Up-converted photorefractive optical transient detection with femtosecond laser pulses.

We report on experimental demonstration of optical transient detection (OTD) based on photorefractive two-wave mixing of femtosecond pulses. The demonstrated technique also combines nonlinear-crystal-based OTD with up-conversion from infrared into the visible range. The approach enables measurement of phase changes of a dynamic signal in the infrared using GaP- or Si-based detectors while suppressing stationary background. Experimental results reveal existence of the relation between input phases in the infrared and output phases in the visible wavelength range. We further present experimental evidence of additional merits of up-converted transient phase analysis under noisy conditions, such as residual continuous-wave emission affecting the ultrashort pulses from the laser.

Interferometric measurement of complex-field changes in transient detection imaging.

We report an experimental method that combines nonlinear-crystal-based transient detection imaging (TDI) with interferometric complex-field retrieval. The system allows measuring both phase and amplitude of a dynamic scene while suppressing stationary background. Theoretical and experimental results prove the linear relation existing between input and output phases, as well as the benefits of phase analysis for both detection and measurement with high resolutions of λ/30, even under noisy conditions. Additionally, we present experimental evidence of the remarkable ability of the technique to detect phase sign changes in the scene -what we call differential-phase TDI- showing great detection sensitivity and no calibration requirements.

Coherent master equation for laser modelocking.

Modelocked lasers constitute the fundamental source of optically-coherent ultrashort-pulsed radiation, with huge impact in science and technology. Their modeling largely rests on the master equation (ME) approach introduced in 1975 by Hermann A. Haus. However, that description fails when the medium dynamics is fast and, ultimately, when light-matter quantum coherence is relevant. Here we set a rigorous and general ME framework, the coherent ME (CME), that overcomes both limitations. The CME predicts strong deviations from Haus ME, which we substantiate through an amplitude-modulated semiconductor laser experiment. Accounting for coherent effects, like the Risken-Nummedal-Graham-Haken multimode instability, we envisage the usefulness of the CME for describing self-modelocking and spontaneous frequency comb formation in quantum-cascade and quantum-dot lasers. Furthermore, the CME paves the way for exploiting the rich phenomenology of coherent effects in laser design, which has been hampered so far by the lack of a coherent ME formalism.

General Linearized Theory of Quantum Fluctuations around Arbitrary Limit Cycles.

The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantum-optical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its accuracy far from critical points or situations where the nonlinearity reaches the strong coupling regime, has turned it into a widespread technique, being the first method of choice in most works on the subject. However, such a technique finds strong practical and conceptual complications when one tries to apply it to situations in which the classical long-time solution is time dependent, a most prominent example being spontaneous limit-cycle formation. Here, we introduce a linearization scheme adapted to such situations, using the driven Van der Pol oscillator as a test bed for the method, which allows us to compare it with full numerical simulations. On a conceptual level, the scheme relies on the connection between the emergence of limit cycles and the spontaneous breaking of the symmetry under temporal translations. On the practical side, the method keeps the simplicity and linear scaling with the size of the problem (number of modes) characteristic of standard linearization, making it applicable to large (many-body) systems.

Strong vacuum squeezing from bichromatically driven Kerrlike cavities: from optomechanics to superconducting circuits.

Squeezed light, displaying less fluctuation than vacuum in some observable, is key in the flourishing field of quantum technologies. Optical or microwave cavities containing a Kerr nonlinearity are known to potentially yield large levels of squeezing, which have been recently observed in optomechanics and nonlinear superconducting circuit platforms. Such Kerr-cavity squeezing however suffers from two fundamental drawbacks. First, optimal squeezing requires working close to turning points of a bistable cycle, which are highly unstable against noise thus rendering optimal squeezing inaccessible. Second, the light field has a macroscopic coherent component corresponding to the pump, making it less versatile than the so-called squeezed vacuum, characterised by a null mean field. Here we prove analytically and numerically that the bichromatic pumping of optomechanical and superconducting circuit cavities removes both limitations. This finding should boost the development of a new generation of robust vacuum squeezers in the microwave and optical domains with current technology.

Phase-bistable pattern formation in oscillatory systems via rocking: application to nonlinear optical systems.

We present a review, together with new results, of a universal forcing of oscillatory systems, termed 'rocking', which leads to the emergence of a phase bistability and to the kind of pattern formation associated with it, characterized by the presence of phase domains, phase spatial solitons and phase-bistable extended patterns. The effects of rocking are thus similar to those observed in the classic 2 : 1 resonance (the parametric resonance) of spatially extended systems of oscillators, which occurs under a spatially uniform, time-periodic forcing at twice the oscillations' frequency. The rocking, however, has a frequency close to that of the oscillations (it is a 1 : 1 resonant forcing) and hence is a good alternative to the parametric forcing when the latter is inefficient (e.g. in optics). The key ingredient is that the rocking amplitude is modulated either in time or in space, such that its sign alternates (exhibits π-phase jumps). We present new results concerning a paradigmatic nonlinear optical system (the two-level laser) and show that phase domains and dark-ring (phase) solitons replace the ubiquitous vortices that characterize the emission of free-running, broad area lasers.

Pattern formation through phase bistability in oscillatory systems with space-modulated forcing.

We propose a novel forcing technique of spatially extended self-oscillatory systems able to excite phase bistability and the dissipative structures associated with it. The forcing is time periodic at a frequency close to the oscillators' frequency and is spatially modulated. The effects of this type of forcing are demonstrated analytically and numerically in a directly driven complex Ginzburg-Landau equation. Both spatially periodic and spatially random drives prove to be effective.

Noncritical quadrature squeezing through spontaneous polarization symmetry breaking.

We discuss the possibility of generating noncritical quadrature squeezing by spontaneous polarization symmetry breaking. We first consider Type II frequency-degenerate optical parametric oscillators but discard them for a number of reasons. Then we propose a four-wave-mixing cavity, in which the polarization of the output mode is always linear but has an arbitrary orientation. We show that in such a cavity, complete noise suppression in a quadrature of the output field occurs, irrespective of the parameter values.

Noise-induced phase bistability via stochastic rocking.

We study the effect of a randomly modulated harmonic driving on the phase behavior of a nonlinear oscillator. A multiple-scale analysis shows that the system is formally equivalent to a rocked oscillator, in which a modulated harmonic driving locks the system at one of two phases, both of which are in quadrature with that of the driving. This theoretically predicted noise-induced bistable phase locking is reproduced with numerical simulations of a stochastic Stuart-Landau model, and verified experimentally in a nonlinear electronic circuit.

Experimental demonstration of hyperbolic patterns.

We give experimental evidence of hyperbolic patterns in a nonlinear optical resonator. Such transverse patterns are a new kind of 2D dissipative structures, characterized by a distribution of the active modes along hyperbolas in the transverse wave-vector domain, in contrast with the usual (elliptic) patterns where the active modes distribute along rings. The hyperbolic character is realized by manipulating diffraction inside the optical resonator with cylindrical lenses. We also investigate theoretically hyperbolic patterns in corresponding Swift-Hohenberg models.

Noncritically squeezed light via spontaneous rotational symmetry breaking.

We predict squeezed light generation through the spontaneous rotational symmetry breaking occurring in a degenerate optical parametric oscillator (DOPO) pumped above threshold. We show, within the linearized theory, that a DOPO with spherical mirrors, in which the signal and idler fields correspond to first-order Laguerre-Gauss modes, produces a perfectly squeezed vacuum with the shape of a Hermite-Gauss mode. This occurs at any pumping level above threshold; hence, the phenomenon is noncritical. Imperfections of the rotational symmetry, due, e.g., to cavity anisotropy, are shown to have a small impact.

Bistable phase locking of a nonlinear optical cavity via rocking: Transmuting vortices into phase patterns.

We report the experimental observation of the conversion of a phase-invariant nonlinear system into a bistable phase-locked one via rocking [G. J. de Valcárcel and K. Staliunas, Phys. Rev. E 67, 026604 (2003)10.1103/PhysRevE.67.026604]. This conversion results in vortices of the phase-invariant system being replaced by phase patterns such as domain walls. A model for the experimental device, a photorefractive oscillator, is given that reproduces the observed behavior.

Subdiffractive band-edge solitons in Bose-Einstein condensates in periodic potentials.

A type of matter wave diffraction management is presented that leads to subdiffractive solitonlike structures. The proposed management technique uses two counter-moving, identical periodic potentials (e.g., optical lattices). For suitable lattice parameters, a different type of atomic bandgap structure appears in which the effective atomic mass becomes infinite at the lowest edge of an energy band. This way, normal matter-wave diffraction (proportional to the square of the atomic momentum) is replaced by fourth-order diffraction, and hence the evolution of the system becomes subdiffractive.

Hysteretic nonequilibrium Ising-Bloch transition.

We show that a parametrically driven cubic-quintic complex Ginzburg-Landau equation exhibits a hysteretic nonequilibrium Ising-Bloch transition for large enough quintic nonlinearity. These results help to understand the recent experimental observation of this phenomenon [A. Esteban-Martín, Phys. Rev. Lett. 94, 223903 (2005)].

Domain wall dynamics in an optical Kerr cavity.

An anisotropic (dichroic) optical cavity containing a self-focusing Kerr medium is shown to display a bifurcation between static--Ising--and moving--Bloch--domain walls, the so-called nonequilibrium Ising-Bloch transition (NIB). Bloch walls can show regular or irregular temporal behavior, in particular, bursting and spiking. These phenomena are interpreted in terms of the spatiotemporal dynamics of the extended patterns connected by the wall, which display complex dynamical behavior as well. Domain wall interaction, including the formation of bound states is also addressed.

Controlled observation of a nonequilibrium Ising-Bloch transition in a nonlinear optical cavity.

We report the controlled observation of the nonequilibrium Ising-Bloch transition in a broad area nonlinear optical cavity (a quasi-1D single longitudinal-mode photorefractive oscillator in a degenerate four-wave mixing configuration). Our experimental technique allows for the controlled injection of the domain walls. We use cavity detuning as control parameter and find that both Ising and Bloch walls can exist for the same detuning values within a certain interval of detunings; i.e., the Ising-Bloch transition is hysteretic in our case. A complex Ginzburg-Landau model is used for supporting the observations.

Excitation of phase patterns and spatial solitons via two-frequency forcing of a 1:1 resonance.

We show that a self-oscillatory system, driven at two frequencies close to that of the unforced system (resonance 1:1), becomes phase locked and exhibits two equivalent stable states of opposite phases. For spatially extended systems this phase bistability results in patterns characteristic for real order parameter systems, such as phase domains, labyrinths, and phase spatial solitons. In variational cases, the phase-locking mechanism is interpreted as a result of the periodic "rocking" of the system potential. Rocking could be tested experimentally in lasers and in oscillatory chemical reactions.

Faraday patterns in bose-Einstein condensates.

Temporal periodic modulation of the interatomic s-wave scattering length in Bose-Einstein condensates is shown to excite subharmonic patterns in the atom density through a parametric resonance. The dominant wavelength of the spatial structures is primarily selected by the excitation frequency but also affected by the depth of the spatial modulation via a nonlinear resonance. These phenomena represent analogues of the Faraday patterns excited in vertically vibrated liquids.

Domain walls and ising-BLOCH transitions in parametrically driven systems.

Parametrically driven systems sustaining sech solitons are shown to support a new kind of localized state. These structures are walls connecting two regions oscillating in antiphase that form in the parameter domain where the sech soliton is unstable. Depending on the parameter set the oppositely phased domains can be either spatially uniform or patterned. Both chiral (Bloch) and nonchiral (Ising) walls are found, which bifurcate one into the other via an Ising-Bloch transition. While Ising walls are at rest Bloch walls move and may display secondary bifurcations leading to chaotic wall motion.