Quantum dynamics of bosons in a double-well potential: Josephson oscillations, self-trapping and ultralong tunneling times

Abstract

The dynamics of the population imbalance of bosons in a double-well potential is investigated from the point of view of many-body quantum mechanics in the framework of the two-mode model. For small initial population imbalances, coherent superpositions of almost equally spaced energy eigenstates lead to Josephson oscillations. The suppression of tunneling at population imbalance beyond a critical value is related to a high concentration of initial state population in the region of the energy spectrum with quasi-degenerate doublets resulting in imbalance oscillations with a very small amplitude. For unaccessible long times, however, the system recovers the regime of Josephson oscillations. The understanding of many-body quantum systems from the theoretical and experimental points of view has undergone a considerable development during the past decade. Unifying concepts of several branches of physics are under development, creating an interdisciplinary scenario for the understanding of quantum mechanical paradigms. One of the simplest many-body systems to be realized experimentally and studied theoretically are ultracold bosons in a double-well potential. This system is very rich exhibiting a great variety of quantum phenomena such as interference [1], tunneling/selftrapping [2,3,4,5,6,7], entanglement of macroscopic superpositions [8]. Lately this system has been extensively studied, especially after the implementation of several experiments in the area. The usual theoretical approach to weakly interacting Bose-Einstein condensates (BECs) is the mean-field approximation, a nonlinear Gross-Pitaevski equation [3,9,10,11,12,13,14,15,16], which has proven very adequate in explaining a wide variety of experiments.More recently, the dynamics of population distribution between two or more wells of an optical lattice have been experimentally investigated. In particular, Josephson oscillations have been observed in a 1D optical lattice [17,18] and recently the density distribution of tunneling 87 Rb particles is directly observed [2]. In this experiment, initial population differences between the left and right well components are controlled by loading the BEC into an asymmetric double-well potential. The Josephson dynamics is initiated at t = 0 by non-adiabatically changing the potential to a symmetric double-well. When the initial population imbalance is below a critical value, the system presents Josephson oscillations between the two sides of the well. However, above this critical value tunneling is not observed. Based on a mean field treatment, this is usually attributed to macroscopic self-trapping. In the present work, we discuss an alternative approach to this system based on exact numerical solutions of the two-mode Bose-Hubbard Hamiltonian [19]:

Interspecies tunneling in one-dimensional Bose mixtures

“…7. Their energy splitting in this two-mode model has been determined to be ω [34]. The tunnel period is thus expected to grow exponentially with the number of particles, as already foreshadowed in Fig.…”

Dynamical effects of exchange symmetry breaking in mixtures of interacting bosons

“…The classical calculation (black solid line) exhibits oscillations in (a) and self-trapping in (b) (note the changed scale for the ordinate). The quantum many-body calculation features the same qualitative behavior, but the oscillations decay due to quantum fluctuations [35].…”

“…Since the scaling of will also be discussed, we keep as an explicit parameter. Equation (1) represents a self-trapping equation [31,32], which has been studied extensively [6,10,11,15,30,[33][34][35]. We review here the essential properties that will be useful for our analysis of the two-component case; in particular, we discuss a nonlinear scaling property for the population imbalance between the wells.…”

Few-boson tunneling dynamics of strongly correlated binary mixtures in a double well

“…Theoretically, the tunneling dynamics of single species through the crossover from weak to strong interaction regimes reveal interesting effects such as Josephson oscillations, pair tunneling, self-trapping, and fermionization [29][30][31][32][33], which have also been observed experimentally [34,35].…”