500 microkelvin nanoelectronics

Fragile quantum effects such as single electron charging in quantum dots or macroscopic coherent tunneling in superconducting junctions are the basis of modern quantum technologies. These phenomena can only be observed in devices where the characteristic spacing between energy levels exceeds the thermal energy, $k_\textrm{B}T$, demanding effective refrigeration techniques for nanoscale electronic devices. Commercially available dilution refrigerators have enabled typical electron temperatures in the $10$ to $100\,$mK regime, however indirect cooling of nanodevices becomes inefficient due to stray radiofrequency heating and weak thermal coupling of electrons to the device substrate. Here we report on passing the millikelvin barrier for a nanoelectronic device. Using a combination of on-chip and off-chip nuclear refrigeration, we reach an ultimate electron temperature of $T_\textrm{e}=421\pm35\,\mu$K and a hold time exceeding $85\,$hours below $700\,\mu$K measured by a self-calibrated Coulomb-blockade thermometer.