Measurement of the absolute Quantum Efficiency of Hamamatsu model R11410-10 photomultiplier tubes at low temperatures down to liquid xenon boiling point

We report on the measurements of the absolute Quantum Efficiency(QE) for Hamamatsu model R11410-10 PMTs specially designed for the use in low background liquid xenon detectors. QE was measured for five PMTs in a spectral range between 154.5 nm to 400 nm at low temperatures down to -110$^0$C. It was shown that during the PMT cooldown from room temperature to -110 $^0$C (a typical PMT operation temperature in liquid xenon detectors), the absolute QE increases by a factor of 1.1 - 1.15 at 175 nm. The QE growth rate with respect to temperature is wavelength dependent peaking at about 165 nm corresponding to the fastest growth of about -0.07 %QE/$^{0}C$ and at about 200 nm corresponding to slowest growth of below -0.01 %QE/$^{0}C$. A dedicated setup and methods for PMT Quantum Efficiency measurement at low temperatures are described in details.