arXiv subjects
Publications and source records attributed to Eugenio Roldan.
We study the influence of field diffusion on the spatial localized structures (cavity solitons) recently predicted in bidirectional lasers. We find twofold positive role of the diffusion: 1) it increases the stability range of the individual (isolated) solitons; 2) it reduces the long-range interaction between the cavity solitons. Latter allows the independent manipulation (writing and erasing) of individual cavity solitons.
In ref. [1] we analyzed the properties of a Degenerate Optical Parametric Oscillator (DOPO) tuned to the first transverse mode family at the signal frequency. Above threshold, a Hermite-Gauss mode with an arbitrary orientation in the transverse plane is emitted, and thus the rotational invariance of the system is broken. When quantum effects were taken into account, it was found on the one hand, that quantum noise is able to induce a random rotation on this classically emitted mode. On the other hand, the analysis of a balanced homodyne detection in which the local oscillator (LO) was orthogonal to the excited mode at any time, showed that squeezing in the quadrature selected by the LO was found for every phase of this one, squeezing being perfect for a pi/2 phase. This last fact revealed an apparent paradox: If all quadratures are below shot noise level, the uncertainty principle seems to be violated. In [1] we stated that the explanation behind this paradox is that the quadratures of the rotating orthogonal mode do not form a canonical pair, and the extra noise is transferred to the diffusing orientation. Thes notes are devoted to prove this claim.
We theoretically address squeezed light generation through the spontaneous breaking of the rotational invariance occuring in a type I degenerate optical parametric oscillator (DOPO) pumped above threshold. We show 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, within the linearized theory. This occurs at any pumping level above threshold, hence the phenomenon is non-critical. Imperfections of the rotational symmetry, due e.g. to cavity anisotropy, are shown to have a small impact, hence the result is not singular.
We generalize the concept of optical Galton board (OGB), first proposed by Bouwmeester et al. {[}Phys. Rev. A \textbf{61}, 013410 (2000)], by introducing the possibility of nonlinear self--phase modulation on the wavefunction during the walker evolution. If the original Galton board illustrates classical diffusion, the OGB, which can be understood as a grid of Landau--Zener crossings, illustrates the influence of interference on diffusion, and is closely connected with the quantum walk. Our nonlinear generalization of the OGB shows new phenomena, the most striking of which is the formation of non-dispersive pulses in the field distribution (soliton--like structures). These exhibit a variety of dynamical behaviors, including ballistic motion, dynamical localization, non--elastic collisions and chaotic behavior, in the sense that the dynamics is very sensitive to the nonlinearity strength.
We show theoretically that a broad area bidirectional laser with slightly different cavity losses for the two counterpropagating fields sustains cavity solitons (CSs). These structures are complementary, i.e., there is a bright (dark) CS in the field with more (less) losses. Interestingly, the CSs can be written/erased by injecting suitable pulses in any of the two counterpropagating fields.
We present a method for the study of quantum fluctuations of dissipative structures forming in nonlinear optical cavities, which we illustrate in the case of a degenerate, type I optical parametric oscillator. The method consists in (i) taking into account explicitly, through a collective variable description, the drift of the dissipative structure caused by the quantum noise, and (ii) expanding the remaining -internal- fluctuations in the biorthonormal basis associated to the linear operator governing the evolution of fluctuations in the linearized Langevin equations. We obtain general expressions for the squeezing and intensity fluctuations spectra. Then we theoretically study the squeezing properties of a special dissipative structure, namely, the bright cavity soliton. After reviewing our previous result that in the linear approximation there is a perfectly squeezed mode irrespectively of the values of the system parameters, we consider squeezing at the bifurcation points, and the squeezing detection with a plane--wave local oscillator field, taking also into account the effect of the detector size on the level of detectable squeezing.
We report experimental observation of the conversion of a phase-invariant nonlinear system into a phase-locked one via the mechanism of rocking [G. J. de Valcarcel and K. Staliunas, Phys. Rev. E 67, 026604 (2003)]. This conversion results in that vortices of the phase-invariant system are being replaced by phase patterns such as domain walls. The experiment is carried out on a photorefractive oscillator in two-wave mixing configuration.A model for the experimental device is given that reproduces the observed behavior.
In this article we present a systematic derivation of the Maxwell-Bloch equations describing amplification and laser action in a ring cavity. We derive the Maxwell-Bloch equations for a two-level medium and discuss their applicability to standard three- and four-level systems. After discusing amplification, we consider lasing and pay special attention to the obtention of the laser equations in the uniform field approximation. Finally, the connection of the laser equations with the Lorenz model is considered.
We introduce quantum walks with a time-dependent coin, and show how they include, as a particular case, the generalized quantum walk recently studied by Wojcik et al. {[}Phys. Rev. Lett. \textbf{93}, 180601(2004){]} which exhibits interesting dynamical localization and quasiperiodic dynamics. Our proposal allows for a much easier implementation of this particular rich dynamics than the original one. Moreover, it allows for an additional control on the walk, which can be used to compensate for phases appearing due to external interactions. To illustrate its feasibility, we discuss an example using an optical cavity. We also derive an approximated solution in the continuous limit (long--wavelength approximation) which provides physical insight about the process.
We show that any optical dissipative structure supported by degenerate optical parametric oscillators contains a special transverse mode that is free from quantum fluctuations when measured in a balanced homodyne detection experiment. The phenomenon is not critical as it is independent of the system parameters and, in particular, of the existence of bifurcations. This result is a consequence of the spatial symmetry breaking introduced by the dissipative structure. Effects that could degrade the squeezing level are considered.
We report the experimental characterization of domain walls dynamics in a photorefractive resonator in a degenerate four wave mixing configuration. We show how the non flat profile of the emitted field affects the velocity of domain walls as well as the variations of intensity and phase gradient during their motion. We find a clear correlation between these two last quantities that allows the experimental determination of the chirality that governs the domain walls dynamics.
We propose an optical cavity implementation of the two-dimensional coined quantum walk on the line. The implementation makes use of only classical resources, and is tunable in the sense that a large number of different unitary transformations can be implemented by tuning some parameters of the device.
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 behaviour, in particular, bursting and spiking. These phenomena are interpreted in terms of the spatio-temporal dynamics of the extended patterns connected by the wall, which display complex dynamical behaviour as well. Domain wall interaction, including the formation of bound states is also addressed.
We describe the controlled observation of the nonequilibrium Ising-Bloch transition in a broad area nonlinear optical cavity, namely, a quasi-1D single longitudinal-mode photorefractive oscilator 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.
It is well known that the squeezing spectrum of the field exiting a nonlinear cavity can be directly obtained from the fluctuation spectrum of normally ordered products of creation and annihilation operators of the cavity mode. In this article we show that the output field squeezing spectrum can be derived also by combining the fluctuation spectra of any pair of s-ordered products of creation and annihilation operators. The interesting result is that the spectrum obtained in this way from the linearized Langevin equations is exact, and this occurs in spite of the fact that no s-ordered quasiprobability distribution verifies a true Fokker-Planck equation, i.e., the Langevin equations used for deriving the squeezing spectrum are not exact. The (linearized) intracavity squeezing obtained from any s-ordered distribution is also exact. These results are exemplified in the problem of dispersive optical bistability.
Einstein's rate equations are derived from the semiclassical Bloch equations describing the interaction of a classical broadband light field with a two--level system.
Two-photon absorption is theoretically analyzed within the semiclassical formalism of radiation-matter interaction. We consider an ensemble of inhomogeneously broadened three-level atoms subjected to the action of two counterpropagating fields of the same frequency. By concentrating in the limit of large detuning in one-photon transitions, we solve perturbatively the Bloch equations in a non-usual way. In this way we derive an analytical expression for the width of the two-photon resonance that makes evident sub-Doppler two--photon spectroscopy. We also derive an analytical expression for the Stark shift of the two-photon resonance.
Domain walls in type I degenerate optical parametric oscillators are numerically investigated. Both steady Ising and moving Bloch walls are found, bifurcating one into another through a nonequilibrium Ising--Bloch transition. Bloch walls are found that connect either homogeneous or roll planforms. Secondary bifurcations affecting Bloch wall movement are characterized that lead to a transition from a steady drift state to a temporal chaotic movement as the system is moved far from the primary, Ising--Bloch bifurcation. Two kinds of routes to chaos are found, both involving tori: a usual Ruelle-Takens and an intermittent scenarios.