  We study the generation of entanglement between two qubits which communicate
through a single cavity mode of quantum light but have no direct interaction.
We show that such entanglement can be generated simply by exchanging quanta
with a third party, which is in our case the cavity mode. Exchanging only a
single quantum creates maximal entanglement. A single quantum can be provided
by an external quantum light source. However, we use a classical light source
to pump quanta which are used for the exchange, and investigate the degree of
two-qubit entanglement. We first identify a characteristic timescale of the
interaction between the cavity mode and each qubit. We investigate two regimes
of the driving pulse length, one is short and the other is long compared to the
characteristic timescale of the interaction. In the first regime, it is known
that the pulse can pump the system by generating a displacement of the cavity
mode. We show that, by using a specific pulse shape, one can make the
displacement to essentially vanish after the pulse finishes interaction with
the cavity mode. In this case, a rotation of the qubits can be invoked. In
addition, higher-order effects of the pulse including a non-local operation on
the joint system of the cavity mode and the qubits are found, and we present a
formalism to compute each term up to a given order. An explicit condition on
the pulse shape for each term to be nonzero or suppressed is derived to enable
an experimental design for verifying the entanglement generation using a
classical light source. In the opposite regime where the driving is
sufficiently long, we utilize a squeezed state which may be obtained
adiabatically. We study how the squeezing and the accompanied rotation of
qubits affect the generated two-qubit entanglement.
