Ultra-high energy neutrinos are detectable through impulsive radio signals generated through interactions in dense media, such as ice. Subsurface in-ice radio arrays are a promising way to advance the observation and measurement of astrophysical high-energy neutrinos with energies above those discovered by the IceCube detector ($geq$1 PeV) as well as cosmogenic neutrinos created in the GZK process ($geq$100 PeV). Here we describe the $textit{NuPhase}$ detector, which is a compact receiving array of low-gain antennas deployed 185 m deep in glacial ice near the South Pole. Signals from the antennas are digitized and coherently summed into multiple beams to form a low-threshold interferometric phased array trigger for radio impulses. The NuPhase detector was installed at an Askaryan Radio Array (ARA) station during the 2017/18 Austral summer season. $textit{In situ}$ measurements with an impulsive, point-source calibration instrument show a 50% trigger efficiency on impulses with voltage signal-to-noise ratios (SNR) of $le$2.0, a factor of $sim$1.8 improvement in SNR over the standard ARA combinatoric trigger. Hardware-level simulations, validated with $textit{in situ}$ measurements, predict a trigger threshold of an SNR as low as 1.6 for neutrino interactions that are in the far field of the array. With the already-achieved NuPhase trigger performance included in ARASim, a detector simulation for the ARA experiment, we find the trigger-level effective detector volume is increased by a factor of 1.8 at neutrino energies between 10 and 100 PeV compared to the currently used ARA combinatoric trigger. We also discuss an achievable near term path toward lowering the trigger threshold further to an SNR of 1.0, which would increase the effective single-station volume by more than a factor of 3 in the same range of neutrino energies.
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