One-Dimensional Transport of Bosons between Weakly Linked Reservoirs

We study a flow of ultracold bosonic atoms through a one-dimensional channel that connects two macroscopic three-dimensional reservoirs of Bose-condensed atoms via weak links implemented as potential barriers between each of the reservoirs and the channel. We consider reservoirs at equal chemical potentials so that a superflow of the quasicondensate through the channel is driven purely by a phase difference $2\mathrm{\Phi }$ imprinted between the reservoirs. We find that the superflow never has the standard Josephson form $\sim \sin 2\mathrm{\Phi }$. Instead, the superflow discontinuously flips direction at $2\mathrm{\Phi }=\pm \mathrm{\pi }$ and has metastable branches. We show that these features are robust and not smeared by fluctuations or phase slips. We describe a possible experimental setup for observing these phenomena.

Figure 1

A sketch of two 3D BEC reservoirs connected by a 1D channel via weak tunneling links. A simplified illustration of an atom chip creating an appropriate magnetic trapping configuration is also shown.

Figure 2

Phase profile along the channel. The solid line ${\phi }_0(x)$ is a typical (symmetric) configuration made up of a linear superfluid contribution and phase jumps $\varphi$ at each tunnel barrier. The dashed line represents a fluctuation around the phase profile. Here we have chosen the phases of the BEC reservoirs as ${\mathrm{\Phi }}_{\mathrm{L}}=-{\mathrm{\Phi }}_{\mathrm{R}}\equiv \mathrm{\Phi }$. The phase profile shown above corresponds to a phase difference of $2\mathrm{\Phi }<\pi$.

Figure 3

The MF phase profile in the channel for $\alpha <1$ ($J<J_c$). (a),(c) Unique symmetric (asymmetric) solutions near $\mathrm{\Phi }=0$ or $\pi$, respectively; (b) these two solutions become degenerate at $\mathrm{\Phi }=\pi /2$, with one of them becoming metastable slightly above or below $\pi /2$.

Figure 4

(a) The MF energies (5), spread between ${ϵ}_{\min }=-4\alpha$ and ${ϵ}_{\max }=2{\alpha }^2$, as functions of the external phase difference $2\mathrm{\Phi }$ at different values of $\alpha$. Thick (thin) solid lines represent symmetric (asymmetric) stable or metastable solutions, the latter lying in the continuum of phononic excitations. (b) The dependence of the superflow on $2\mathrm{\Phi }$, with thick (thin) lines representing stable (metastable) flow. Dashed lines represent unstable solutions drawn as a guide to the eye.