  We analyse the Einstein-Podolsky-Rosen (EPR) steering properties in a
three-well Bose-Hubbard model under the mechanism of coherent transport of
atomic population (CTAP). This process, also known as transport without transit
(TWT), transfers condensed atoms from one well of a lattice potential to
another, non-adjacent well, without macroscopic occupation of the middle well.
The dynamics and entanglement properties of this system have previously been
analysed and shown to be dependent on the initial quantum state of the atoms in
the first well. In this work we utilise the phase-space method of stochastic
integration in the positive-P representation. The system demonstrated
inseparability between the wells for Fock initial states, and we show that
steering is also only found for an initial Fock state. Depending on how we
write our steering inequalities, steering is seen at different times, showing a
basic asymmetry. This means that for part of the evolution, Alice can steer Bob
but not vice versa. After the midpoint of the population transfer, this
situation reverses.
