Theory of momentum resolved tunneling into a short quantum wire

Motivated by recent tunneling experiments in the parallel wire geometry[1], we calculate results for momentum resolved tunneling into a short one-dimensional wire containing a small number of electrons. We derive some general theorems about the momentum dependence, and we carry out exact calculations for up to N=4 electrons in the final state, for a system with screened Coulomb interactions that models the situation of the experiments. Both the case of electrons with spin and the case of completely polarized electrons are considered. The electron density and momentum-dependent tunneling matrix elements at various inter-particle spacings are analyzed. At large interactions the spin dynamics of the system can be approximated with a Heisenberg model, and we derive an effective Heisenberg coupling constant J from the gap between ground state and first excited state. We shall discuss implications of the calculations for the experiments on parallel wires. [1] O. Auslaender et. al, unpublished.