Spinor BECs in a double-well: population transfer and Josephson oscillations

The dynamics of an F=1 spinor condensate in a two-well potential is studied within the framework of the Gross-Pitaevskii equation. We derive two-mode equations relating the population imbalances, the phase differences among the condensates at each side of the barrier and the time evolution of the different Zeeman populations for the case of small population imbalances. The case of zero total magnetization is scrutinized in this limit demonstrating the ability of a two mode analysis to describe to a large extent the dynamics observed in the Gross-Pitaevskii equations. It is also demonstrated that the time evolution of the different total populations fully decouples from the Josephson tunneling phenomena. All the relevant time scales are clearly identified with microscopic properties of the atom-atom interactions

Dynamic generation of spin-squeezed states in bosonic Josephson junctions

We analyze the formation of squeezed states in a condensate of ultracold bosonic atoms confined by a double-well potential. The emphasis is set on the dynamical formation of such states from initially coherent many-body quantum states. Two cases are described: the squeezing formation in the evolution of the system around the stable point, and in the short time evolution in the vicinity of an unstable point. The latter is shown to produce highly squeezed states on very short times. On the basis of a semiclassical approximation to the Bose-Hubbard Hamiltonian, we are able to predict the amount of squeezing, its scaling with $N$ and the speed of coherent spin formation with simple analytical formulas which successfully describe the numerical Bose-Hubbard results. This new method of producing highly squeezed spin states in systems of ultracold atoms is compared to other standard methods in the literature.Comment: 12 pages, revised discussion + added reference

Spin-driven spatial symmetry breaking of spinor condensates in a double-well

The properties of an F=1 spinor Bose-Einstein condensate trapped in a double-well potential are discussed using both a mean-field two-mode approach and a simplified two-site Bose-Hubbard Hamiltonian. We focus in the region of phase space in which spin effects lead to a symmetry breaking of the system, favoring the spatial localization of the condensate in one well. To model this transition we derive, using perturbation theory, an effective Hamiltonian that describes N/2 spin singlets confined in a double-well potential.Comment: 12 pages, 5 figure

Self-trapping of a binary Bose-Einstein condensate induced by interspecies interaction

The problem of self-trapping of a Bose-Einstein condensate (BEC) and a binary BEC in an optical lattice (OL) and double well (DW) is studied using the mean-field Gross-Pitaevskii equation. For both DW and OL, permanent self-trapping occurs in a window of the repulsive nonlinearity $g$ of the GP equation: $g_{c1}<g<g_{c2}$. In case of OL, the critical nonlinearities $g_{c1}$ and $g_{c2}$ correspond to a window of chemical potentials $\mu_{c1}<\mu<\mu_{c2}$ defining the band gap(s) of the periodic OL. The permanent self-trapped BEC in an OL usually represents a breathing oscillation of a stable stationary gap soliton. The permanent self-trapped BEC in a DW, on the other hand, is a dynamically stabilized state without any stationary counterpart. For a binary BEC with intraspecies nonlinearities outside this window of nonlinearity, a permanent self trapping can be induced by tuning the interspecies interaction such that the effective nonlinearities of the components fall in the above window

A dipolar self-induced bosonic Josephson junction

We propose a new scheme for observing Josephson oscillations and macroscopic quantum self-trapping phenomena in a toroidally confined Bose-Einstein condensate: a dipolar self-induced Josephson junction. Polarizing the atoms perpendicularly to the trap symmetry axis, an effective ring-shaped, double-well potential is achieved which is induced by the dipolar interaction. By numerically solving the three-dimensional time-dependent Gross-Pitaevskii equation we show that coherent tunneling phenomena such as Josephson oscillations and quantum self-trapping can take place. The dynamics in the self-induced junction can be qualitatively described by a two-mode model taking into account both s-wave and dipolar interactions.Comment: Major changes. Accepted for publication in EP

Weakly linked binary mixtures of F = 1 87Rb Bose-Einstein condensates

We present a study of binary mixtures of Bose-Einstein condensates confined in a double-well potential within the framework of the mean field Gross-Pitaevskii (GP) equation. We re-examine both the single component and the binary mixture cases for such a potential, and we investigate what are the situations in which a simpler two-mode approach leads to an accurate description of their dynamics. We also estimate the validity of the most usual dimensionality reductions used to solve the GP equations. To this end, we compare both the semi-analytical two-mode approaches and the numerical simulations of the one-dimensional (1D) reductions with the full 3D numerical solutions of the GP equation. Our analysis provides a guide to clarify the validity of several simplified models that describe mean-field nonlinear dynamics, using an experimentally feasible binary mixture of an F = 1 spinor condensate with two of its Zeeman manifolds populated, m = ±1