Microkelvin electronics on a pulse-tube cryostat with a gate Coulomb blockade thermometer

Abstract

Access to lower temperatures has consistently enabled scientific breakthroughs. Pushing the limits of on-chip temperatures deep into the microkelvin regime would open the door to unprecedented quantum coherence, novel quantum states of matter, and also the discovery of unexpected phenomena. Adiabatic demagnetization is the workhorse of microkelvin cooling, requiring a dilution refrigerator precooling stage. Pulse-tube dilution refrigerators have grown enormously in popularity due to their vast experimental space and independence of helium, but their unavoidable vibrations are making microkelvin cooling very difficult. On-chip thermometry in this unexplored territory is also not a trivial task due to extreme sensitivity to noise. Here, we present a pulse-tube compatible microkelvin sample holder with on-board cooling and microwave filtering and introduce a new type of temperature sensor, the gate Coulomb blockade thermometer (gCBT), working deep into the microkelvin regime. Using on-and off-chip cooling, we demonstrate electronic temperatures as low as 224±7 µK, remaining below 300 µK for 27 hours, thus providing sufficient time for measurements. Finally, we give an outlook for cooling below 50 µK for a new generation of microkelvin transport experiments.

Influence of device non-uniformities on the accuracy of Coulomb blockade thermometry

“…The Coulomb blockade thermometer (CBT) [1] has proven to provide calibration-free thermometry over a wide range from sub-mK up to 70 K [2][3][4][5][6][7] temperatures T, i.e., over five decades. Its operation is based on bias voltage V dependent conductance G of an array of tunnel junctions under the competition between single-electron charging effects (energy scale E C ) and thermal energy k B T. The ideal operation range is when E C k B T; in this linear regime a universal relation [1] V 1/2 5.439Nk B T/e (1) holds, where V 1/2 is the full width at half-minimum of the conductance dip around zero bias voltage and N is the number of junctions in series in the array.…”

“…Pure capacitance variations with uniform resistances do not lead to temperature corrections in the linear regime, but only to renormalization of charging energy. Devices of type (i) are the ones commonly employed in very low temperature thermometry [2,3,13], where self-capacitance of the islands between junctions is intentionally increased to bring E C down in order to satisfy the conditions discussed above down to low temperatures. On the other hand class (ii) refers to sensors in higher temperature regimes where junction capacitances dominate over self-capacitances of the islands.…”

“…In this work we present a comprehensive picture of the nonuniformity induced uncertainty in Coulomb blockade thermometry. We discuss two different device classes, (i) the ones where junction resistances vary along the array but capacitance variances are negligible, recently coined gCBT [2], and (ii) those where both resistances and capacitances vary but such that their product remains constant for each element composed of a junction and island between the junctions, jCBT. These two types of CBT are shown schematically in figure 1.…”