Quantum structures in nonlinear optics and atomic physics: a background overview (original) (raw)
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Nonlinear Excitations in Ultracold Atoms Trapped in Triple Optical Lattices
Condensed Matter
Various solitary wave excitations are found for a Bose-Einstein condensate in presence of two hybrid potentials in the form of triple mixtures of optical lattices. One of these potentials comprises of a combination of two important lattice profiles, such as frustrated optical lattice and double-well super-lattice, within one. Another represents a composite lattice combination, resulting in a wider and deeper frustrated optical lattice. The dynamical equation for such a system is solved by the exact analytical method to obtain a bright solitary wave, periodic wave and cnoidal wave excitations. We also report Anderson localization, bifurcation of condensate at the center and a competition between two different types of localizations upon trap engineering. Dynamical and structural stability analyses are also carried out, which reveal the obtained solutions as extremely stable for structural noise incorporation and sufficiently stable for dynamical stability. These triple mixtures of op...
Hofstadter butterflies in nonlinear Harper lattices, and their optical realizations
New Journal of Physics, 2010
The ubiquitous Hofstadter butterfly describes a variety of systems characterized by incommensurable periodicities, ranging from Bloch electrons in magnetic fields and the quantum Hall effect to cold atoms in optical lattices and more. Here, we introduce nonlinearity into the underlying (Harper) model and study the nonlinear spectra and the corresponding extended eigenmodes of nonlinear quasiperiodic systems. We show that the spectra of the nonlinear eigenmodes form deformed versions of the Hofstadter butterfly and demonstrate that the modes can be classified into two families: nonlinear modes that are a 'continuation' of the linear modes of the system and new nonlinear modes that have no counterparts in the linear spectrum. Finally, we propose an optical realization of the linear and nonlinear Harper models in transversely modulated waveguide arrays, where these Hofstadter butterflies can be observed. This work is relevant to a variety of other branches of physics beyond optics, such as disorder-induced localization in ultracold bosonic gases, localization transition processes in disordered lattices, and more. The study of wave propagation in nonlinear periodic or quasiperiodic structures, both discrete and continuous, deals with many fascinating issues [1]: how fast does a localized wavepacket spread [2] and under what circumstances will it self-localize to form a soliton [3]? How does
Quantum effects in nonlinear optics and polaritonics
2018
The main scope of this thesis is the investigation of quantum properties of nonlinear, dissipative, optical and condensed matter systems. Compared with previous studies on this subjects, we reached several milestone of general interests for the theoretical and experimental community. The main experimental platform we refer to in this thesis is microcavity polaritons: polaritons arise from the coupling of light with excitons in a quantum well, i.e., a 2D semiconductor material embedded in the microcavity. They have attracted the interest of the scientific community for their rich physics. Polaritons can form out-of-equilibrium Bose-Einstein condensates, they can experience superfluid phase transition and, due to their interaction via the excitonic component, they show a variety of phenomena which are typical of nonlinear physics, such as bistability and parametric scattering. In particular, motivated by recent proposals about the generation of single photons from weakly nonlinear sys...
Nonlinear localized modes in Glauber–Fock photonic lattices
Optics Letters, 2012
We study a nonlinear Glauber-Fock lattice and the conditions for the excitation of localized structures. We investigate the particular linear properties of these lattices, including linear localized modes. We investigate numerically nonlinear modes centered in each site of the lattice. We found a strong disagreement of the general tendency between the stationary and the dynamical excitation thresholds, and we give a new definition based on both considerations.
Nonlinear Optics of Photons and Atoms
Computational Methods in Science and Technology, 2010
In this presentation we intend to focus on the exchange of experience between nonlinear optics (optical pulse and beam propagation in nonlinear media) and atom optics (dynamics of coherent waves generated from Bose-Einstein condensates). A common ground here is the nonlinear Schrödinger equation, which with the proper substitution of variables describes both types of phenomena. In nonlinear optics it is a light propagation equation that relates the signal at the end of the nonlinear crystal to the signal at the input face of the medium. In Bose-Einstein condensate dynamics it is the called the Gross-Pitaevskii equation. We will discuss various types of phenomena which have realisations both in the nonlinear optics and atom optics. We will concentrate our consideration on soliton formation, which is a challenge to fundamental and applied research in these two domains of physics.
Physical review, 2021
We study the landscape of solutions of the coherent quantum states in a ring-shaped lattice potential in the context of ultracold atoms with an effective positive nonlinearity induced by interatomic interactions. The exact analytical solutions in the absence of lattice are used as a starting point, and the transformation of those solutions is mapped as the lattice is introduced and strengthened. This approach allows a simple classification of all the solutions into states with periods commensurate or incommensurate with the lattice period and those with or without nodes. Their origins are traced to the primary dispersion curve and the swallowtail branches of the latticefree spectrum. The commensurate states tend to remain delocalized with increasing lattice depth, whereas the incommensurate ones may be localized. The symmetry and stability properties of the solutions are examined and correlated with branch energies. The crucial importance of rotation is highlighted by its utility in continuously transforming solutions and accessing in a finite ring with a few sites the full spectrum of nonlinear Bloch waves on an infinite lattice.
International Journal of Modern Physics B, 2015
The stability and collective excitations of binary Bose-Einstein condensates with cubic and quintic nonlinearities in variable anharmonic optical lattices are investigated. By using the variational approach, the influences of the quintic nonlinearities and the shape of the external potential on the stability are discussed in details. It is found that the quintic intraspecies and interspecies interatomic interactions profoundly affect the stability criterion and collective excitations of the system. The shape dependent potential form that characterizes the optical lattice deeply alters the stability regions. Direct numerical simulations of the mean-field coupled Gross-Pitaevskii equation describing the system agree well with the analytical predictions.
Influence of geometry and topology of quantum graphs on their nonlinear optical properties
Physical Review A, 2013
We analyze the nonlinear optics of quasi one-dimensional quantum graphs and manipulate their topology and geometry to generate for the first time nonlinearities in a simple system approaching the fundamental limits of the first and second hyperpolarizabilities. Changes in geometry result in smooth variations of the nonlinearities. Topological changes between geometrically-similar systems cause profound changes in the nonlinear susceptibilities that include a discontinuity due to abrupt changes in the boundary conditions. This work may inform the design of new molecules or nanoscale structures for nonlinear optics and hints at the same universal behavior for quantum graph models in nonlinear optics that is observed in other systems.
Quantum optics of nonlinear systems in cascade
2018
In this letter, we investigate the quantum optical properties of driven-dissipative nonlinear systems in a cascade configuration. We show that pumping a nonlinear system with a state having a noncoherent statistics, can improve the antibunching of the output state and, consequently, the nonclassicality of the whole system. Furthermore, we show that is possible to generate entanglement through dissipative coupling. These results applies to a broad category of physical systems with a Kerr-like non-linearity, from Rydberg atoms to exciton polaritons in microcavities.