  We theoretically investigate photo-thermoelectric transport through a quantum
wire in a photon cavity coupled to electron reservoirs with different
temperatures. Our approach, based on a quantum master equation, allows us to
investigate the influence of a quantized photon field on the heat current and
thermoelectric transport in the system. We find that the heat current through
the quantum wire is influenced by the photon field resulting in a negative heat
current in certain cases. The characteristics of the transport are studied by
tuning the ratio, $\hbar\omega_{\gamma} / k_{\rm B} \Delta T$, between the
photon energy, $\hbar\omega_{\gamma}$, and the thermal energy, $k_{\rm B}
\Delta T$. The thermoelectric transport is enhanced by the cavity photons when
$k_{\rm B} \Delta T > \hbar\omega_{\gamma}$. By contrast, if $k_{\rm B} \Delta
T < \hbar\omega_{\gamma}$, the photon field is dominant and a suppression in
the thermoelectric transport can be found in the case when the cavity-photon
field is close to a resonance with the two lowest one-electron states in the
system. Our approach points to a new technique to amplify thermoelectric
current in nano-devices.
