  We show that quantum absorption refrigerators, which has traditionally been
studied as of three qubits, each of which is connected to a thermal reservoir,
can also be constructed by using three qubits and two thermal baths, where two
of the qubits, including the qubit to be cooled, are connected to a common
bath. With a careful choice of the system, bath, and qubit-bath interaction
parameters within the Born-Markov and rotating wave approximations, one of the
qubits attached to the common bath achieves a cooling in the steady-state. We
observe that the proposed refrigerator may also operate in a parameter regime
where no or negligible steady-state cooling is achieved, but there is
considerable transient cooling. The steady-state temperature can be lowered
significantly by an increase in the strength of the few-body interaction terms
existing due to the use of the common bath in the refrigerator setup, proving
the importance of the two-bath setup over the conventional three-bath
construction. The proposed refrigerator built with three qubits and two baths
is shown to provide steady-state cooling for both Markovian qubit-bath
interactions between the qubits and canonical bosonic thermal reservoirs, and a
simpler reset model for the qubit-bath interactions.
