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arXiv:1011.5177 · Europhysics Letters (EPL)

A dipolar self-induced bosonic Josephson junction

M. Abad, M. Guilleumas, R. Mayol, M. Pi, D. M. Jezek

Published Apr 1, 2011• 46 citations
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Abstract

We propose a new scheme for observing Josephson oscillations and macroscopic quantum self-trapping 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.

DOI
10.1209/0295-5075/94/10004

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We propose a new scheme for observing Josephson oscillations and macroscopic quantum self-trapping 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.
We propose a new scheme for observing Josephson oscillations and macroscopic quantum self-trapping 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. © 2011 Europhysics Letters Association.
A dipolar condensate confined in a toroidal trap constitutes a self-induced Josephson junction when the dipoles are oriented perpendicularly to the trap symmetry axis and the sss-wave scattering length is small enough. The ring-shaped double-well potential coming from the anisotropic character of the mean-field dipolar interaction is robust enough to sustain self-trapping dynamics, which takes place when the initial population imbalance between the two wells is large. We show that, in this system, the self-trapping regime is directly related to a vortex-induced phase-slip dynamics. A vortex and antivortex are spontaneously nucleated in the low-density regions before a minimum of the population imbalance is reached and then cross the toroidal section in opposite directions through the junctions. This vortex dynamics yields a phase slip between the two weakly linked condensates causing an inversion of the particle flux.
We study the Josephson oscillation and self-trapping dynamics of a cigar-shaped dipolar Bose-Einstein condensate of 52{}^{52}52Cr atoms polarized along the symmetry axis of an axially symmetric double-well potential using the numerical solution of a mean-field model, for dominating repulsive contact interaction (large positive scattering length aaa) over an anisotropic dipolar interaction. Josephson-type oscillation emerges for small and very large numbers of atoms, whereas self-trapping is noted for an intermediate number of atoms. The dipolar interaction pushes the system away from self-trapping towards Josephson oscillation. We consider a simple two-mode description for a qualitative understanding of the dynamics.
The quantum self-trapping phenomenon of a Bose-Einstein condensate (BEC) represents a remarkable nonlinear effect of wide interest. By considering a purely dipolar BEC in a double-well potential, we study how the dipole orientation affects the ground-state structure and the transition between self-trapping and Josephson oscillations in dynamics. Three-dimensional numerical results and an effective two-mode model demonstrate that the onset of self-trapping of a dipolar BEC can be radically modified by the dipole orientation. We also analyze the failure of the two-mode model in predicting the rate of Josephson oscillations. We hope that our results can motivate experimental work as well as future studies of self-trapping of ultracold dipolar gases in optical lattices.
Abstract We theoretically study the effects of trap-confinement and interatomic interactions on Josephson oscillations (JO) and macroscopic quantum self-trapping (MQST) for a Bose–Einstein condensate confined in a trap which has a symmetric double-well potential along z -axis and 2D harmonic potentials along x - and y -axis. We consider three types of model interaction potentials: contact, long-range dipolar and finite-range potentials. Our results show that by changing the aspect ratio between the axial and radial trap sizes, one can induce a transition from JO to MQST for contact interactions with a small scattering length. For long-range dipolar interatomic interactions, we analyze transition from Rabi to Josephson regime and Josephson to MQST regime by changing the aspect ratio of the trap for a particular dipolar orientation. For a finite-range interaction, we study the effects of relatively large scattering length and effective range on JO and MQST. We show that JO and MQST are possible even if scattering length is relatively large, particularly near a narrow Feshbach resonance due to the finite-range effects.
We study an atomic Josephson junction (AJJ) in the presence of two interacting Bose–Einstein condensates (BECs) confined in a double-well trap. We assume that bosons of different species interact with each other. The macroscopic wavefunctions of the two components obey a system of two 3D coupled Gross–Pitaevskii equations (GPEs). We write the Lagrangian of the system, and from this we derive a system of coupled ordinary differential equations (ODEs), for which the coupled pendula represent the mechanical analogues. These differential equations control the dynamical behaviour of the fractional imbalance and of the relative phase of each bosonic component. We perform the stability analysis around the points which preserve the symmetry and get an analytical formula for the oscillation frequency around the stable points. Such a formula could be used as an indirect measure of the inter-species s-wave scattering length. We also study the oscillations of each fractional imbalance around zero and nonzero—the macroscopic quantum self-trapping (MQST)—time averaged values. For different values of the inter-species interaction amplitude, we carry out this study both by directly solving the two GPEs and by solving the corresponding coupled pendula equations. We show that, under certain conditions, the predictions of these two approaches are in good agreement. Moreover, we calculate the crossover value of the inter-species interaction amplitude which signals the onset of MQST.