Competition between vortex unbinding and tunneling in an optical lattice

We study a system of two-dimensional Bose gases trapped in minima of a deep one-dimensional optical lattice potential. Increasing the tunneling amplitude between adjacent gases drives a deconfinement transition to a phase where coherence is established between neighboring two-dimensional gases. We compute the signature of this transition in the interference pattern of the system as well as in its rotational response, which provides a direct measurement of the superfluidity in the system.

Figure 1

Upper panel: Ratio of the moment of inertia to the classical moment of inertia: $I∕I_{\mathrm{cl}}=(1-{\rho }_s∕\rho )$ for $N=2$ and $N\to \infty$; $t_{\perp }=0.05\mu$. To mimic finite size effects we have assumed that the 1D lattice is made of circular pancake-shaped 2D Bose gases of radius $R=100\xi$, where $\xi$ is the healing length, and therefore we have stopped the renormalization-group flow at the scale of $R$ (furthermore, we have assumed that ${\rho }_0∕\rho =0.95$). Lower panel: Phase diagram (in the thermodynamic limit). We have indicated with an arrow the jump in the exponent $\left(\alpha \right)$ that describes the scaling of the interference contrast with the imaged length $L_x$ [see, e.g., Eqs. (6, 7)]. An estimate for smallest value of $t_{\perp }>\hslash ∕t_{\exp }$ (where $t_{\exp }$ is the typical duration of an experiment) is indicated by the vertical dashed line.