentally.

Operation of an optical in-well-pumped vertical-external-cavity surface-emitting laser.

We report the operation of an optical in-well-pumped vertical-external-cavity surface-emitting laser. The laser delivers 1 W at 855 nm and is pumped with a cost-effective fiber-coupled laser diode emitting at 806 nm. The laser modal gain is examined and ways of optimizing the system are investigated and discussed.