Phase diagram of a bosonic ladder with two coupled chains

We study a bosonic ladder with two coupled chains using the finite size density matrix renormalisation group method. We show that in a commensurate bosonic ladder the critical on-site interaction ($U_C$) for the superfluid to Mott insulator transition becomes larger as the inter-chain hopping ($t_{\mathrm{\perp }}$)increases. We analyze this quantum phase transition and obtain the phase diagram in the $t_{\mathrm{\perp }}-U$ plane.