We report on the first observations of neutron star low-mass X-ray binaries with the Atacama Large Millimeter/submillimeter Array (ALMA) at $sim$300 GHz. Quasi-simultaneous observations of 4U 1728-34 and 4U 1820-30 were performed at radio (ATCA), infrared (VLT) and X-ray (Swift) frequencies, spanning more than eight decades in frequency coverage. Both sources are detected at high significance with ALMA. The spectral energy distribution of 4U 1728-34 is consistent with synchrotron emission from a jet with a break from optically thick to optically thin emission at 1.3-11.0$times$10$^{13}$ Hz. This is the third time a jet spectral break has been reported for a neutron star X-ray binary. The radio to mm spectral energy distribution of 4U 1820-30 has significant detections at 5 and 300~GHz. This confirms the presence of radio emission during a soft state for this neutron star and represents the first detection of mm emission during such a state, unambiguously pointing to the presence of a jet. We also report on three additional unrelated sources - showing mm emission - in the ALMA fields of view of 4U 1728-34 and 4U 1820-30.
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