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Um modelo esquemático e um modelo realistico para tunelamento coerente em poco duplo

Gabriela Barreto Lemos

Published Aug 9, 2006• 0 citations
OpenAlex

Abstract

We present two examples of tunneling in double well potentials. Therst is a study of the localization in a dissipative one-particle system bymeans of an analogy with a spin-1/2 system in a uniform magnetic eld.The second example is an investigation of the tunneling process of a Bose-Einstein Condensate in a double well potential from the point of view ofa many body Hamiltonian. Although the two-mode model for the processis not realistic for large enough number of particles (N 200), for certaininitial conditions, it points out a completely dierent explanation for thenon-observation of tunneling from that given in Michael Albiez et al, Phys.Rev. Lett. 95, 010402 (2005). We observe a \phase transition" related to spectral properties of the Hamiltonian and the initial conditions which, for large enough initial population imbalance, presents occupation probabilitiesconcentrated in doublets.

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We present two examples of tunneling in double well potentials. Therst is a study of the localization in a dissipative one-particle system bymeans of an analogy with a spin-1/2 system in a uniform magnetic eld.The second example is an investigation of the tunneling process of a Bose-Einstein Condensate in a double well potential from the point of view ofa many body Hamiltonian. Although the two-mode model for the processis not realistic for large enough number of particles (N 200), for certaininitial conditions, it points out a completely dierent explanation for thenon-observation of tunneling from that given in Michael Albiez et al, Phys.Rev. Lett. 95, 010402 (2005). We observe a \phase transition" related to spectral properties of the Hamiltonian and the initial conditions which, for large enough initial population imbalance, presents occupation probabilitiesconcentrated in doublets.
We study the tunneling of a spin polarized Fermi gas in a three-dimensional double well potential, focusing on the time dynamics starting from an initial state in which there is an imbalance in the number of particles in the two wells. Although fermions in different doublets of the double well tunnel with different frequencies, we point out that (incoherent) oscillations of a large number of particles can arise, as a consequence of the presence of transverse degrees of freedom. Estimates of the doublet structure and of the occupation of transverse eigenstates for a realistic experimental setup are provided.
We study quantum dynamical properties of a spin-1 atomic Bose-Einstein condensate in a double-well potential. Adopting a mean field theory and single spatial mode approximation, we characterize our model system as two coupled spins. For certain initial states, we find full magnetization oscillations between wells not accompanied by mass (or atom numbers) exchange. We identify dynamic regimes of collective spin variables arising from nonlinear self-interactions that are different from the usual Josephson oscillations. We also discuss magnetization beats and incomplete oscillations of collective spin variables other than the magnetization. Our study points to an alternative approach to observe coherent tunnelling of a condensate through a (spatial) potential barrier.
In this work, our primary goal has been to explore the range of validity of two-mode models for Bose-Einstein condensates in double-well potentials. Our derivation, like others, uses symmetric and antisymmetric condensate basis functions for the Gross-Pitaevskii equation. In what we call an ``improved two-mode model'' (I2M), the tunneling coupling energy explicitly includes a nonlinear interaction term, which has been given previously in the literature but not widely appreciated. We show that when the atom number (and hence the extent of the wave function) in each well vary appreciably with time, the nonlinear interaction term produces a temporal change in the tunneling energy or rate, which has not previously been considered to our knowledge. In addition, we obtain a parameter, labeled ``interaction tunneling,'' that produces a decrease of the tunneling energy when the wave functions in the two wells overlap to some extent. Especially for larger values of the nonlinear interaction term, results from this model produce better agreement with numerical solutions of the time-dependent Gross-Pitaevskii equation in one and three dimensions, as compared with models that have no interaction term in the tunneling energy. The usefulness of this model is demonstrated by good agreement with recent experimental results for the tunneling oscillation frequency [Albiez et al., Phys. Rev. Lett. 95, 010402 (2005)]. We also present equations and results for a multimode approach, and use the I2M model to obtain modified equations for the second-quantized version of the Bose-Einstein double-well problem.
The Josephson effect can be observed in a Bose-Einstein condensate in a double-well potential, which is attributed to the tunneling of bosons between two wells. We propose a multi-mode theory to investigate the dynamics of local excitations in a one-dimensional condensate in a double-well potential. We show that the system can be described by two independent two-mode models. The Josephson oscillation and the self-trapping of local collective excitations are predicted analytically and confirmed by numerical simulation.
Neste trabalho, estudamos a dinâmica de bósons de spin 1 em potenciais de poço duplo ou triplo. Temos por base o modelo de Bose-Hubbard, muito utilizado para o estudo teórico de átomos ultrafrios confinados em potenciais ópticos. Esse modelo leva em conta o tunelamento das partículas entre os poços e uma interação repulsiva local. Para bósons de spin não nulo, a extensão aqui considerada introduz uma interação local que favorece alto ou baixo spin total em um poço, dependendo do sinal da constante de acoplamento. A matriz do hamiltoniano é construída em uma base apropriada e diagonalizada numericamente, determinando-se os seus autovalores e autovetores. Processos de evolução temporal a partir de diferentes estados iniciais são estudados em função dos parâmetros de controle, escolhidos como a interação dependente de spin e as profundidades relativas dos poços. Especial atenção é dada ao modelo de três poços em configuração linear, usando a variação da energia do poço central como equivalente ao efeito de um potencial de porta em um transistor de efeito de campo. Para este caso, são determinadas diversas condições sobre os parâmetros do sistema para que exista fluxo de partículas entre os poços laterais, controlado pelas características do poço central. Também exploramos as condições para a existência de dinâmica ressonante na presença de um campo magnético constante aplicado no poço central. Finalmente, permitimos que a intensidade do campo magnético varie no tempo para controlar o período de oscilação do fluxo de partículas entre os poços laterais.
In terms of exact solution of the time-dependent Schrodinger equation. we examine the quantum tunneling process in Bose condensates of two interacting species trapped in a double well configuration. We use the two series of time-dependent SU(2) gauge transformation to diagonalize the Hamilton operator obtain analytic time-evolution formulas of the population imbalance and the berry phase. The particle population imbalance (a(L)(+)a(L) - a(R)(+)a(R)) of species A between the two wells is studied analytically.