  The similarities to cuprates make iridates an interesting potential platform
for investigating superconductivity. Equally attractive are their puzzling
complex intrinsic interactions. Here, we report an ultrafast optical
spectroscopy investigation of a coherent phonon mode in Sr3Ir2O7, a bilayer
Ruddlesden-Popper perovskite iridate. An anomaly in the A1g optical phonon
({\nu} = 4.4 THz) is unambiguously observed below the N\'eel temperature (TN),
which we attribute to pseudospin-lattice coupling (PLC). Significantly, we find
that PLC is the dominant interaction at low temperature, and we directly
measure the PLC coefficient to be {\lambda} = 150 +/- 20 cm-1, which is two
orders of magnitude higher than that in manganites (< 2.4 cm-1) and comparable
to that in CuO (50 cm-1, the strongest PLC or spin-lattice coupling (SLC)
previously known). Moreover, we find that the strong PLC induces an anisotropic
negative thermal expansion. Our findings highlight the key role of PLC in
iridates and uncovers another intriguing similarity to cuprates.
