Damping of Josephson Oscillations in Strongly Correlated One-Dimensional Atomic Gases

We study Josephson oscillations of two strongly correlated one-dimensional bosonic clouds separated by a localized barrier. Using a quantum-Langevin approach and the exact Tonks-Girardeau solution in the impenetrable-boson limit, we determine the dynamical evolution of the particle-number imbalance, displaying an effective damping of the Josephson oscillations which depends on barrier height, interaction strength, and temperature. We show that the damping originates from the quantum and thermal fluctuations intrinsically present in the strongly correlated gas. Because of the density-phase duality of the model, the same results apply to particle-current oscillations in a one-dimensional ring where a weak barrier couples different angular momentum states.

Figure 1

Scheme of the geometries considered in this work: two weakly coupled atomic waveguides (a) and a ring potential split by a weak barrier (b). (c) Single-particle wave functions ${\psi }_j(x)$ used as initial condition in the TG solution and the corresponding confining potential.

Figure 2

Dynamics of imbalance $\mathcal{I}(t)$ (dimensionless) for relative number $N(t)/N(0)$ in tunnel-coupled wires or for current oscillations $J(t)/J(0)$ in a ring, from the LL approach, for various values of ${\gamma }_Q=\gamma /{\omega }_0$ or ${\gamma }_Q={\gamma }^{\mathrm{r}}/{\omega }_0^{\mathrm{r}}$, respectively. The corresponding uncertainties due to the stochastic noise are indicated in the shaded areas.

Figure 3

Relative-number oscillations in the TG regime following a quench of the initial step potential $\delta V_0$: (a) at zero temperature for $\delta V_0/E_F=0.07$ (blue dotted line), 0.14 (black dashed line), and 0.72 (brown solid line), with $E_F$ the Fermi energy and (b) at finite temperature for $\delta V_0/E_F=0.07$. (c) Exact TG excitation spectrum (dimensionless, gray-scale points) in the frequency-wave vector plane for $T/T_F=0.1$ and LL excitation spectrum (magenta points). Inset: zoom on the small-$k$ region. In all panels, $N_T=101$ and $\lambda \equiv 2mL{U}_0/{\hslash }^2{\pi }^2{N}_T=200$.