Low-noise, ultra-low temperature dissipative devices
A dissipative device has a planar configuration with one or more resistor elements formed on an insulating substrate. Conductors are formed on the insulating substrate and are coupled to the resistor element(s) to transmit signals to/from the resistor element(s). The geometry of and materials for the dissipative device allow the conductors to act as heat sinks, which conduct heat generated in the resistor element(s) to the substrate (and on to a coupled housing) and cool hot electrons generated by the resistor element(s) via electron-phonon coupling. The dissipative device can be used in cooling a signal to a qubit, a cavity system of a quantum superconducting qubit, or any other cryogenic device sensitive to thermal noise.
1. A dissipative device comprising:
a substrate;
at least one resistor element in contact with the substrate, each resistor element having first and second ends in plan view and comprising a first material having a first electrical conductivity value;
at least two heat sinks in contact with the substrate, one of the heat sinks being coupled to the first end in plan view, another of the heat sinks being coupled to the second end in plan view, each heat sink comprising a second material having a second electrical conductivity value higher than the first electrical conductivity value; and
ground planes in contact with the substrate and comprising the second material,
wherein the at least two heat sinks are constructed to conduct heat generated in the at least one resistor element to the substrate and to cool hot electrons generated by the at least one resistor element via electron-phonon coupling,
wherein the at least one resistor element is at least three resistor elements arranged in one of a T-pad configuration and a π-pad configuration, and constructed as a coplanar waveguide microwave attenuator, and
wherein each resistor element is coupled at the first end thereof to one of the heat sinks and ground planes, and is coupled at the second end thereof to another of the heat sinks and ground planes.
2. The dissipative device according to claim 1 , wherein each resistor element comprises:
a plurality of resistor sub-elements arranged in series, each resistor sub-element being formed of the first material; and
a plurality of spacers arranged between the resistor sub-elements in plan view, each spacer comprising the second material,
wherein the plurality of spacers are also constructed to conduct heat generated in the plurality of resistor sub-elements to the substrate and to cool hot electrons generated by the plurality of resistor sub-elements via electron-phonon coupling.
3. The dissipative device according to claim 1 , wherein the first material comprises a pure metal, a metal oxide, or a metal alloy.
4. The dissipative device according to claim 3 , wherein the first material is 80 weight percent Ni and 20 weight percent Cr.
5. The dissipative device according to claim 1 , wherein the first material has a temperature coefficient of resistance that is less than 1×10 −3 per K.
6. The dissipative device according to claim 1 , wherein the first material and/or the second material are non-superconductive at a temperature less than 10 mK.
7. The dissipative device according to claim 1 , wherein the device is constructed as a dissipative cryogenic microwave device for cooling of electromagnetic signals from L-band up to K-microwave band.
8. The dissipative device according to claim 1 , wherein the second material comprises Ag, Au, Cu, or another noble metal.
9. The dissipative device according to claim 1 , further comprising a housing that encloses the substrate, the housing having first and second ports coupled to the at least one resistor element.
10. The dissipative device according to claim 9 , wherein the housing comprises Ag or Cu.
11. The dissipative device according to claim 9 , wherein a back surface of the substrate is in thermal contact with the housing through a thermally-conductive layer comprising a third material having a third electrical conductivity value higher than the first electrical conductivity value.
12. The dissipative device according to claim 11 , wherein the thermally-conductive layer is a paste or an epoxy comprising Ag, Au, Cu, or another noble metal.
13. The dissipative device according to claim 9 , wherein the housing comprises separate pieces coupled together so as to apply pressure to the substrate.
14. The dissipative device according to claim 1 , further comprising a directional coupler, wherein the at least one resistor element is connected to a terminating port of the directional coupler.
15. The dissipative device according to claim 1 , wherein the attenuator is constructed to provide 20 dB attenuation and such that, for input microwave power of less than 30 nW, a resulting noise temperature of the attenuator is less than 120 mK in an operating environment less than 20 mK.
16. The dissipative device according to claim 1 , wherein the attenuator has a bandwidth from 1 GHz to at least 10 GHz.
17. The dissipative device according to claim 1 , wherein the substrate comprises a material having a thermal conductivity of at least 1 Wm −1 K −1 at 1 K and a relative permittivity less than or equal to 3.9.
18. The dissipative device according to claim 1 , wherein the substrate comprises fused quartz, single crystal quartz, sapphire, or silicon having a resistivity greater than 40 ohm-cm.
19. The dissipative device according to claim 1 , further comprising a mixing chamber with the substrate thermally coupled thereto and configured to maintain a temperature therein below 1 K.
20. A system comprising:
(a) a dissipative device comprising:
a substrate;
at least one resistor element in contact with the substrate, each resistor element having first and second ends in plan view and comprising a first material having a first electrical conductivity value; and
at least two heat sinks in contact with the substrate, one of the heat sinks being coupled to the first end in plan view, another of the heat sinks being coupled to the second end in plan view, each heat sink comprising a second material having a second electrical conductivity value higher than the first electrical conductivity value; and
(b) a refrigerator configured to cool the substrate to a temperature below 1 K,
wherein the at least two heat sinks are constructed to conduct heat generated in the at least one resistor element to the substrate and to cool hot electrons generated by the at least one resistor element via electron-phonon coupling.
21. The system of claim 20 , wherein the dissipative device further comprises:
ground planes in contact with the substrate and comprising the second material,
wherein the at least one resistor element is at least three resistor elements arranged in one of a T-pad configuration and a π-pad configuration, and constructed as a coplanar waveguide microwave attenuator, and
wherein each resistor element is coupled at the first end thereof to one of the heat sinks and ground planes, and is coupled at the second end thereof to another of the heat sinks and ground planes.