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arXiv:1401.7693 · Physical Review A

Josephson physics of spin-orbit-coupled elongated Bose-Einstein condensates

Miguel Ángel García-March, G. Mazzarella, Luca Dell’Anna, Bruno Juliá-Díaz, Luca Salasnich, A. Polls

Published Jun 6, 2014• 60 citations
arXivHTMLPDF

Abstract

We consider an ultracold bosonic binary mixture confined in a quasi-one-dimensional double-well trap. The two bosonic components are assumed to be two hyperfine internal states of the same atom. We suppose that these two components are spin-orbit coupled to each other. We employ the two-mode approximation starting from two coupled Gross-Pitaevskii equations and derive a system of ordinary differential equations governing the temporal evolution of the interwell population imbalance of each component and of the polarization, which is the imbalance of the total populations of the two species. From this set of equations we disentangle the different macroscopic quantum tunneling and self-trapping scenarios occurring for both population imbalances and the polarization in terms of the interplay between the interatomic interactions and the other relevant energies in the problem, like the spin-orbit coupling or the conventional tunneling term. We find a rich dynamics in all three variables and discuss the experimental feasibility of such a system.

DOI
10.1103/physreva.89.063607

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We consider an ultracold bosonic binary mixture confined in a quasi-one-dimensional double-well trap. The two bosonic components are assumed to be two hyperfine internal states of the same atom. We suppose that these two components are spin-orbit coupled to each other. We employ the two-mode approximation starting from two coupled Gross-Pitaevskii equations and derive a system of ordinary differential equations governing the temporal evolution of the interwell population imbalance of each component and of the polarization, which is the imbalance of the total populations of the two species. From this set of equations we disentangle the different macroscopic quantum tunneling and self-trapping scenarios occurring for both population imbalances and the polarization in terms of the interplay between the interatomic interactions and the other relevant energies in the problem, like the spin-orbit coupling or the conventional tunneling term. We find a rich dynamics in all three variables and discuss the experimental feasibility of such a system.
One-dimensional quantum tunneling dynamics between two-component Bose-Einstein condensates confined in a double-well magnetic trap is investigated. One-dimensional Gross-Pitaevskii equations for two-component Bose-Einstein condensates are derived from the three-dimensional ones. We derive Feynman equations from one-dimensional Gross-Pitaevskii equations. To study tunneling dynamics we solve Feynman equations in terms of a completely numerical procedure. In contrast to single-component condensates between two-component condensates, we find that this system can take on abundant tunneling results, the full tunneling dynamical behavior is summarized in phase portrait with constant energy lines. It is found that this system can achieve self-trapping when increase interatomic interactions exceed a critical value. We give the analytical critical expressions of interatomic interactions from the system Hamiltonian.
We investigate the dynamics of two-component Bose–Einstein condensates, composed of atoms in two distinct hyperfine states, which are linearly coupled by two-photon Raman transitions. The condensate is loaded into a double-well potential. A variety of dynamical behaviour, ranging from regular Josephson oscillations to mixed Rabi–Josephson oscillations and to regimes featuring increasing complexity are described in terms of a reduced Hamiltonian system with four degrees of freedoms, which are the numbers of atoms in each component in the left and right potential wells, whose canonically conjugate variables are phases of the corresponding wavefunctions. Using the system with four degrees of freedom, we study the dynamics of fractional imbalances of the two bosonic components and compare the results to direct simulations of the Gross–Pitaevskii equations describing the bosonic mixture. We perform this analysis when the fractional imbalance oscillates around a zero-time averaged value and in the self-trapping regime as well.
We study atomic Josephson junctions (AJJs) with one and two bosonic species confined by a double-well potential. Proceeding from the second quantized Hamiltonian, we show that it is possible to describe the zero-temperature AJJ microscopic dynamics by means of extended Bose–Hubbard (EBH) models, which include usually neglected nonlinear terms. Within the mean-field approximation, the Heisenberg equations derived from such two-mode models provide a description of AJJ macroscopic dynamics in terms of ordinary differential equations (ODEs). We discuss the possibility of distinguishing the Rabi, Josephson and Fock regimes in terms of the macroscopic parameters which appear in the EBH Hamiltonians, and then in the ODEs. We compare the predictions for the relative populations of the Bose gas atoms in the two wells obtained from the numerical solutions of the two-mode ODEs, with those deriving from the direct numerical integration of the Gross–Pitaevskii equations (GPEs). Our investigations show that the nonlinear terms of the ODEs are crucial to achieve a good agreement between the ODE and GPE approaches, and in particular to give quantitative predictions of the self-trapping regime.
The dynamics of an F=1F=1F=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.
In this paper, we study the interaction-modulated tunneling dynamics of a Bose-Fermi superfluid mixture, where a Bose-Einstein condensate (BEC) with weak repulsive interaction is confined in a symmetric deep double-well potential and an equally populated two-component Fermi gas in a harmonic potential symmetrically is positioned in the center of the double-well potential. The tunneling between the two wells is modulated by fermions trapped in a harmonic potential. When the temperature is adequately low and the bosonic particle number is adequately large, we can employ the mean-field theory to describe the evolution of the BEC in the double-well potential through the time-dependent Gross-Pitaevskii equation. For the Fermi gas in the harmonic potential trap, we consider the case where the inter-fermion interaction is tuned on the deep Bose-Einstein condensate of the inter-fermion Feshbach resonance, where two fermions of spin-up and spin-down form a two-body bound state. Within the regime, the Fermi gas is well described by a condensate of these fermionic dimers, and hence can be simulated as well by a Gross-Pitaevskii equation of dimers. The inter-species interactions couple the dynamics of the two species, which results in interesting features in the tunneling oscillations. The dynamic equations of the BEC in the double-well potential is described by a two-mode approximation. Coupling it with time-dependent Gross-Pitaevskii equation of the harmonically potential trapped molecular BEC, we numerically investigate the dynamical evolution of the Boson-Fermi hybrid system under different initial conditions. It is found that the interaction among fermions in a harmonic potential leads to strong non-linearity in the oscillations of the bosons in the double-well potential and enriches the tunneling dynamics of the bosons. Especially, it strengthens macroscopic quantum self-trapping. And the macroscopic quantum self-trapping can be expressed in three forms: the phase tends to be negative and monotonically decreases with time, the phase evolves with time, and the phase tends to be positive and increases monotonically with time. This means that it is possible the tunneling dynamics of the BEC in double-well potential is adjustable. Our results can be verified experimentally in a Bose-Fermi superfluid mixture by varying different interaction parameters via Feshbach resonance and confinement-induced resonance.
We study binary mixtures of Bose–Einstein condensates confined in a two-well potential within the framework of the Gross–Pitaevskii equation. We re-examine both the single component and the binary mixture cases for such a potential. We investigate the most usual dimensional reductions used to solve the Gross–Pitaevskii equations, including the one proposed by Reatto and collaborators. To this end, we compare numerical simulations of the 1D reductions with the full 3D numerical solutions of the Gross–Pitaevskii equation. Our analysis considers an experimentally feasible binary mixture of an F = 1 spinor condensate where two of its Zeeman manifolds are populated.