Search for Double Beta Decays of ^{134}Xe with EXO-200 Phase II

EXO-200 was a leading double beta decay experiment consisting of a single-phase, enriched liquid xenon time projection chamber filled with an admixture of 80.672% ^{136}Xe and 19.098% ^{134}Xe. The detector operated at the Waste Isolation Pilot Plant between 2010 and 2018 and was designed to search for double beta decay of ^{136}Xe. Data were acquired in two phases separated by a period of detector upgrades. We report on the search for 0νββ and 2νββ decay of ^{134}Xe with Phase II EXO-200 data, with median 90% CL exclusion sensitivity to half-life T_{1/2}^{0ν}≥3.7×10^{23}  yr and T_{1/2}^{2ν}≥2.6×10^{21}  yr, respectively. No statistically significant signal is observed for either decay mode. We set a world-leading lower limit on the half-life of the neutrinoless decay mode of ^{134}Xe of T_{1/2}^{0ν}≥8.7×10^{23} (90% CL) and the second strongest constraint on the two-neutrino decay of T_{1/2}^{2ν}≥2.9×10^{21} (90% CL), a threefold improvement over the EXO-200 Phase I measurement. New constraints are also set for the 2νββ and 0νββ decays of ^{134}Xe to the lowest excited state of ^{134}Ba.