  Background: Two-phonon excitations originating from the coupling of two
collective one-phonon states are of great interest in nuclear structure
physics. One possibility to generate low-lying $E1$ excitations is the coupling
of quadrupole and octupole phonons.
  Purpose: In this work, the $\gamma$-decay behavior of candidates for the
$(2_1^+\otimes 3_1^-)_{1^-}$ state in the doubly-magic nucleus $^{40}$Ca and in
the heavier and semi-magic nucleus $^{140}$Ce is investigated.
  Methods: $(\vec{\gamma},\gamma')$ experiments have been carried out at the
High Intensity $\gamma$-ray Source (HI${\gamma}$S) facility in combination with
the high-efficiency $\gamma$-ray spectroscopy setup $\gamma^3$ consisting of
HPGe and LaBr$_3$ detectors. The setup enables the acquisition of
$\gamma$-$\gamma$ coincidence data and, hence, the detection of direct decay
paths.
  Results: In addition to the known ground-state decays, for $^{40}$Ca the
decay into the $3^-_1$ state was observed, while for $^{140}$Ce the direct
decays into the $2^+_1$ and the $0^+_2$ state were detected. The experimentally
deduced transition strengths and excitation energies are compared to
theoretical calculations in the framework of EDF theory plus QPM approach and
systematically analyzed for $N=82$ isotones. In addition, negative parities for
two $J=1$ states in $^{44}$Ca were deduced simultaneously.
  Conclusions: The experimental findings together with the theoretical
calculations support the two-phonon character of the $1^-_1$ excitation in the
light-to-medium-mass nucleus $^{40}$Ca as well as in the stable even-even
$N=82$ nuclei.
