On-chip microfluid dilution refrigerating machine

Abstract

A microfluidic dilution refrigerator includes a microfluidic system including a mixing chamber in which helium-3 is dissolved in helium-4 to form a heat-absorbing mixture, thereby cooling a device in thermal contact with the mixing chamber; a distiller, wherein helium-3 in the mixture evaporates from the mixture; and a heat exchanger thermally coupled with the distiller. The system further includes a first microfluidic channel directing the helium-3 from the heat exchanger to the mixing chamber, the first microfluidic channel sized to control a flow rate of the helium-3 into the mixing chamber; and a second microfluidic channel that directs the mixture from the mixing chamber to the distiller. A pumping system is provided for circulating helium-3 from the distiller and back into the mixing chamber via the heat exchanger. An apparatus cooled by the MDR includes a quantum sensor or quantum processor in a quantum computer for performing operations on qubits.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims the benefit pursuant to 35 U.S.C. § 119(e) of the following co-pending and commonly assigned applications:

[0003] U.S. Provisional Application Serial No. 63 / 432,234, filed by Benjamin Mazin on December 13, 2022, entitled “MICROFLUIDIC DILUTION REFRIGERATOR ON A CHIP,” attorney docket No. G&C30794.0832USP1 (UC 2023-871-1); and

[0004] U.S. Provisional Application Serial No. 63 / 483,796, filed by Benjamin Mazin on February 8, 2023, entitled “MICROFLUIDIC DILUTION REFRIGERATOR ON A CHIP,” attorney docket No. G&C30794.0832USP2 (UC 2023-871-2);

[0005] These applications are incorporated herein by reference. Technical Field

[0006] The present disclosure relates to a microfluidic dilution refrigerator and a method for manufacturing the same. Background Art

[0007] (NOTE: This application references a number of different publications, as indicated throughout the specification by one or more reference numerals in parentheses, such as [x]. A list of these different publications, sorted according to these reference numerals, can be found below in the section entitled "References." Each of these publications is incorporated herein by reference).

[0008] Quantum computers operating at room temperature need to operate at optical wavelengths to avoid thermal population of their qubit states (hν k B T ). On the other hand, using hν < k B T-manipulated qubits (e.g., superconducting qubits) need to operate at low temperatures to avoid thermal population of their qubit states. Nevertheless, despite the current challenges of reaching low temperatures, low-temperature quantum computers are a more likely commercial reality due to the relative ease of manipulating electrons in cryogenic systems (compared to photons at room temperature). However, conventional cooling systems (e.g., dilution refrigerators) are bulky and costly, so a more practical cooling method for reaching these low temperatures is needed. The present invention addresses this need. Summary of the Invention

[0009] The present invention discloses a microfluidic dilution refrigerator (MDR), which is a microfluidic system comprising: a mixing chamber, wherein helium-3 (also referred to herein as 3 He) dissolved in helium-4 (also referred to herein as 4 The system further comprises a device comprising: a first microfluidic channel that directs the helium-3 from the heat exchanger to the mixing chamber, wherein the first microfluidic channel is sized to control the flow rate of the helium-3 entering the mixing chamber; and a second microfluidic channel that directs the mixture from the mixing chamber to the still. A pumping system is provided for circulating the helium-3 from the still and returning it to the mixing chamber via the heat exchanger. Example devices cooled by the MDR include, but are not limited to, quantum sensors or quantum processors in quantum computers used to perform operations on qubits. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] This patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee.

[0011] Referring now to the drawings, wherein like reference numerals designate corresponding parts throughout:

[0012] Figure 1 FIG. 1 is a block diagram of a dilution cooling circuit in a conventional dilution refrigerator based on Oxford's dilution cooling principle.

[0013] Figure 2 is a block diagram of an MDR according to one or more embodiments of the present invention.

[0014] Figure 3 is a flow chart illustrating a method of manufacturing an MDR.

[0015] Figure 4A is an image of the turbine section of a micro-turbomolecular pump made of micromachined silicon. Figure 4B yes Figure 4A an enlarged portion of the image, and Figure 4C Here is an image of a 28-stage diaphragm pump from the same program.

[0016] Figure 5 This is a depiction of a 3D model of an 80×20×3 mm MDR.

[0017] Figure 6 is a block diagram of an example MDR coupled to a sorption pump.

[0018] Figure 7A and 7Bis the melting temperature T M A plot of heat exchanger pressure (mK) versus flow rate (µmol / s) shows a cooling power approaching 100 mK for heat exchanger lengths of 3 m and 2 m, respectively, including the heat load from viscous heating. The 3 m heat exchanger length represents the upper limit of plausibility, while 2 m is more practical given the original chip size.

[0019] Figure 8A and 8B It's T M Graph of flow rate (µmol / s) versus flow rate (mK) showing the cooling power close to the base temperature for heat exchangers 2 m and 3 m long.

[0020] Figure 9 This is a fluent simulation of a heat exchanger of approximately 1.2 m in length. By dividing the heat exchanger into four different interfacial resistances, roughly including T 3 Kapitza resistance. The dense phase enters at 2K and cools to 915 mK by the time it reaches the mixing chamber. DETAILED DESCRIPTION

[0021] In the following description of the preferred embodiment, reference is made to the accompanying drawings which form a part hereof, and in which is shown by way of illustration specific embodiments in which the invention may be practiced. It should be understood that other embodiments may be utilized and structural changes may be made without departing from the scope of the invention.

[0022] Technical Description

[0023] Figure 1 A conventional dilution refrigerator 100 that can be used to cool a superconducting quantum computer is shown, wherein the conventional dilution refrigerator 100 includes 3 He and 4 The mixing chamber 102, the heater 106, the heat exchanger 108, the phase boundary 104 of the He mixture, and the like are also shown. 3 He and 4 The still 110 of the phase boundary 104 of the He mixture, the impedance 112, the conduit 114 leading to the still pump (not shown) and the 3 The He returns to the pulse tube 116 of the mixing chamber 102 .

[0024] The dilution refrigerator 100 includes a mechanical cooler, typically a pulse tube 116, for cooling to approximately 4 Kelvin (K), which is coupled to a dilution cooling system that receives heat from the cooling tube. 3 He and 4 He evaporates from the mixture 3The He is further cooled to below 4 K. The mixture is recirculated in a cooling loop driven by a large, powerful room temperature pump (not shown), typically a turbomolecular pump backed by a dry scroll pump. Great care is taken to thermalize the incoming mixture and to thermally isolate the various stages of the dilution refrigerator 100.

[0025] Commercial dilution refrigerators for quantum computers are typically suitable for cooling large connectorized components (RF wiring, attenuators, isolators, duplexers, parametric amplifiers, etc.) to scale qubit counts. However, it is believed that this approach is flawed and that true scaling to useful qubit counts requires large-scale integration on-chip rather than implementing connectorized components. While full on-chip integration may increase manufacturing complexity, the significant benefits in size and the huge improvements in wiring scaling and readout integration outweigh this disadvantage. It is believed that if fully integrated quantum processors can be combined with compact, low-power, affordable cryogenic coolers, they will have much lower size and cooling power requirements and be a more viable path towards commercial quantum computing, as described herein. Coolers as described herein will also have applications in many other fields, such as quantum sensing and space-based applications (with slightly modified designs to address the lack of gravity [1]), where cooling requirements are a major constraint. The present invention provides a revolutionary approach to cryogenics in field applications.

[0026] Exemplary Microfluidic Dilution Refrigerator

[0027] Figure 2 A microfluidic dilution refrigerator (MDR) 200 is shown in accordance with one or more embodiments of the present invention. MDR 200 is a microfluidic system that includes a mixing chamber 202 in which helium-3 is dissolved in helium-4 to form a mixture that absorbs heat, thereby cooling equipment in thermal contact with mixing chamber 202; a distiller 204 in which helium-3 in the mixture evaporates from the mixture; and a heat exchanger 206 thermally coupled to distiller 204. MDR 200 also includes a first microfluidic channel 208 that directs the helium-3 from heat exchanger 206 to mixing chamber 202, and a second microfluidic channel 210 that directs the mixture from mixing chamber 202 to distiller 204. The dimensions of first microfluidic channel 208 are designed to control the flow rate of helium-3 into mixing chamber 202. Figure 2 Also shown is a pumping system comprising a roughing pump 212 and a turbo pump 214 for circulating helium-3 from the still 204 and back into the mixing chamber 202 via the heat exchanger 206, a dump 216, valves 218 and 220 for controlling the flow of helium, and a primary impedance 222. The MDR 200 is enclosed in a 4K radiation shield 224 without the dump 216. Finally, a gold thermalization layer 226 is located between the still 204 and the heat exchanger 206.

[0028] Exemplary Manufacturing Steps

[0029] Figure 3 is a flow chart illustrating a method of manufacturing the MDR 200 .

[0030] Block 300 represents obtaining a wafer. Example materials for the wafer include fused silica (amorphous SiO2), which is easily etched with standard cleanroom tools and has a relatively low thermal conductivity (0.25T) below 1K. 1.9 mW / (cm K). However, other wafer materials, including those with lower thermal conductivity, may be used. In one or more examples, the wafer primarily comprises crystalline quartz that is irradiated with high-energy photons or particles (such as, but not limited to, gamma rays from cobalt-60, or particles such as protons or neutrons) to locally reduce the thermal conductivity of the wafer to a desired level. This treatment can be selectively applied to different portions to selectively reduce the thermal conductivity in different portions of the MDR 200.

[0031] Block 302 represents fabricating the microfluidic system of the MDR 200 as an on-chip structure on a wafer, for example, using photolithography to direct liquids and gases in a precisely controlled manner. Processing methods may include those used to fabricate microfluidic systems in wafers (e.g., fused silica), for example, as known in the art for fabricating microfluidic DNA microassays, optofluidic systems, and inkjet printers.

[0032] The manufacturing steps typically include etching the components of the dilution loop into the wafer so that the return 3 He is controlled by the primary impedance 222 3 The rate at which He enters the heat exchanger 206. This is one of the most difficult components of a conventional dilution refrigerator and is typically handcrafted from a piece of steel wire inserted into a capillary of similar diameter. In the microfluidic system of the MDR 200 described herein, primary impedance 222 control can be achieved by fabricating a controlled, narrow channel of the desired length using photolithographic precision. A trench plasma-etched through the silicon dioxide wafer can thermally isolate the 4K stage 228 from the still 204, for example, at the ~700 mK stage 230.

[0033] The heat exchanger 206 is located after the primary impedance 222. The heat exchanger 206 can be designed to operate with the distiller 204 at a mK temperature (e.g., at ~700 mK stage 230) in normal operation. The heat exchanger 206 is further designed to cool the returning 3He, because excessive return heat inhibits operation of the dilution cooling process. In one or more examples, the heat exchanger 206 is fabricated by creating (e.g., etching) a plurality of SiO2 nanopillars over a large area of ​​a wafer and then coating the nanopillars with gold. Gold is also used to form a thermal contact with the distiller 204. In another example, the heat exchanger 206 may comprise nanostructured "black" gold. An active electronic cooler, such as a normal insulator superconductor (NIS) tunnel junction [3] (not shown) may be included to assist in cooling and allow for efficient thermalization of the return gas. The first microfluidic channel 208 between the heat exchanger 206 and the mixing chamber 202 is further sized to thermally isolate the heat exchanger 206 from the mixing chamber 202 at a subsequent ~50 mK stage 232.

[0034] The mixing chamber 202 is formed (e.g., etched) as a large enclosed volume in the chip / wafer, with a second microfluidic channel 210 exiting from the bottom of the mixing chamber 202 and proceeding to the still 204. The mixing chamber 202 is also configured to thermally couple the device being cooled to the mixture in the mixing chamber 202. To this end, a coupling structure can be formed by creating metal vias that connect to metal pads on the bottom cover of the mixing chamber 202. The device can then be thermally melted into this structure, although care must be taken to avoid leakage due to differential thermal contraction.

[0035] The distiller 204 in the next 700 mK stage 230 is formed (e.g., etched) as another large enclosed volume in the wafer. The distiller 204 is configured to enable evaporative cooling of the separated mixture received from the mixing chamber 202. In one or more examples, a small resistive heater (not shown) may be included to facilitate 3 Evaporation of He in order to increase the cooling power. If the MDR 200 is transparent, a laser (not shown) can also be used to deliver heating power to the absorbing metal in the still 204.

[0036] In one or more examples, where further tuning or reduction of thermal conductivity is desired, additional structures can be formed in the MDR 200, including etching phonon control structures (phononic crystals) into the interstage legs. Alternatively, each stage 228, 230, 232 can be connected to a thin-walled stainless steel or NbTi capillary.

[0037] If the various components of the MDR 200 (heat exchanger 206, mixing chamber 202, first and second microfluidic channels 208, 210, and distiller 204) are formed on multiple wafers, the wafers may be optionally attached together and the wafer connections may be sealed, as indicated in block 304. This attachment and leak-proofing may be achieved using microfluidic processes known in the art, including the use of polymers, epoxies, metal-to-metal bonding, or even directly fusing silica wafers together in a precisely controlled oven.

[0038] Box 306 represents the fabrication and connection of a pumping system comprising a roughing pump 212 and a turbo pump 214 for pumping into the distiller 204 to deliver the mixture to the 4K cooling stage 228 and then recirculating the mixture to the heat exchanger 206. The pumping system comprising the roughing pump 212 and the turbo pump 214 is designed so that the pressure in the distiller 204 is low enough to allow the dilution effect to operate. In one example, the mixture can be brought to room temperature so that a conventional pumping system can be used. In another example, the pumping is performed on the chip itself, for example using a chip-scale vacuum micropump (CSVMP) [4].

[0039] Figure 4A 、 4B and 4C are images of an on-chip micro-turbomolecular pump fabricated using silicon micromachining. Figure 4A As shown, pumps operating at or near 4K can include a magnetic film on the bottom of the turbine rotor, so that the superconducting Nb ground plane on the MDR chip can be used to magnetically levitate the rotor. Figure 4B As shown, photolithographically defined coils around the pump edge can be used to generate a magnetic field that is used to turn the turbine rotor into the stator of a DC brushless motor, forming an integrated micro-turbomolecular pump. This flat motor may be adapted from [5].

[0040] Reference again Figure 2 The turbo pump 214 is supported by a roughing pump 212 to keep the pressure on the back side low. In one example, the roughing pump 212 comprises an on-chip microelectromechanical system (MEMS) pump, similar to the 24-stage micro roughing pump developed for the CSVMP project. If the power consumption of this pump 214 exceeds the cooling power at 4K (on the order of a few hundred mW), it can be moved to a higher temperature stage (e.g., 50K) where higher cooling power is available and connected to the MDR 200 via a CuNi capillary.

[0041] Block 308 represents anchoring the entire MDR 200 to an intermediate (e.g., 4K) stage 228. This intermediate stage 228 can be provided by a mechanical refrigerator, such as a pulse tube or Stirling cycle cooler. In another example, the refrigerator for the intermediate stage 228 comprises a compact Stirling cycle cooler, such as used in cell phone base stations with superconducting filters [6], although an intermediate Joule-Thomson stage can also be included to assist in cooling to 4K. Such a Stirling cycle cooler can be easily fitted inside a personal computer housing while using electricity from a standard wall outlet.

[0042] Block 310 represents providing a control system for controlling the operation of the MDR 200. Starting the dilution cycle is often the most challenging part of running a dilution refrigerator. The cycle can be initiated by cooling the entire chip / wafer system including the MDR 200 to 4K within the metal 4K radiation shield 224. Anything within this volume for rapid cooling 4 He exchange gas can be captured in the carbon adsorption pump (not shown) before the cycle starts. In order to start the cycle, the mixture must be slowly entered into the MDR 200 and pressurized to about 2 atmospheres so that it can be condensed into a liquid at the 4K stage 228. For this purpose, a dump 216 (it is a tank) is provided and maintained at a temperature above 4.2 K, and the mixture slowly and intermittently enters the front side of the low vacuum pump 212 through the on-chip valve 220. The low vacuum pump 212 can be used to pressurize the mixture to 2 atmospheres so that it is condensed in the distiller 204 and the mixing chamber 202. Once all the mixture is condensed, valve 220 will be closed, allowing the cycle to start. The on-chip valve 218 between the turbo pump 214 and the low vacuum pump 212 is required to allow the mixture to be pressurized for condensation.

[0043] Block 312 represents the final result, MDR 200. In one example, MDR 200 includes a linear arrangement of components. Figure 5 is a depiction of a 3D model of an example 80×20×3 mm MDR 500 including a stacked arrangement including a mixing chamber 502 , a distiller 504 , a heat exchanger 506 , a first microfluidic channel 508 , a second microfluidic channel 510 , a roughing pump 512 , a turbo pump 514 , and a 4K radiation shield 524 . Figure 5 One chip 550 is shown comprising layers including a top chip / layer 550a and a bottom chip / layer 550b which are wafer bonded to a main chip 550c to seal the channels / ducts 508 , 510 .

[0044] For clarity, the top cover is omitted, and a fused silica wafer 534 is shown for comparison. For clarity, small features (such as the turbine blades of the turbo pump 514 and the nanopillars of the heat exchanger 506) are shown much larger than their actual size. In addition, the mixing chamber 502 includes a gold coating. In addition, the 4K radiation shield 524 is shown as transparent.

[0045] In this arrangement, each stage is fabricated individually and then connected to the next stage below it using NbTi or stainless steel capillaries, much like a conventional dilution refrigerator. Advantages of this configuration include easier thermal isolation and the ability to customize the fabrication of each stage. A disadvantage is that it is not possible to use the MDR 500 chip itself for photolithographic routing.

[0046] Box 314 represents attaching / integrating a device (e.g., a quantum device, a quantum processor, or a microwave dynamic inductance detector (MKID) camera) or an array of devices to the MDR 200. Example methods for attaching devices to the MDR 200 include using an indium ball grid array (BGA) located on each dilution refrigerator stage if a permanent solution is required, or a land grid array (LGA) type socket similar to those used in modern CPUs for reinstallable devices. This pattern allows the quantum processor to fit into the MDR 200 at the lowest temperature stage and allows other readout components (such as a high electron mobility transistor (HEmT) amplifier or a 4K complementary metal oxide semiconductor (CMOS) custom application specific integrated circuit (ASIC)) to be attached at higher temperature stages. Wiring can be integrated directly into the bottom cover of the MDR 200 chip, allowing for significant wiring density.

[0047] Since the thermal mass / heat load of the device being cooled is very small, the MDR 200 can be designed for a higher target cooling power of 10 μW at 100 mK (less cooling power than a conventional dilution refrigerator). In addition, the photolithographic NbTi wiring also significantly reduces the heat load. The MDR 200 can be implemented with or without the distiller 204 shield. Omitting the distiller 204 shield prevents the coldest temperature from being reached. If necessary, integrating the distiller 204 shield into the design can enable lower temperatures (<20 mK) to be reached. In addition, multiple MDR 200s can be used in parallel to increase the cooling power. Adiabatic demagnetization refrigerators (ADRs) have a cooling power of about 1 μW at 100 mK and are still frequently used to cool large devices, such as the 20,000 pixel MKID Exoplanet Camera (MEC) at Subaru Observatory [7].

[0048] Example MDR coupled to a sorption pump

[0049] Figure 6Another example MDR 600 is shown, comprising a mixing chamber 602, a distiller 604, a heat exchanger 606, a first microfluidic channel 608, a second microfluidic channel 610, a dump 616, a primary impedance 622, and a 4K radiation shield 624. In this example, the MDR 600 includes a helium sorption pump 636 (which operates using the properties of materials such as, but not limited to, charcoal that absorbs helium at 4K but readily outgases it at higher temperatures), and an active electronics cooler, such as an NIS tunnel junction 638. Figure 6 An example system is shown that includes an MDR 600 coupled to three sorption pumps 636, which are attached to a 4K stage 628 with a weak thermal link and also include a resistive heater (not shown). A series of 4K valves 640, 642 allow one sorption pump 636 to pump on the still 604 until it reaches its storage capacity, and then turn on the second sorption pump 636. The first pump 636 can then be heated to provide helium-3 to the primary impedance 622. The third sorption pump 636 is added to smooth the delivery of helium-3 by avoiding transients during switching between pumps 636.

[0050] Heat exchanger performance analysis

[0051] Ideal continuous heat exchanger model

[0052] If a passive, continuous heat exchanger is sufficient to remove 3 If the heat load of He is reduced to below that required to meet the desired performance targets, the manufacture of the refrigerator will be greatly simplified.

[0053] To place an upper limit on the potential performance of the heat exchanger, a perfect continuous countercurrent heat exchanger model solved in [8] was used, which consists of a countercurrent exchanger characterized by two long channels separated by a thin barrier. This model neglects viscous heat and transverse conduction and assumes that all heat leaving the dense phase enters the dilute phase. Their thermodynamic analysis yields the following equations:

[0054]

[0055]

[0056] where x is the coordinate along the length of the heat exchanger, C and D refer to the dense and dilute phases, respectively, γ = dS / dT, R3 is the Kapitza resistance coefficient, A is the heat exchanger area, and n is 3 He flow rate. Integrate these equations with T = ∞ for the hot side and T = T for the mixing chamber side. M , resulting in a set of transcendental equations that can be solved numerically to calculate the performance of the refrigerator. [8] also gives an approximation to the full solution, which will be used to generate the forward plot,

[0057]

[0058] Where T 00 is the base temperature when there is no heat leak

[0059]

[0060] In the presence of heat leaks In the case of [1], the base temperature is replaced by

[0061]

[0062] Figure 7A and Figure 7B The cooling power around 100 mK is shown, including the heat load from viscous heating. A heat exchanger length of 3 m represents the upper limit of plausibility, while 2 m is more practical given the original chip size.

[0063] Figure 8A and 8B The cooling capacity of heat exchangers with a length of 2 m and 3 m is shown around the base temperature.

[0064] Figure 9 The fluent simulation of a heat exchanger of approximately 1.2 m in length is shown. By dividing the heat exchanger into four different interfacial resistances, roughly including T 3 Kapitza resistance. The dense phase enters at 2K and cools to 915mK by the time it reaches the mixing chamber.

[0065] Device and System Embodiments

[0066] Example devices according to the embodiments described herein include, but are not limited to, the following (see also Figure 1-9 ).

[0067] 1. Microfluidic Dilution Refrigerator (MDR) 500, including:

[0068] A microfluidic system comprising:

[0069] a mixing chamber 502 in which helium-3 dissolves in helium-4 to form a mixture that absorbs heat, thereby cooling the device when the device is in thermal contact with the mixing chamber (or when helium-3 and helium-4 are provided in the mixing chamber, the mixing chamber is configured, positioned, or dimensioned to dissolve helium-3 in helium-4 to form the mixture);

[0070] a distiller / chamber / cavity 504 in which helium-3 in the mixture is evaporated from the mixture (or a distiller / chamber configured for (e.g., positioned and dimensioned to) evaporate the mixture);

[0071] a heat exchanger 506 thermally coupled to the distiller; and

[0072] a first microfluidic channel 508 configured to (size and / or position to) direct or couple helium-3 from the heat exchanger to the mixing chamber, the first microfluidic channel being sized to control the flow rate of helium-3 into the mixing chamber; and

[0073] a second microfluidic channel 510 configured (sized and / or positioned) to direct or couple the mixture from the mixing chamber to the still; and

[0074] The pumping system 552 is configured (sized and / or positioned) to circulate helium-3 from the still and back into the mixing chamber via the heat exchanger.

[0075] 2. The dilution refrigerator of Example 1, further comprising one or more chips 550 or substrates 534 comprising a microfluidic system.

[0076] 3. The dilution refrigerator of example 2, wherein:

[0077] The mixing chamber includes a first cavity 554 in one or more chips or substrates.

[0078] The distiller includes a second cavity in the one or more chips or substrates, and

[0079] The first microfluidic channel, the second microfluidic channel, and the heat exchanger are formed in one or more chips 550 or substrate 534 .

[0080] 4. The dilution refrigerator of Example 3, wherein the first cavity, the second cavity, the heat exchanger, the first microfluidic channel, and the second microfluidic channel are photolithographically patterned in the one or more chips or substrates.

[0081] 5. The dilution refrigerator of example 4, wherein:

[0082] The heat exchanger comprises an array of micro- or nanostructures 560 formed in the one or more chips or substrates and in thermal contact with the distiller, and

[0083] The sizes and positions of these structures are designed to direct and thermally contact the flow of helium-3 from the pumping system through the array and into the second microfluidic channel, allowing the heat exchanger to transfer heat from the helium-3 to the distiller, thereby cooling the helium-3 received from the pumping system.

[0084] 6. The dilution refrigerator of example 5, wherein the structure comprises metal-coated silicon oxide pillars.

[0085] 7. The dilution refrigerator of any of Examples 2-6, wherein the chip or substrate comprises or consists essentially of silicon, silicon dioxide, or any semiconductor.

[0086] 8. The dilution refrigerator of any of Examples 1-7, further comprising a cooling system 228, 628 (e.g., comprising a liquid cryogen bath) for providing first-stage cooling such that helium-3 can be liquefied in the microfluidic system using a pumping system.

[0087] 9. The dilution refrigerator of any of examples 2-8, wherein the pumping system comprises a micro-turbomolecular pump 514 formed in one or more chips or substrates.

[0088] 10. The dilution refrigerator of Example 7, wherein the micro-turbomolecular pump comprises a magnetic rotor suspended above a superconducting ground plane on the one or more chips or substrates.

[0089] 11. The dilution refrigerator of example 9, wherein the micro-turbomolecular pump is fed by a first backing pump comprising a MEMS pump 512 formed in the one or more chips or substrates.

[0090] 12. The dilution refrigerator of any of examples 1-11, further comprising an adhesive material that seals the one or more chips or substrates to prevent helium-3 from leaking from the microfluidic system.

[0091] 13. The dilution refrigerator of any of examples 1-12, further comprising a valve 220 and a computer 250 for controlling the pressure and temperature of the helium-3 in the microfluidic system, wherein the computer:

[0092] a control valve 220 to control the flow of helium-3 and helium-4 from a reservoir 216 containing helium-3 and helium-4 at a temperature greater than 4 Kelvin into the pumping system;

[0093] controlling the pumping system to increase the pressure in the microfluidic system so that the helium-3 and helium-4 condense into liquids in the microfluidic system; and

[0094] Close the valve to allow circulation of the helium-3 using the pumping system.

[0095] 14. The dilution refrigerator of any of examples 1-13, wherein the microfluidic channel is sized to thermally isolate the mixing chamber from the heat exchanger and the distiller.

[0096] 15. The dilution refrigerator of any of examples 1-14, further comprising a heating system coupled to the still to facilitate evaporation of helium-3 from the mixture in the still. In one or more examples, the heating system comprises a resistive heater comprising wires coupled to a portion of the chip 550 coupled to the still chamber and a power source for supplying current to the wires.

[0097] 16. The dilution refrigerator of any of Examples 1-15, further comprising a mount for thermally coupling the device to the mixing chamber, for example comprising indium bump bonds for electrical connection and gold wire bonds for thermal connection.

[0098] 17. The dilution refrigerator of any one of examples 1-16, configured such that the temperature T of the mixing chamber is such that k B T is less than the excitation energy used to manipulate the qubit using the device.

[0099] 18. The dilution refrigerator of any of examples 1-17, wherein the device mounted to the MDR comprises a quantum sensor or a quantum processor in a quantum computer for performing operations on qubits.

[0100] 19. The dilution refrigerator of any of examples 16-18, wherein the mounting comprises a land grid array, a ball grid array, wire bonds, or pogo pins on one or more chips or substrates comprising the mixing chamber.

[0101] 20. The dilution refrigerator of any of examples 1-19, wherein the mixing chamber, the distiller, the heat exchanger, the first microfluidic channel, and the second microfluidic channel each have a length, width, and depth in the range of 1 nm to 1000 microns.

[0102] 21. The dilution refrigerator of example 20, wherein the structures in the heat exchanger have a diameter, height, and pitch in the range of 1 nm to 1000 microns.

[0103] 22. An MDR or dilution refrigerator comprising any of examples 1-21, wherein one or more chips or substrates comprising a mixing chamber, a distiller, a heat exchanger, a microfluidic channel, and a pumping system are composed of or comprise at least 50% crystalline quartz, wherein selected portions of the crystalline quartz are treated with radiation to locally reduce thermal conductivity to a desired level (e.g., similar to or below 0.25°F). 1.9 mW / (cm K) (below 1K)).

[0104] 23. The dilution refrigerator 600 according to any one of Examples 1-22, further comprising:

[0105] a 4 Kelvin (4K) stage 628 (e.g., including or coupled to a mechanical refrigerator);

[0106] A first sorption pump 636(1) and a second sorption pump 636(2) connected to the 4 K stage by a weak thermal link; and a series of valves 640:

[0107] allowing the first adsorption pump to pump helium-3 by absorbing it into the still until the still reaches its storage capacity, collecting the absorbed helium-3, and

[0108] Then turn on the second pump;

[0109] A primary impedance valve 622 connecting the adsorption pump to the heat exchanger;

[0110] a heater 638 that heats the first adsorption pump so that the first adsorption pump outputs the absorbed helium-3 to the primary impedance valve; and

[0111] The third sorption pump 636 ( 3 ) is connected to smoothly deliver the absorbed helium-3 by avoiding transients during switching between the first sorption pump and the second sorption pump.

[0112] 24. A computer or controller coupled to the valve of example 23 to control the opening and closing of the valve and the operation of the heater.

[0113] 25. A microfluidic dilution refrigerator consisting essentially of crystalline quartz, wherein selective irradiation of portions of the device locally reduces thermal conductivity.

[0114] 26. The microfluidic dilution refrigerator of any of Examples 2-25, wherein the chip or substrate comprising the microfluidic system comprises essentially crystalline quartz, wherein selected irradiation of portions of the chip or substrate locally reduces the thermal conductivity to a desired level (e.g., no more than 0.25°F below 1°C). 1.9 mW / (cm K)).

[0115] 27. An MDR according to any of Examples 1-26, wherein the computer that controls the MDR (e.g., controlling pressure, temperature by controlling the opening and closing of a heater or a control valve) includes one or more integrated circuits, one or more microprocessors or microcontrollers, one or more application-specific integrated circuits, or one or more field programmable gate arrays coupled to the MDR, or a computer including one or more processors; one or more memories; and an application stored in the one or more memories, wherein the application executed by the one or more processors controls the valves and / or heaters as described herein.

[0116] 28. The MDR according to any example, wherein the distiller is defined as a chamber coupled to a heater for evaporating the mixture in the chamber and further having a conduit leading to the mixing chamber.

[0117] References

[0118] The following publications are incorporated herein by reference.

[0119] [1] Zheng, M. et al., “A Brief Review of Dilution Refrigerator Development for Space Applications”, Low Temperature Physics 197, 1-9 (2019).

[0120] [2] “30 years of microfluidics” by Convery, N. & Gadegaard, N., Micro and Nano Engineering 2, 76–91 (2019).

[0121] [3] Clark, AM et al., "Cooling of bulk material by electron-tunnelingrefrigerators", "Applied Physics Letters" 86, 173508 (2005).

[0122] [4] "Mems vacuum pumps" by Grzebyk, T., Microelectromechanical Systems 26, 705-717 (2017).

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[0127] in conclusion

[0128] The foregoing is a description of preferred embodiments of the present invention. The foregoing description of one or more embodiments of the present invention has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise forms disclosed. Many modifications and variations are possible in light of the above teachings. It is intended that the scope of the present invention be limited not by this detailed description, but rather by the claims appended hereto.

Claims

1. A microfluidic dilution refrigerator, comprising: Microfluidic systems, including: a mixing chamber in which helium-3 dissolves in helium-4 to form a mixture that absorbs heat, thereby cooling equipment in thermal contact with the mixing chamber; a still in which the helium-3 in the mixture is evaporated from the mixture; a heat exchanger thermally coupled to the distiller; a first microfluidic channel positioned to direct the helium-3 from the heat exchanger to the mixing chamber, the first microfluidic channel being sized to control a flow rate of the helium-3 into the mixing chamber; a second microfluidic channel positioned to direct the mixture from the mixing chamber to the still; and A pumping system is positioned to circulate the helium-3 from the still and back into the mixing chamber via the heat exchanger.

2. The microfluidic dilution refrigerator according to claim 1, further comprising one or more chips or substrates, wherein the one or more chips or substrates include the microfluidic system.

3. The microfluidic dilution refrigerator according to claim 2, wherein: The mixing chamber comprises a first cavity in the one or more chips or substrates, The distiller includes a second cavity in the one or more chips or substrates, and The first microfluidic channel, the second microfluidic channel, and the heat exchanger are formed in one or more chips or substrates.

4. The microfluidic dilution refrigerator according to claim 3, wherein: The first cavity, the second cavity, the heat exchanger, the first microfluidic channel, and the second microfluidic channel are photolithographically patterned in the one or more chips or substrates.

5. The microfluidic dilution refrigerator according to claim 4, wherein: The heat exchanger comprises an array of micro- or nanostructures formed in the one or more chips or substrates and in thermal contact with the distiller, and The structures are sized and positioned to direct and thermally contact the flow of helium-3 from the pumping system through the array and into the second microfluidic channel, allowing the heat exchanger to transfer heat from the helium-3 to the distiller, thereby cooling the helium-3 received from the pumping system.

6. The microfluidic dilution refrigerator according to claim 5, wherein: The structure includes silicon oxide pillars coated with metal.

7. The microfluidic dilution refrigerator according to claim 2, wherein: The chip or substrate comprises or consists essentially of silicon, silicon dioxide, or any semiconductor.

8. The microfluidic dilution refrigerator according to claim 7, wherein: The micro-turbomolecular pump includes a magnetic rotor suspended above a superconducting ground plane on the one or more chips or substrates.

9. The microfluidic dilution refrigerator of claim 1 , further comprising a cooling system for providing a first stage of cooling to enable the helium-3 to be liquefied in the microfluidic system using the pumping system.

10. The microfluidic dilution refrigerator according to claim 1, wherein: The pumping system includes a micro-turbomolecular pump formed in the one or more chips or substrates.

11. The microfluidic dilution refrigerator according to claim 10, wherein: The micro-turbomolecular pump is fed by a first backing pump comprising a micro-electromechanical system (MEMS) pump formed in the one or more chips or substrates.

12. The microfluidic dilution refrigerator of claim 1, further comprising an adhesive material that seals the one or more chips or substrates to prevent leakage of the helium-3 from the microfluidic system.

13. The microfluidic dilution refrigerator according to claim 2, wherein: The one or more chips or substrates comprising the mixing chamber, the distiller, the heat exchanger, the microfluidic channels, and the pumping system consist of or comprise at least 50% crystalline quartz, wherein selected portions of the crystalline quartz are treated with radiation to locally reduce thermal conductivity to a desired level.

14. The microfluidic dilution refrigerator according to claim 1 , further comprising a valve and a computer for controlling the pressure and temperature of helium-3 in the microfluidic system, wherein The computer: controlling the valve to control the flow of the helium-3 and the helium-4 from a reservoir containing helium-3 and helium-4 at a temperature greater than 4 Kelvin into a pumping system; controlling the pumping system to increase the pressure in the microfluidic system so that the helium-3 and helium-4 condense into liquids in the microfluidic system; and Close the valve to allow circulation of the helium-3 using the pumping system.

15. The microfluidic dilution refrigerator according to claim 1, wherein: The microfluidic channels are sized to thermally isolate the mixing chamber from the heat exchanger and the distiller.

16. The microfluidic dilution refrigerator of claim 1, further comprising a heating system coupled to the still to facilitate evaporation of the helium-3 from the mixture in the still.

17. The microfluidic dilution refrigerator of claim 1, further comprising a mount for thermally coupling the device to the mixing chamber.

18. The microfluidic dilution refrigerator according to claim 17, wherein: The mounting means may include a land grid array, a ball grid array, wire bonds or pogo pins on the mixing chamber.

19. The microfluidic dilution refrigerator according to claim 1, configured so that the temperature T of the mixing chamber is such that k B T is less than the excitation energy used to manipulate the qubit using the device.

20. The microfluidic dilution refrigerator according to claim 1, wherein: The devices include quantum sensors or quantum processors in a quantum computer for performing operations on qubits.

21. The microfluidic dilution refrigerator according to claim 1, wherein: The mixing chamber, the distiller, the heat exchanger, the first microfluidic channel, and the second microfluidic channel each have a length, a width, and a depth in a range of 1 nm to 1000 microns.

22. The microfluidic dilution refrigerator according to claim 20, wherein: The structures in the heat exchanger have diameters, heights, and spacings ranging from 1 nm to 1000 microns.

23. The microfluidic dilution refrigerator according to claim 1, further comprising: 4 Kelvin (4K) level; A first sorption pump and a second sorption pump attached to the 4K stage with a weak thermal link; and A range of valves: allowing the first adsorption pump to absorb helium-3 and pump it into the still until the still reaches its storage capacity, collecting the absorbed helium-3, and then switching on the second adsorption pump; A primary impedance valve connecting the adsorption pump to the heat exchanger; a heater configured to heat the first adsorption pump so that the first adsorption pump outputs the absorbed helium-3 to the primary impedance valve; and A third adsorption pump is connected to smoothly deliver absorbed helium-3 by avoiding transients during switching between the first adsorption pump and the second adsorption pump.

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