Nonequilibrium Josephson Oscillations in Bose-Einstein Condensates without Dissipation

We perform a detailed quantum dynamical study of nonequilibrium Josephson oscillations between interacting Bose-Einstein condensates confined in a finite-size double-well trap. We find that the Josephson junction can sustain multiple undamped Josephson oscillations up to a characteristic time scale ${\tau }_c$ without quasipartcles being excited in the system. This may explain recent related experiments. Beyond a characteristic time scale ${\tau }_c$ the dynamics of the junction is governed by fast, quasiparticle-assisted Josephson tunneling as well as Rabi oscillations between the discrete quasiparticle levels. We predict that an initially self-trapped state of the Bose-Einstein condensates will be destroyed by these fast dynamics.

Figure 1

A BEC in a double-well potential after abrupt decrease of the barrier height. The definitions of the parameters are explained in the text, see Eqs. (3, 4, 5).

Figure 2

Time-evolution of condensed and noncondensed particles for the initial conditions $z(0)=-0.6$, $\theta (0)=0$ and interaction parameters $u=u^{\prime }=5$, $j^{\prime }=60$, $k=0$ (delocalized regime). 5 QP levels were included in the numerical evaluation. (a) The dynamics of the BEC population imbalance $z(T)$ is shown (solid black line). The dashed, blue line shows, for comparison, the behavior without QP coupling, $u^{\prime }=j^{\prime }=k=0$, in agreement with Ref. 5. (b) $z(T)$ vs $\theta (T)$ map. The arrow indicates the direction of time evolution. The time $T={\tau }_c$ is marked by the black dot. It is seen that at $T={\tau }_c$ the system changes dynamically from a $\theta =0$ to a $\theta =\pi$ junction with more erratic phase evolution. (c) Time evolution of the noncondensed particle population. The black curve (also in the inset) shows the particle occupation of the first level $n_b^{(1)}$, while the red curve is the sum of all five levels $n_b$. For $T<{\tau }_c$ the two curves practically coincide.

Figure 3

Same as in Fig. 2, but for $u=u^{\prime }=25$ (self-trapped regime) and $j^{\prime }=30$. In (a) the dashed, blue line shows the behavior without QP interactions, $u^{\prime }=0$.

Figure 4

Dependence of the inverse time scale ${\tau }_c^{-1}$ on two main parameters $j^{\prime }$ and $k$, for the initial conditions as in Fig. 3. In the left panel the white area corresponds to $j^{\prime }$ and $k$ values for which ${\tau }_c$ was not found; we assume ${\tau }_c\to \infty$ in this case. The right panel shows a collapse of all ${\tau }_c^{-1}$ curves onto a single one with the simple law ${\tau }_c^{-1}\sim j^{\prime }-k$. The scatter is due to the ambiguity in the numerical definition of ${\tau }_c$.