We are taught by conventional wisdom that the transmission and detection of signals is hindered by noise. However, during the last two decades, the paradigm of stochastic resonance (SR) proved this assertion wrong: indeed, addition of the appropriate amount of noise can boost a signal and hence facilitate its detection in a noisy environment. Due to its simplicity and robustness, SR has been implemented by mother nature on almost every scale, thus attracting interdisciplinary interest from physicists, geologists, engineers, biologists and medical doctors, who nowadays use it as an instrument for their specific purposes. At the present time, there exist a lot of diversified models of SR. Taking into account the progress achieved in both theoretical understanding and practical application of this phenomenon, we put the focus of the present review not on discussing in depth technical details of different models and approaches but rather on presenting a general and clear physical picture of SR on a pedagogical level. Particular emphasis will be given to the implementation of SR in generic quantum systems-an issue that has received limited attention in earlier review papers on the topic. The major part of our presentation relies on the two-state model of SR (or on simple variants thereof), which is general enough to exhibit the main features of SR and, in fact, covers many (if not most) of the examples of SR published so far. In order to highlight the diversity of the two-state model, we shall discuss several examples from such different fields as condensed matter, nonlinear and quantum optics and biophysics. Finally, we also discuss some situations that go beyond the generic SR scenario but are still characterized by a constructive role of noise.

Stochastic resonance[02.50.Ey Stochastic processes; 05.40.Ca Noise; 32.80.-t Photon interactions with atoms; 42.50.Lc Quantum fluctuations, quantum noise, and quantum jumps; 87.10.+e General theory and mathematical aspects;]

The dynamics of colloidal particles in potential energy landscapes have mainly been investigated theoretically. In contrast, here we discuss the experimental realization of potential energy landscapes with the help of laser light fields and the observation of the particle dynamics by video microscopy. The experimentally observed dynamics in periodic and random potentials are compared to simulation and theoretical results in terms of, e.g. the mean-squared displacement, the time-dependent diffusion coefficient or the non-Gaussian parameter. The dynamics are initially diffusive followed by intermediate subdiffusive behaviour which again becomes diffusive at long times. How pronounced and extended the different regimes are, depends on the specific conditions, in particular the shape of the potential as well as its roughness or amplitude but also the particle concentration. Here we focus on dilute systems, but the dynamics of interacting systems in external potentials, and thus the interplay between particle-particle and particle-potential interactions, are also mentioned briefly. Furthermore, the observed dynamics of dilute systems resemble the dynamics of concentrated systems close to their glass transition, with which it is compared. The effect of certain potential energy landscapes on the dynamics of individual particles appears similar to the effect of interparticle interactions in the absence of an external potential.

Colloids in light fields: Particle dynamics in random and periodic energy landscapes

Disorder plays a fundamental role in many fields of physics such as condensed-matter physics, optics, acoustics, or atomic physics. It is responsible for a number of surprizing effects, such as Anderson localization, metal-insulator transitions and intriguing glass phases. The inherent complexity of disordered systems poses outstanding challenges to the full understanding of these phenomena. In the last years, disorder has emerged as a major line of research in the field of ultracold quantum gases. The latter offer fascinating perspectives to better understand the effects of disorder in quantum systems, thanks not only to an unprecedented control of parameters, but also to their original properties. This Habilitation thesis reviews our recent contributions to the theory of disordered quantum gases along three main lines: - Anderson localization in disordered quantum gases; - Disorder in interacting Bose gases; - Simulating extended Hubbard and spin models with ultracold gases. On the one hand, we propose and analyze experiments aiming at realizing quantum simulators to address open questions of fundamental importance for the field of disordered systems. In this respect, we show that quantum gases offer promising perspectives. On the other hand, we lead prospective works, which in particular show that quantum gases have original properties. They hence shed new light on issues of broad interest in the field of disordered systems.

Disordered, ultracold quantum gases: Theoretical studies and experimental perspectives

We report the first direct observation of Brillouin-like propagation modes in a dissipative periodic optical lattice. This has been done by observing a resonant behavior of the spatial diffusion coefficient in the direction corresponding to the propagation mode with the phase velocity of the moving intensity modulation used to excite these propagation modes. Furthermore, we show theoretically that the amplitude of the Brillouin mode is a nonmonotonic function of the strength of the noise corresponding to the optical pumping, and discuss this behavior in terms of nonconventional stochastic resonance.

/pdf/brillouin-propagation-modes-in-optical-lattices-59uzvof63u.pdf

Brillouin propagation modes in optical lattices: interpretation in terms of nonconventional stochastic resonance.

A critical interplay of two correlated noises in a nonlinear symmetrical two-well potential system is experimentally demonstrated. One state can become completely noise free, leading to an infinite Kramers time. If an independent lever breaks the potential symmetry, stochastic resonance is recovered. In this new regime, we obtain a plateau, i.e., a high signal-to-noise ratio even for vanishing forcing signals.

Lever-assisted two-noise stochastic resonance.

We describe the pump-probe spectroscopy of atoms cooled in a 3D lin⊥lin optical lattice. Our pump-probe configuration consists of two laser fields detuned with respect to the lattice fields. This scheme allows to clearly identify in the probe transmission spectrum the Brillouin and Raman resonances, by studying their positions as functions of the angle between the pump and probe beams. We describe these resonances in detail, and compare the experimental results to the theoretical predictions. Our conclusions are supported by transport-spectroscopy measurements, which allow to distinguish between contributions to the light scattering from propagating and non-propagating atoms.

Pump-probe spectroscopy of atoms cooled in a 3D lin⊥lin optical lattice

Observing stochastic resonance in dissipative optical lattices

Directed diffusion of cold atoms in a symmetric optical lattice

Summary form only given. We report the observation of directed diffusion in a symmetric periodic potential. This has been realized with cold atoms in a one-dimensional dissipative optical lattice. A zero mean force temporary asymmetric induces the directed motion of a Brownian particle.

Directed diffusion in a 1D symmetric optical lattice

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