Eugenio Roldán

Quantum walk on the line as an interference phenomenon

We show that the coined quantum walk on a line can be understood as an interference phenomenon, can be classically implemented, and indeed already has been. The walk is essentially two independent walks associated with the different coin sides, coupled only at initiation. There is a simple analogy between the evolution of walker positions and the propagation of light in a dispersive optical fiber.

Quantum walk with a time-dependent coin

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. 93, 180601 (2004)] which exhibits interesting dynamical localization and quasiperiodic dynamics. Our proposal allows for a much easier implementation of this particularly 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.

Optical Cavity Implementations of the Quantum Walk

We discuss how the coined quantum walk on the line or on the circle can be implemented using optical waves. We propose several optical cavity configurations for these implementations.

Nonlinear optical Galton board

We generalize the concept of optical Galton board (OGB), first proposed by Bouwmeester et al. [Phys. Rev. A 61, 013410 (2000)], by introducing the possibility of nonlinear self-phase modulation on the wave function 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 nondispersive pulses in the field distribution (solitonlike structures). These exhibit a variety of dynamical behaviors, including ballistic motion, dynamical localization, nonelastic collisions, and chaotic behavior, in the sense that the dynamics is very sensitive to the nonlinearity strength.

Deviation from Lorenz-type dynamics of an NH3 ring laser

Abstract We show that the differences of the intensity spiral dynamics of an optically pumped NH 3 ring laser from that of the Lorenz model are caused by counterpropagating emission and by three-level coherence effects. In particular we find that under appropriate conditions the differences disappear and the laser emits purely according to the Lorenz model.

Tailoring discrete quantum walk dynamics via extended initial conditions

We study the evolution of initially extended distributions in the coined quantum walk (QW) on the line. By analysing the dispersion relation of the process, continuous wave equations are derived whose form depends on the initial distribution shape. In particular, for a class of initial conditions, the evolution is dictated by the Schrodinger equation of a free particle. As that equation also governs paraxial optical diffraction, all of the phenomenology of the latter can be implemented in the QW. This allows us, in particular, to devise an initially extended condition leading to a uniform probability distribution whose width increases linearly with time, with increasing homogeneity.

Vectorial Kerr-cavity solitons.

It is shown that a Kerr cavity with different losses for the two polarization components of the field can support both dark and bright cavity solitons (CSs). A parametrically driven Ginzburg-Landau equation is shown to describe the system for large-cavity anisotropy. In one transverse dimension the nonlinear dynamics of the bright CSs is numerically investigated.

Models, predictions, and experimental measurements of far-infrared NH3-laser dynamics and comparisons with the Lorenz-Haken model

Dynamics of the intensity and optical field amplitude of a coherently pumped far-infrared NH3-laser are measured and characterized. The experimental findings in certain parameter ranges closely follow the dynamics of the Lorenz model and its generalization for laser systems. Similarities and some specific differences are found in geometrical or statistical characterizations of the attractors. The experimental results are also consistent with the results of a model of optically pumped three-level lasers which takes into account the presence of a multiplicity of velocity groups as well as three-level coherence effects. For a certain region in parameter space, this far more complex model with a much larger phase space produces results similar to the dynamics of the Lorenz model. The model also provides explanations of differences between the experimental results and results from the Lorenz model.

Quantum squeezing of optical dissipative structures

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.

Risken–Nummedal–Graham–Haken instability in class-B lasers

We determine analytical expressions for the Risken-Nummedal-Graham-Haken multimode laser instability outside the uniform field limit in the case of very fast polarization decay (class-B laser). A new condition for the observability of that instability, concerning the value of the cavity mirrors reflectivity, is predicted.