Examinando por Materia "Redes ópticas"

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    The anisotropic Bose-Hubbard dimer in the mean field approximation
    (Universidad del Valle, 2025) Becerra Arbeláez, Isabella; Madronero, Javier
    This project studies the system formed by two coupled Bose-Einstein condensates, also known as the bosonic Josephson junction. A double-well model is used to trap the ultracold atoms, and special attention is paid to the understudied case of asymmetric wells. A brief introduction to Bose- Einstein condensates and their relationship to optical lattices is provided. The Bose-Hubbard model restricted to two wells is also described, and a large number of particles is considered, allowing for the use of the semiclassical mean-field approximation. By introducing anisotropy into this system, a symmetry breaking in phase space is found, which can be interpreted as a dissipative process emerging in semiclassical dynamics, although the total particle flux is conserved. Additionally, this same system is studied using the spin formalism considering a large number of bosons. Under this approach, the anisotropy affects the system in the same way as a Zeeman effect, where the dimer behaves as an N/2 spin model in the presence of an external magnetic field proportional to ∆. The expectation values of the spin components and their variances are studied, especially for ˆSz , which by definition represents the difference of particles for both wells and depends strongly on the anisotropy. The quantum fluctuations for ˆSx, ˆSy, and ˆSz decrease with increasing particle number, particularly as ∝ 1/N , suggesting that ˆSx, ˆSy, and ˆSz becomes more quantum localized near the semiclassical limit.
  • Miniatura
    PublicaciónAcceso abierto
    Propiedades de coherencia cuántica en sistemas bosónicos de baja dimensionalidad.
    (2019-10-31) Rodriguez Ramirez, Karem Cecilia; Marin Alvarado, Gustavo Adolfo; Olaya Agudelo, Vanessa Carolina
    En este proyecto, presentamos la implementación de un interferómetro Mach-Zehnder explorando las propiedades de coherencia de ondas de materia bosónicas ultra frías. El sistema es modelado mediante la ecuación de Gross-Pitaevskii. La onda incidente es dividida 50:50 por un potencial doble pozo dependiente del tiempo. Un haz experimenta un corrimiento de fase controlado y finalmente los dos haces se recombinan. Las soluciones son obtenidas mediante diferencias finitas para la discretización espacial y Runge-Kutta para la evolución temporal. Se presentan la densidad y la fase para diferentes potenciales externos desarrollados, para cada caso la fidelidad es monitoreada para analizar la adiabaticidad del proceso dinámico. El otro sistema bosónico bajo estudio es un sistema molecular reticular unidimensional de moléculas LiCs que se encuentra en la fase fuertemente interactuante de aislante de Mott, con una molécula por sitio preparada en el estado base y primer estado excitado rovibracional en presencia de un campo eléctrico perpendicular a la red. A grandes distancias intermoleculares, la interacción dipolo-dipolo en la aproximación de primeros vecinos domina la dinámica del problema. La entropía de entrelazamiento de Von Neumann generada durante la dinámica es presentada para evoluciones temporales cortas. El potencial de este tipo de sistemas moleculares para ser usados en protocolos de información cuántica se evidencia en la aparición temprana de un ordenamiento a largo alcance en la matriz densidad de una partícula. Las simulaciones numéricas son hechas usando el algoritmo de evolución temporal de decimación en bloque basado en el formalismo de estados producto de matriz y la descomposición de Susuki-Trotter.
  • No hay miniatura disponible
    PublicaciónAcceso abierto
    Tensor network-based ansatz for the analysis of a spin-1 system quadrupolar phases
    (Universidad del Valle, 2024) Enríquez Zamudio, Ana María; Rodriguez-Ramirez, Karen
    The precision achieved by experimental techniques with ultracold atoms has enabled the creation of quantum simulators, facilitating the exploration of one-dimensional systems in the laboratory. In these systems, fluctuations are inherently collective and propagate over large distances due to frequent collisions. As a result, theoretical frameworks have been developed that leverage these fluctuations to describe such systems. Ultracold gases confined in optical lattices not only serve as quantum simulators for traditional condensed matter systems but also act as platforms to create new many-body quantum systems. In this work, two numerical techniques are proposed to explore a spin-1 bosonic gas contained in a one-dimensional optical lattice, in the strongly interacting phase and in the Mott insulator regime. The first technique is a mean-field approach, known as the Gutzwiller ansatz, which approximates the many-body wave function as the product of individual contributions at each site. Additionally, a more advanced ansatz has been developed that considers pairs of coupled sites, allowing for the exploration of regions in the phase space that are not accessible with the traditional ansatz. The second technique is based on tensor networks, specifically representing the state as a Matrix Product State (MPS), combined with the Time-Evolving Block Decimation (TEBD) algorithm. This technique is used to analyze the ground state properties and magnetic behavior of the system under the influence of an external magnetic field. Both techniques were evaluated within the context of a Bilinear-Biquadratic Heisenberg Hamiltonian, incorporating perturbative corrections to account for the quadratic Zeeman effect. The results of this work demonstrate that tensor networks, particularly MPS, provide a robust numerical technique for capturing the quantum phenomena exhibited by spin-1 bosons. The calculations of ground state energy and magnetization profiles confirm the effectiveness of tensor networks in representing the essential physics of the system. Furthermore, the investigation of entanglement properties reveals that the system’s entanglement entropy obeys an area law, characteristic of gapped one-dimensional systems. Chirality and spin correlation observables were also explored, revealing relevant information about the system’s behavior under various interaction parameters. The results are consistent with previous theoretical and numerical studies, highlighting the potential of tensor networks to address challenges in many-body quantum physics. This work introduces a novel numerical perspective within the context of Solid State research at the University of Valle, paving the way for future studies utilizing advanced tensor network techniques.
  • Miniatura
    PublicaciónAcceso abierto
    Teoría de Floquet para el estudio de correlaciones en sistemas atómicos dependientes periódicamente en el tiempo.
    (2018-04-25) Rodríguez Ramírez, Karem Cecilia; Madroñero Pabón, Javier; González Melán, Alejandro; Muñoz Arias, Manuel Humberto; Guzmán Naranjo, Isabel; Ortiz Girón, Jhoan Sebastían
    Los conceptos de correlaciones y complejidad van de la mano en sistemas atómicos. Incluso sistemas relativamente ``pequeños'' pueden ser extremadamente complejos debido a las fuertes correlaciones entre sus constituyentes. En este proyecto se estudiaron las correlaciones y sus consecuencias en dos clases de sistemas atómicos con dependencia periódica en el tiempo: el átomo de helio forzado periódicamente y átomos fríos en redes ópticas que incluyen modulaciones periódicas en el tiempo.