Single particle entanglement

If a and b are modes, then we can present a state as numeric:


 * n>|m> where first position if for a mode and second position is for b mode.

Then, to represent a coherent superposition of two modes, we can consider


 * 0>|1>+|1>|0>

which looks like an entangled state.

Can we then say that in the basis of number states, the superposed state is entangled??? Should not we rather write it as |0,1>+|1,0> ? Is there anything new we can understand considering this superposed state as entangled? If it is an entanglement than of what with what???