  We develop a scheme for deterministic generation of an entangled state
between two atoms on different Rydberg states via a chirped adiabatic passage,
which directly connects the initial ground and target entangled states and also
does not request the normally needed blockade effect. The occupancy of
intermediate states suffers from a strong reduction via two pulses with proper
time-dependent detunings and the electromagnetically induced transparency
condition. By solving the analytical expressions of eigenvalues and eigenstates
of a two-atom system, we investigate the optimal parameters for guaranteeing
the adiabatic condition. We present a detailed study for the effect of pulse
duration, changing rate, different Rydberg interactions on the fidelity of the
prepared entangled state with experimentally feasible parameters, which reveals
a good agreement between the analytic and full numerical results.
