79 research outputs found

    Theoretical Methods in the Non-Equilibrium Quantum Mechanics of Many Bodies

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    A toolbox of theoretical methods pertinent to the study of non-equilibrium many-body quantum mechanics is presented with an eye to specific applications in cold atoms systems and solids. We discuss the generalization from unitary quantum mechanics to the non-unitary framework of open quantum systems. Theoretical techniques include the Keldysh close-time-path integral and its associated correlation functions, the quantum kinetic equation, and numerical integration of equations of motion both unitary and non-unitary. We explore how the relaxation of the assumption of equilibrium yields a whole new array of sometimes counterintuitive effects. We treat such examples as the non-equilibrium enhancement of BCS superfluidity by driving, bistability and coherent population transfer in Feshbach coupled fermions, and the dynamic stimulation of quantum coherence in bosons confined to a lattice. These systems are considered with an eye to enhancing some useful quantum properties and making them available in wider parameter regimes

    Exploiting nonlinearity and noise in optical tweezers and semiconductor lasers : from resonant damping to stochastic logic gates and extreme pulses

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    This thesis is focused on the study of stochastic and nonlinear dynamics in optical systems. First, we study experimentally the dynamics of a Brownian nanometer particle in an optical trap subjected to an external forcing. Specifically, we consider the effects of parametric noise added to a monostable or bistable optical trap and discovered a new effect which we named stochastic resonant damping (SRD). SRD concerns the minimization of the output variance position of a particle held in a harmonic trap, when an external parametric noise was added to the position trap. We compared the classical stochastic resonance (SR) with SRD and found that they are two phenomena which coexist in the same system but in different regimes. The experimentally studied monostable system showed a maximum in the signal to noise ratio, a clear signature of a resonance. We also developed a new technique to increase 10-fold the detection range of the quadrant photodiode that we used in this study, which exploits the channel crosstalk. Second, we study the stochastic dynamics of a type of semiconductor laser (SCL), known as vertical-cavity surface-emitting laser (VCSEL), that exhibits polarization bistability and hysteresis, either when the injection current or when the optically injected power are varied. We have shown how these properties can be exploited for logic operations due to the effect of the spontaneous emission noise. Two logical input signals have been encoded in three levels of optically injected power from a master laser, and the logical output response was decoded from the emitted polarization of the injected VCSEL. Correct and robust operation was obtained when the three levels of injected power were adjusted to favor one polarization at two levels and to favor the orthogonal polarization at the third level. We numerically demonstrated that the VCSEL-based logic operator allows to reproduce the truth table for the OR and NOR logic operators, while the extension to AND and NAND is straightforward. With this all-optical configuration we have been able to reduce the minimum bit time required for correct operation from 30 ns, obtained in a previous work with an optoelectronic configuration, to 5 ns. The third focus of this thesis is the study of the chaotic nonlinear dynamics of a SCL optically injected, in the regime where it can display sporadic huge intensities pulses, referred to as Rogue Waves (RWs). We found that, when adding optical noise, the region where RWs appear becomes wider. This behavior is observed for high enough noise; however, on the contrary, for very weak noise we found that noise diminishes the number of RW events in certain regions. In order to suppress or induce extreme pulses, we investigated the effects of an external periodic modulation of the laser current. We found that the modulation at specific frequencies modifies the dynamics from chaotic to periodic. Depending on the parameter region, current modulation can contribute to an increased threshold for RWs. Therefore, we concluded that the modulation can be effective for suppressing the RWs dynamics

    Nonlinear and Quantum Optics with Whispering Gallery Resonators

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    Optical Whispering Gallery Modes (WGMs) derive their name from a famous acoustic phenomenon of guiding a wave by a curved boundary observed nearly a century ago. This phenomenon has a rather general nature, equally applicable to sound and all other waves. It enables resonators of unique properties attractive both in science and engineering. Very high quality factors of optical WGM resonators persisting in a wide wavelength range spanning from radio frequencies to ultraviolet light, their small mode volume, and tunable in- and out- coupling make them exceptionally efficient for nonlinear optical applications. Nonlinear optics facilitates interaction of photons with each other and with other physical systems, and is of prime importance in quantum optics. In this paper we review numerous applications of WGM resonators in nonlinear and quantum optics. We outline the current areas of interest, summarize progress, highlight difficulties, and discuss possible future development trends in these areas.Comment: This is a review paper with 615 references, submitted to J. Op

    Spatio-temporal dynamics of lasers and photorefractive oscillators under rocking: phase-bistable patterns and localized structures

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    El objectiu de aquesta tesi es l’estudi teòric, analític i numèric, de la dinàmica espaciotemporal d’oscil·ladors òptics no lineals sotmesos a un forçament bicromàtic (rocking). Aquest tipus d’injecció té la característica principal de trencar la invariància de fase (qualsevol fase del camp complex) del sistema lliure (sense forçament) i genera un sistema que és biestable en fase, ja que únicament dues fases (separades per ¼) són permeses per a les solucions estacionàries homogènies. Aquest canvi en la naturalesa del sistema provoca l’aparició d’una nova dinàmica caracteritzada per la presència d’un nou tipus d’estructures espacials en el pla transversal bidimensional: patrons biestables de fase en els quals dominis d’ambdues fases conviuen separades per parets de domini (Ising si la intensitat s’anul·la en elles o Bloch, en cas contrari). Aquests dominis poden evolucionar a patrons homogenis (d’una de les dues fases) o uns altres, més complexos, que els efectes de curvatura condueixen a la creació de patrons laberíntics segons els valors dels paràmetres del sistema. A més, poden existir estructures localitzades (dominis de grandària mínima estables) en la forma de solitons de cavitat d’anell fosc. Altres mètodes de trencament de la simetria de fase han sigut usats per a controlar la dinàmica de molts sistemes. Un dels més populars és la ressonància paramètrica, i.e. injectar un camp la freqüència del qual és aproximadament el doble de la freqüència natural de oscil·lació del sistema. No obstant això, aquests mètodes són menys versàtils que el rocking, el qual pot aplicar-se a una àmplia gamma de sistemes com el làser, que són insensibles a la ressonància paramètrica. De fet, s’han fet múltiples propostes teòriques i experimentals d’aplicació del rocking a diferents sistemes (òptics i no òptics). En el domini d’aquesta tesi, ens centrarem en la influència del rocking en dos sistemes que han sigut estudiats profusament en la literatura, donat el seu gran interès tant des del punt de vista fonamental compràctic:làsers i oscil·ladors fotorrefractius. Al llarg d’aquesta tesi, estudiarem detalladament la influència del rocking en aquests sistemes. Com és usual en el camp de la ciència no lineal, és convenient deduir equacions que descriguen el comportament d’aquests sistemes prop dels punts (punts crítics) on emergeixen les solucions estacionàries del sistema. Aquestes equacions (anomenades de paràmetre d’ordre) tenen una forma aparentment simple i són capaces de descriure multitud de sistemes no lineals, físics, químics, biològics.. (l’única diferència és el significat dels diferents paràmetres, però l’estructura matemàtica és la mateixa), per la qual cosa posseeixen un caràcter universal. Així mateix, analitzarem l’estabilitat de les solucions trobades i realitzarem simulacions numèriques dels diferents models teòrics. Es presentaran els següents resultats: A partir de les equacions de MB amb injecció rocking, es deduirà una equació de paràmetre d’ordre per a làsers de classe C amb desintonia positiva de la cavitat i s’estudiaran numèricament els patrons del sistema. Per a làsers de classe B, s’obtindrà un model reduït de dues equacions i s’analitzarà la seua dinàmica temporal i la influència de la desintonia de la injecció rocking. També esmostraran patrons espacials obtinguts a partir de la simulació de les equacions de MB.Es desenvoluparà un model unificat (vàlid per a desintonies de la cavitat positives i negatives) per a làsers de dos nivells (classe C i A) i oscil·ladors fotrorefractius, proporcionant els dominis d’estabilitat dels estats biestables en fase i estudiant numèricament els patrons espacials que apareixen. S’analitzarà la dinàmica temporal d’un làser bidireccional amb injecció rocking i es presentaran alguns resultats preliminars de patrons espacialsThe objective of this thesis is the theoretical, analytical and numerical, study of the spatio-temporal dynamics of optical oscillators under bichromatic forcing (rocking). This kind of injection possesses the feature of breaking the phase invariance (any phase of the complex field is possible) of the free-running system and generates a phase-bistable system in which two only phases are allowed for the homogeneous stationary solutions. This change in the nature of the system enables a new dynamics characterized by the presence of a new kind of spatial structures in the bidimensional transverse plane: bistable phase patterns in which both phases coexist separated by domain walls (Ising if they have null intensity or Bloch if it is different from zero). These domains can evolve either to homogeneous patterns (in which only one phase is present) or to more complex ones, in which curvature effects lead to the emergence of labyrinthic patterns depending on the value of the parameters of the system. Moreover, localized structures (stable minimum-size domains) as dark-ring cavity solitons can exist. In the scope of this thesis, we have focused on the influence of rocking in two systems which have been studied profusely in the literature, as they are very interesting both from a fundamental and a practical point of views: lasers and photorefractive oscillators. Along this thesis, we will study the influence of rocking in those systems in detail. As it is usual in nonlinear science, is convenient to derive equations describing the behaviour of those systems close to (critical) points where the stationary solutions emerge. These equations (called order parameter equations) are relatively simple and are able to describe a large number of nonlinear systems: physical, chemical, biological.. (the meaning ot the parameters being the only difference , but the mathematical structure is the same). Moreover, we will analyze the stability of the solutions and we will perform numerical simulations of the theoretical models. The following results will be presented: Starting from the MB equations under rocking injection, an order parameter equation will be derived for class C lasers with positive cavity detuning and the patterns of the system will be studied numerically. A reduced model of two equations will be obtained for class B lasers and its temporal dynamics and the influence of the detuning of rocking injection will be studied. We will also show spatial patterns obtained from simulations of the MB equations. A unified model (valid for positive and negative cavity detunings) for two level lasers (class C and A) and photorefractive oscillators will be developed, providing the stability domains of the phase bistable states and studying numerically the spatial patterns that arise from the system. The temporal dynamics of a bidirectional laser under rocking injection will be analyzed and some preliminary results regarding spatial patterns will be given

    Synchronization of a large number of continuous one-dimensional stochastic elements with time delayed mean field coupling

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    We study synchronization as a means of control of collective behavior of an ensemble of coupled stochastic units in which oscillations are induced merely by external noise. We determine the boundary of the synchronization domain of a large number of onedimensional continuous stochastic elements with time delayed non-homogeneous mean-field coupling. Exact location of the synchronization threshold is shown to be a solution of the boundary value problem (BVP) which was derived from the linearized Fokker-Planck equation. Here the synchronization threshold is found by solving this BVP numerically. Approximate analytics is obtained by expanding the solution of the linearized Fokker-Planck equation into a series of eigenfunctions of the stationary Fokker-Planck operator. Bistable systems with a polynomial and piece-wise linear potential are considered as examples. Multistability and hysteresis is observed in the Langevin equations for finite noise intensity. In the limit of small noise intensities the critical coupling strength was shown to remain finite

    Levitation of non-magnetizable droplet inside ferrofluid

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    The central theme of this work is that a stable levitation of a denser non-magnetizable liquid droplet, against gravity, inside a relatively lighter ferrofluid -- a system barely considered in ferrohydrodynamics -- is possible, and exhibits unique interfacial features; the stability of the levitation trajectory, however, is subject to an appropriate magnetic field modulation. We explore the shapes and the temporal dynamics of a plane non-magnetizable droplet levitating inside ferrofluid against gravity due to a spatially complex, but systematically generated, magnetic field in two dimensions. The effect of the viscosity ratio, the stability of the levitation path and the possibility of existence of multiple-stable equilibrium states is investigated. We find, for certain conditions on the viscosity ratio, that there can be developments of cusps and singularities at the droplet surface; this phenomenon we also observe experimentally and compared with the simulations. Our simulations closely replicate the singular projection on the surface of the levitating droplet. Finally, we present an dynamical model for the vertical trajectory of the droplet. This model reveals a condition for the onset of levitation and the relation for the equilibrium levitation height. The linearization of the model around the steady state captures that the nature of the equilibrium point goes under a transition from being a spiral to a node depending upon the control parameters, which essentially means that the temporal route to the equilibrium can be either monotonic or undulating. The analytical model for the droplet trajectory is in close agreement with the detailed simulations. (See draft for full abstract).Comment: This article has been published in a revised form in Journal of Fluid Mechanics http://dx.doi.org/10.1017/jfm.2018.733. Copyright: copyright holde

    Spatial localization and pattern formation in discrete optomechanical cavities and arrays

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    We investigate theoretically the generation of nonlinear dissipative structures in optomechanical (OM) systems containing discrete arrays of mechanical resonators. We consider both hybrid models in which the optical system is a continuous multimode field, as it would happen in an OM cavity containing an array of micro-mirrors, and also fully discrete models in which each mechanical resonator interacts with a single optical mode, making contact with Ludwig and Marquardt (2013 Phys. Rev. Lett. 101, 073603). Also, we study the connections between both types of models and continuous OM models. While all three types of models merge naturally in the limit of a large number of densely distributed mechanical resonators, we show that the spatial localization and the pattern formation found in continuous OM models can still be observed for a small number of mechanical elements, even in the presence of finite-size effects, which we discuss. This opens new venues for experimental approaches to the subject

    Quantum fluids of light

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    This article reviews recent theoretical and experimental advances in the fundamental understanding and active control of quantum fluids of light in nonlinear optical systems. In presence of effective photon-photon interactions induced by the optical nonlinearity of the medium, a many-photon system can behave collectively as a quantum fluid with a number of novel features stemming from its intrinsically non-equilibrium nature. We present a rich variety of photon hydrodynamical effects that have been recently observed, from the superfluid flow around a defect at low speeds, to the appearance of a Mach-Cherenkov cone in a supersonic flow, to the hydrodynamic formation of topological excitations such as quantized vortices and dark solitons at the surface of large impenetrable obstacles. While our review is mostly focused on a class of semiconductor systems that have been extensively studied in recent years (namely planar semiconductor microcavities in the strong light-matter coupling regime having cavity polaritons as elementary excitations), the very concept of quantum fluids of light applies to a broad spectrum of systems, ranging from bulk nonlinear crystals, to atomic clouds embedded in optical fibers and cavities, to photonic crystal cavities, to superconducting quantum circuits based on Josephson junctions. The conclusive part of our article is devoted to a review of the exciting perspectives to achieve strongly correlated photon gases. In particular, we present different mechanisms to obtain efficient photon blockade, we discuss the novel quantum phases that are expected to appear in arrays of strongly nonlinear cavities, and we point out the rich phenomenology offered by the implementation of artificial gauge fields for photons.Comment: Accepted for publication on Rev. Mod. Phys. (in press, 2012
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