Patent Publication Number: US-2023135323-A1

Title: Dilution refrigerator with continuous flow helium liquefier

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application claims priority to U.S. Provisional Patent Application No. 63/274,633 filed on Nov. 2, 2021, the entire contents of which are hereby incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     The disclosure generally relates to the field of cryogenics. More specifically, the present disclosure relates to dilution refrigerators. 
     BACKGROUND 
     Quantum computers are machines that harness the properties of quantum states, such as superposition, interference, and entanglement, to perform computations. In a quantum computer, the basic unit of memory is a quantum bit, or qubit. Superconducting qubits are one of the most promising candidates for developing commercial quantum computers. Indeed, superconducting qubits can be fabricated using standard microfabrication techniques. Moreover, they operate in the few GHz bandwidth such that conventional microwave electronic technologies can be used to control qubits and readout the quantum states. However, superconducting qubits need to operate at temperatures dose to absolute zero. This requires cryogenic refrigeration systems with multiple stages of cooling. 
     A quantum computer with enough qubits has a computational power inaccessible to a classical computer, which is referred to as “quantum advantage”. As the number of qubits in a quantum computer scales, the cryogenic refrigeration systems need to provide increased cooling capacity. Therefore, improvements are needed. 
     SUMMARY 
     There is accordingly provided, in accordance with one aspect, a dilution refrigerator comprising: a cryostat comprising a plurality of temperature-controlled flanges inside a vacuum chamber, the temperature-controlled flanges including a first group of flanges cooled to a first set of progressively lower temperatures and a second group of flanges cooled to a second set of progressively lower temperatures that are higher than the first set of progressively lower temperatures; a dilution unit disposed inside the cryostat and operable to cool the first group of flanges to the first set of progressively lower temperatures; and a continuous flow helium refrigerator in heat transfer communication with a lowest temperature flange of the second group of flanges to provide primary cooling thereto to a first temperature, the continuous flow helium refrigerator residing at least partially in the cryostat and comprising a helium liquefier and a first closed-loop circuit thermally coupling the helium liquefier to the lowest temperature flange of the second group of flanges, the helium liquefier including a compressor, an expander downstream from the compressor, at least one heat exchanger between the compressor and the expander, and a liquid helium reservoir downstream from the expander and providing liquid helium to the lowest temperature flange of the second group of flanges via the first closed-loop circuit. 
     The dilution refrigerator as defined above and described herein may further include one or more of the following features, in whole or in part, and in any combination. 
     In certain aspects, the continuous flow helium refrigerator further comprises a second closed-loop circuit thermally coupled to the at least one heat exchanger, the second closed-loop circuit thermally coupling the continuous flow helium refrigerator to one or more flanges of the second group of flanges to provide cooling thereto to a second temperature. 
     In certain aspects. the second closed-loop circuit provides liquid nitrogen to the one or more flanges of the second group of flanges. 
     In certain aspects, the second closed-loop circuit diverts compressed helium gas exiting the compressor to cool the one or more flanges of the second group of flanges to the second temperature. 
     In certain aspects, a second expander is coupled to an inlet and an outlet of the compressor. 
     In certain aspects, a pulse tube cryocooler provides additional cooling to the second group of flanges at a second temperature higher than the first temperature. 
     In certain aspects, the helium liquefier further includes a second expander and a second heat exchanger, the second heat exchanger operable to cool, via liquid helium in the liquid helium reservoir, a portion of helium diverted downstream of the at least one heat exchanger to a second temperature below the first temperature, and direct the portion of helium through the second expander and through the first closed-loop circuit. 
     In certain aspects, the helium liquefier further includes a second liquid helium reservoir thermally coupled to a second heat exchanger, the second liquid helium reservoir operable to receive a portion of liquid helium from the liquid helium reservoir, with a remainder of the liquid helium from the liquid helium reservoir diverted to the second heat exchanger to cool the portion of liquid helium before the portion of liquid helium is directed through the first closed-loop circuit. 
     In certain aspects, the dilution unit includes a second liquid helium reservoir thermally coupled to a second heat exchanger and disposed in the first group of flanges, the second liquid helium reservoir operable to receive liquid helium from the liquid helium reservoir and provide cooling, via the second heat exchanger, to a flange of the second group of flanges and/or a supply line to the dilution unit. 
     In certain aspects, the expander, the at least one heat exchanger, and the liquid helium reservoir are disposed inside the cryostat. 
     There is also provided, in accordance with another aspect, a dilution refrigerator comprising: a cryostat comprising a plurality of temperature-controlled flanges inside a vacuum chamber, the temperature-controlled flanges composed of a first group of flanges cooled to a first set of progressively lower temperatures and a second group of flanges cooled to a second set of progressively lower temperatures that are higher than the first set of progressively lower temperatures; a dilution unit disposed inside the cryostat and operable to cool the first group of flanges to the first set of progressively lower temperatures; and a continuous flow helium refrigerator in heat transfer communication with a lowest temperature flange of the second group of flanges to maintain the lowest temperature flange at a first temperature of 2.5 K to 5 K using a recuperative thermodynamic cycle, the continuous flow helium refrigerator residing at least partially in the cryostat and including a helium liquefier and a first closed-loop circuit fluidly interconnecting the helium liquefier and the lowest temperature flange of the second group of flanges. 
     The dilution refrigerator as defined above and described herein may further include one or more of the following features, in whole or in part, and in any combination. 
     In certain aspects, the continuous flow helium refrigerator further comprises a second closed-loop circuit thermally coupled to the helium liquefier, the second closed-loop circuit thermally coupling the continuous flow helium refrigerator to one or more flanges of the second group of flanges to provide cooling thereto to a second temperature. 
     In certain aspects, the second closed-loop circuit diverts compressed helium gas from the helium liquefier to cool the one or more flanges of the second group of flanges to the second temperature. 
     In certain aspects, a pulse tube cryocooler provides additional cooling to the second group of flanges at a second temperature higher than the first temperature. 
     In certain aspects, the helium liquefier includes a compressor, an expander downstream from the compressor, at least one heat exchanger between the compressor and the expander, and a liquid helium reservoir downstream from the expander and providing liquid helium to the lowest temperature flange of the second group of flanges via the first closed-loop circuit. 
     In certain aspects, a second expander is coupled to an inlet and an outlet of the compressor. 
     In certain aspects, the helium liquefier further includes a second expander and a second heat exchanger, the second heat exchanger operable to cool, via liquid helium in the liquid helium reservoir, a portion of helium diverted downstream of the at least one heat exchanger to a second temperature below the first temperature, and direct the portion of helium through the second expander and through the first closed-loop circuit. 
     In certain aspects, the helium liquefier further includes a second liquid helium reservoir thermally coupled to a second heat exchanger, the second liquid helium reservoir operable to receive a portion of liquid helium from the liquid helium reservoir, with a remainder of the liquid helium from the liquid helium reservoir diverted to the second heat exchanger to cool the portion of liquid helium before the portion of liquid helium is directed through the first closed-loop circuit. 
     In certain aspects, the dilution unit includes a second liquid helium reservoir thermally coupled to a second heat exchanger and disposed in the first group of flanges, the second liquid helium reservoir operable to receive liquid helium from the liquid helium reservoir and provide cooling, via the second heat exchanger, to a flange of the second group of flanges and/or a supply line to the dilution unit. 
     In certain aspects, the expander, the at least one heat exchanger, and the liquid helium reservoir are disposed inside the cryostat. 
     There is further provided, in accordance with another aspect, a continuous flow helium refrigerator for a dilution refrigerator of a quantum computing system, comprising: a helium liquefier including a compressor, an expander downstream from the compressor, at least one heat exchanger between the compressor and the expander, and a liquid helium reservoir downstream from the expander; and a closed-loop circuit thermally coupling the helium liquefier to a flange of the dilution refrigerator; wherein the helium liquefier is operable to maintain the flange of the dilution refrigerator at a temperature of 2.5 K to 5 K. 
     The continuous flow helium refrigerator for a dilution refrigerator as defined above and described herein may further include one or more of the above-noted features, in whole or in part, and in any combination. 
     Many further features and combinations thereof concerning the present improvements will appear to those skilled in the art following a reading of the instant disclosure. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a schematic view of a dilution refrigerator according to an embodiment; 
         FIGS.  2 A- 2 C  are schematic views of exemplary continuous flow helium liquefiers for the dilution refrigerator of  FIG.  1   ; 
         FIG.  3 A  is a schematic view of a dilution refrigerator according to another embodiment; 
         FIG.  3 B  is a schematic view of an exemplary continuous flow helium liquefier for the dilution refrigerator of  FIG.  3 A ; 
         FIG.  4    is a schematic view of a dilution refrigerator according to another embodiment; 
         FIG.  5    is a schematic view of a dilution refrigerator according to another embodiment; 
         FIG.  6    is a schematic view of a dilution refrigerator according to another embodiment; 
         FIG.  7    is a schematic view of a dilution refrigerator according to another embodiment; and 
         FIG.  8    is a schematic view of a dilution refrigerator according to another embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     Dilution refrigerators are cryogenic devices that provide continuous cooling in a cryostat from ambient temperature all the way down to millikelvin temperatures without any moving part at the low temperature stages (below 3 Kelvin (K)). 
     Dilution refrigerators may comprise a number of temperature stages used to thermally anchor radiation shields and wiring in order to reduce the amount of heat leaking to the colder stages. Aside from a room-temperature (300 K) stage, there can be, for example, stages at 50 K, 10 K, and 4 K, and additional stages at temperatures below 1 K. The cooling of these stages, or “flanges”, may be achieved by one or more different cooling systems including, for example, dilution units and pulse tube cryocoolers. 
     The pulse tube cryocooler serves many purposes. It is typically used 1) to cool and maintain the 50 K, 10 K, and 4 K stages at their cold temperature, 2) to achieve the initial cool down of the coldest stages of the dilution refrigerator to around 4 K prior to activating the dilution unit, and 3) to cool circulating 3He (Helium-3, a stable isotope of Helium (He)) from ambient temperature to 4 K during the steady state operation of the dilution unit. 
     Dilution refrigerators are used in various applications, including low temperature detectors, superconductivity research, low temperature solid state physics, and quantum computing. The latter is a rapidly developing field which will require larger and larger cryogenic systems as the number of qubits in quantum processors increases. For example, in some cases superconducting quantum computers use coaxial cables to route signals from room temperature electronics to the quantum processor in the dilution refrigerator. As the number of cables scales linearly with the number of qubits, a larger number of qubits will result in more cables in the cryostat. The space occupied by the cables may require larger cryostats, and the heat leak through the cables to the lower temperature stages of the cryostat may require a greater flow rate of 3He through the dilution unit to provide more cooling power. The increased conductive heat leak through the cables and supports, radiative heat leak to the larger radiation shields, and heat load from increased 3He circulation mean that the cooling power provided by the pulse tube cryocooler will also need to be increased. 
     However, the cooling power of pulse tube cryocoolers does not scale easily. Indeed, flow instabilities in larger tubes make it very difficult to make more powerful pulse tubes. Hence, making larger pulse tubes is not practical and additional cooling power is provided by multiple pulse tubes. However, this solution does not scale well since 1) multiple pulse tubes require additional space inside the cryostat, where space is usually limited, and 2) power consumption, the amount and cost of the regenerator material and the number and/or size of compressors scale linearly with the number of pulse tubes. 
     In the present disclosure, a dilution refrigerator is provided that includes a continuous flow helium liquefier, which is a recuperative-type cooling device, for providing primary cooling to one or more flanges of the dilution refrigerator. In accordance with some embodiments of the present disclosure, the pulse tube cryocooler typically used for cooling one or more flanges of a dilution refrigerator may be replaced by the continuous flow helium liquefier. In other embodiments, the continuous flow helium liquefier provides primary cooling for one or more flanges, and a pulse tube cryocooler may be used to provide supplemental, albeit secondary, cooling. For a given capital cost and electrical power consumption, continuous flow helium liquefiers can provide higher cooling power than pulse tube cryocoolers. For example, a continuous flow helium liquefier can provide 100 to 1000 W of cooling power at 4.5 K while consuming 50 to 300 kW of electrical power whereas a pulse tube cryocooler provides 2 to 3 W of cooling at 4.2 K with 12.5 kW of electricity. 
       FIG.  1    shows an embodiment fora dilution refrigerator  100 . The dilution refrigerator  100  comprises a cryostat  101  having temperature-controlled flanges, illustratively five flanges  101 A,  101 B,  101 C,  101 D and  101 E defining five temperature stages of decreasing temperature. The flange  101 A, also called an outer vacuum can or vacuum chamber, is at the 300 K stage while flanges  101 B,  101 C,  101 D and  101 E can, for example, be at the 50 K, 4 K, 800 mK, and 8 mK stages. These temperatures are exemplary, and other temperature stages may be contemplated. Flanges  101 B,  101 C,  101 D and  101 E need not be perfectly sealed. These flanges may serve for supporting radiation shields as well as for thermal anchoring of other components of the dilution refrigerator  100 . The flanges  101 A,  101 B,  101 C,  101 D and  101 E can be made of plates (where components can be affixed). In some embodiments, the plates also act as radiation shields. Additional thermal anchoring stages which may not take the form of a flange may also be present, for example at the 800 mK stage. Other embodiments may have a different number of flanges at different temperatures. A device  102  resides inside the coldest flange  101 E. The device  102  can, for example, be a quantum processor. Note that some of the temperature stages illustrated as flanges in  FIG.  1   , for example the flange  101 E, could also alternatively take the shape of an open structure. In some cases, the flanges  101 A- 101 E may take the form of nested enclosures, where the innermost flange is at a lowest temperature and the outermost flange is at a highest temperature, with intermediate flanges being maintained at progressively lower temperatures from the outermost flange towards the innermost flange. 
     Cooling of the lower temperature stages, such as those defined by flanges  101 D,  101 E, is provided by a dilution unit  103 , which is schematically represented by a simple rectangle in  FIG.  1   . The dilution unit  103  may comprise a mixing chamber, liquid counter flow (recuperative) heat exchangers, a still and a condenser, which can be a vapor counter flow (recuperative) heat exchanger, or a liquid 4He heat exchanger coupled to a liquid 4He bath supplied via a separate circulation circuit. The dilution unit  103  is supplied by a 3He supply line  104  which is thermally anchored at different temperature stages and in some cases connected to a gas handling system  105  outside the cryostat  101 . A pumping line used to extract 3He from the cryostat  101  towards the gas handling system  105  is not illustrated for clarity. 
     The dilution unit  103  provides cooling power by the energy required to mix two isotopes of helium, liquid 3He and 4He. Indeed, at low temperature, the mixture of both isotopes separates into two phases: a 3He rich phase and a 4He rich phase. When liquid 3He is circulated into a mixing chamber containing 4He, it mixes with the 4He rich phase which requires energy and thus removes heat from the mixing chamber&#39;s environment. 
     Continuous cooling power is produced by circulating 3He, for example using vacuum pumps located in a gas handling system outside the cryostat, such that 3He evaporated from the 3He/4He mixture is returned to the dilution unit  103  to be condensed before entering the mixing chamber again. The dilution unit  103  comprises a condenser to turn the gaseous 3He supply to liquid 3He. The condenser can be a recuperative heat exchanger cooled by the enthalpy of the 3He evaporated from the still. Alternatively, the condenser can be a heat exchanger cooled by a liquid 4He bath at a temperature around 1 K. 
     In operation, the dilution unit  103  and the 3He supply are first cooled from room temperature, and then maintained at temperatures close to liquid helium temperature (4.2 K) to condense the incoming 3He supply in the condenser. 
     In cases where the device  102  employs electronic control from outside the cryostat  101 , as is the case for quantum processors, the cryostat  101  can be wired with control cables thermally anchored at each temperature stage through various heat exchangers similarly to the 3He supply line  104 . 
     The flanges  101 A- 101 E may be split into a first group of flanges cooled to a first set of progressively lower temperatures and a second group of flanges cooled to a second set of progressively lower temperatures that are higher than the first set of progressively lower temperatures. Illustratively, flanges  101 D and  101 E form the first group of flanges and are cooled by the dilution unit  103 , whereas flanges  101 A- 101 C form the second group of flanges and may be cooled via various means, as will be discussed in further detail below. 
     Primary cooling of one or more of the flanges of the cryostat  101 , and in particular the innermost flange  101 C of the second group of flanges (i.e., the lowest temperature flange of the second group of flanges), is provided by a continuous flow helium refrigerator  106  as will now be described. The helium refrigerator  106  includes a first closed loop piping circuit  107  and a helium liquefier  108 , the first closed loop piping circuit  107  provided between the helium liquefier  108  and the cryostat  101 . For example, the piping circuit  107  is coupled to flange  101 C through heat exchanger  110  so that the helium liquefier  108  is thermally coupled to the flange  101 C. As helium flows through the first closed loop piping circuit  107 , it circulates through the heat exchanger  110 , thus cooling the flange  101 C. The first closed loop piping circuit  107  can also be used to cool the dilution unit 3He supply line  104 , for example by coupling the 3He supply line  104  to the heat exchanger  110 . Other heat exchangers may be used to couple the 3He supply line  104  to the first closed loop piping circuit  107 . 
     In some embodiments, a second closed loop piping circuit  109  is provided between the helium liquefier  108  and the cryostat  101 . For example, the piping circuit  109  is coupled to flange  101 B through a heat exchanger  112 . As helium flows through the second closed loop piping circuit  109 , it circulates through the heat exchanger  112 , thus cooling the flange  101 B. The second closed loop piping circuit  109  can also be used to cool the dilution unit 3He supply line  104 , for example by coupling the 3He supply line  104  to the heat exchanger  112 . Other heat exchangers may be used to couple the 3He supply line  104  to the second closed loop piping circuit  109 . 
     The helium flowing out of the helium liquefier  108  and into the first closed loop piping circuit  107  flows at a first temperature T 1 . The helium flowing out of the helium liquefier  108  and into the second closed loop piping circuit  109  flows at a second temperature T 2 &gt;T 1 . In this manner, flange  101 C is cooled to a temperature that is lower than the temperature to which flange  101 B is cooled. For example, flange  101 C may be cooled to 4 K and flange  101 B may be cooled to 50 K. Other temperatures values are also considered. For instance, in various embodiments, flange  101 C may be cooled to temperatures varying between about 2.5 K to 5 K. The helium liquefier  108  may be operable to provide primary cooling to the flange  101 C, i.e., capable of cooling the flange  101 C to its target temperature (e.g., to about 2.5 K to 5 K, and preferably to about 4 K) without the need for other cooling means such as pulse tubes. This cooling power and the ability of the helium liquefier  108  to operate independently from other cooling means comes from the use of a recuperative cycle to liquefy helium. Some of the compressed helium is quasi-isentropically expanded, and the cooling that comes from the expansion allows the cycle to operate independently. This arrangement can readily be scaled up to large flow rates so as to provide large cooling powers. 
     With reference to  FIG.  2 A , there is illustrated an example embodiment for the helium liquefier  108 . In this example, the helium liquefier  108  uses a recuperative cycle (for example the Linde-Hampson cycle) because cold gas is recuperated via a heat exchanger to cool down an incoming compressed gas. Indeed, a cold block  204  comprises a heat exchanger  206  and an expander  210 , illustratively an expansion valve. Other types of expanders  210  may be contemplated, for instance an expansion turbine, a piston expander, and a throttling valve. The first closed loop piping circuit  107  has an incoming branch  212 A and an outgoing branch  212 J. Helium gas coming in through the incoming branch  212 A is used to cool a compressed version of that same gas that has passed through a compressor  208  and is flowing down into the heat exchanger  206  in the opposite direction. More specifically, gas coming in through branch  212 A combines with gas flowing through branch  212 G to form gas flowing in branch  212 B through the heat exchanger  206 . The gas through branch  212 B gets compressed by the compressor  208  and flows back into the heat exchanger  206  through branch  212 C. The gas through branch  212 C mixes with incoming gas through branch  214 A coming from the second closed loop piping circuit  109  to form the gas in branch  212 D, which then gets split between branch  214 B and branch  212 E (for example using a pump and an orifice or an adjustable valve). Gas in branch  214 B is flowing out to the cryostat  101  via the second closed loop piping circuit  109 . Gas through branch  212 E flows through the expander  210 , resulting in a mixture of liquid and gas in branch  212 F. Most of the gas from branch  212 F gets directed to branch  212 G, most of the liquid from branch  212 F gets directed to branch  212 H and flows into a reservoir  202 . 
     More generally, the helium liquefier  108  includes a compressor  208 , an expander  210  downstream from the compressor  208 , at least one heat exchanger  206  between the compressor  208  and the expander  210 , and a liquid helium reservoir  202  downstream from the expander  210  and providing liquid helium to the lowest temperature flange  101 C of the second group of flanges via a closed-loop circuit  107 . It will be understood that the embodiment illustrated in  FIG.  2 A  requires the helium flowing within the helium liquefier  108  to be cold enough for the recuperative cycle to begin. In certain embodiments of the expander  210 , for example as a piston expander or a turbine, no additional assistance is needed. In other embodiments of the expander  210 , for example as a valve, additional assistance may be provided using one or more additional component within the continuous flow helium refrigerator  106  or externally thereto to cool the helium flowing in the closed-loop circuit  107  to a given initial temperature until the cycle can become self-sustaining. 
     Cold helium flows out of branch  212 J at about 4 K to cool the flange  101 C through heat exchanger  110  and returns to the helium liquefier  108  through branch  212 A. This helium then passes through the heat exchanger  206  via branch  212 B to cool compressed gas flowing out of the helium liquefier  108  through branch  214 B at about 50 K. In some embodiments, an adjustable valve or an orifice may be provided on incoming branch  212 A, outgoing branch  212 J and/or branch  212 G in order to control the flow rate in the first closed loop piping circuit  107 . It will be understood that various pumps, which are omitted from  FIG.  2 A  for clarity, are used to allow the gas and/or liquid to flow in the indicated directions, in view of the various pressure levels present in the different branches of the piping circuits. Also omitted for clarity are the different chambers at different temperature stages within the cold box  204 . 
     In some embodiments, the heat exchanger  206  may be replaced by a plurality of heat exchangers  206 A,  206 B,  206 C,  206 D as illustrated in the example of  FIG.  2 B . Gas flowing through branch  212 B flows through the heat exchangers  206 A,  206 B,  206 C,  206 D in a first direction, gas flowing through branch  212 C flows through the heat exchangers  206 A,  206 B,  206 C,  206 D in a second direction opposite the first direction. Another variant to the embodiment of  FIG.  2 A  is shown in  FIG.  2 B , where branches  214 A and  214 B of the second closed loop piping circuit  109  are coupled through branch  214 C that flows gas through heat exchanger  206 C and gets cooled by compressed gas flowing through branch  212 C. Other variants may also be provided, such as more or less heat exchangers and additional gas expanders to cool the helium in the closed-loop circuit  107  to a given initial temperature until the cycle can become self-sustaining. 
     In embodiments where the second closed loop piping circuit  109  is independent from the circuit through which the helium flows within the helium liquefier  108 , as shown in  FIG.  2 B , a liquid substance may flow through the second closed loop piping circuit  109  instead of gaseous helium. Indeed, any substance in a liquid state at the temperature and pressure of the second closed loop piping circuit  109  will provide good heat transfer through heat exchanger  112  in the cryostat  101  and through heat exchanger  206 C in the helium liquefier  108 . 
     With reference to  FIG.  2 C , there is illustrated another example for the helium liquefier  108 . In this example, the helium liquefier uses a variation of the Linde-Hampson cycle, referred to as the Claude cycle. As in the case of the helium liquefier  108  shown in  FIG.  2 A , the Claude cycle type liquefier of  FIG.  2 C  may be referred to as a recuperative cycle because cold gas is recuperated via a heat exchanger to cool down an incoming compressed gas. The helium refrigerator  106  shown in  FIG.  2 C  includes two stages of heat exchangers  206 A,  206 B, defining two temperature stages. The second stage heat exchanger  206 B, along with expander  210 , are located inside cold block or chamber  204 . The helium refrigerator  106  further includes compressor  208  and liquid helium reservoir  202 . In addition, an expansion turbine  216  is provided in conjunction with heat exchanger  206 B. Expansion turbine  216  is operable to extract work from the working fluid in order to increase the cooling of the compressed gas. After the compressed gas exits the first heat exchanger  206 A and before entering second heat exchanger  206 B, a portion of the compressed gas is diverted to the expansion turbine  216  (for example using orifices/valves) to be expanded before being returned to the cold, low-pressure side of the second heat exchanger  206 B. This may aid in the cooling of the hot compressed gas in heat exchanger  206 B while maintaining a sufficiently high pressure in the main helium flow to allow for liquefaction of the helium across the expander  210 . 
     In some embodiments, and with reference to  FIGS.  3 A- 3 B , a first flange of the cryostat  101  is cooled using the helium liquefier  108  while a second flange of the cryostat  101  is cooled using a different cooling mechanism. For example, one of the flanges may be cooled using liquid nitrogen. As shown in  FIG.  3 A , the first closed loop piping circuit  107  is coupled between the cryostat  101  and the helium liquefier  108 , and cools flange  101 C through heat exchanger  110 . The helium flowing through the first closed loop piping circuit  107  may also be used to cool the dilution unit 3He supply line  104  through heat exchanger  110  if the 3He supply line  104  is coupled to the heat exchanger  110 . The second closed loop piping circuit  109  is coupled between the cryostat  101  and a liquid nitrogen module  302 , and cools flange  101 B through heat exchanger  112 . The liquid nitrogen can also be used to cool the dilution unit 3He supply line  104  through the heat exchanger  112  if the 3He supply line  104  is coupled to the heat exchanger  112 . 
     The liquid nitrogen module  302  forms part of the gas handling system  105  and may be provided separately from or integrated with the helium refrigerator  106 . As shown in  FIG.  3 B , the liquid nitrogen module  302  comprises a liquid nitrogen reservoir  304  from which the liquid nitrogen flows into the second closed loop piping circuit  109  through branch  214 A and returns through branch  214 B. In some embodiments, the liquid nitrogen can also be used to initially cool helium in the helium liquefier  108  by redirecting part of the liquid nitrogen towards a heat exchanger  206 A via circuit  306 . Compressed gas carried by branch  212 C is cooled by the liquid nitrogen as it flows through the heat exchanger  206 A. The various flows of nitrogen may be set using orifices/valves. The liquid nitrogen module  302  can be a nitrogen liquefier based on a closed loop cycle (e.g., the Linde-Hampson cycle) or an open loop system where the liquid nitrogen reservoir  304  is periodically re-filled. 
     In some embodiments, a first flange of the cryostat  101  is cooled using the helium liquefier  108  while a second flange of the cryostat  101  is cooled using a pulse tube cryocooler. An example is shown in  FIG.  4   , where the first closed loop piping circuit  107  is coupled between the cryostat  101  and the helium liquefier  108 , and cools flange  101 C through heat exchanger  110 . The helium flowing through the first closed loop piping circuit  107  may also be used to cool the dilution unit 3He supply line  104  through heat exchanger  110  if the 3He supply line  104  is coupled to the heat exchanger  110 . A first pulse tube  404  of a two-stage pulse tube cryocooler provides cooling to the flange  101 B and to the 3He supply line  104  through the heat exchanger  112 . A second pulse tube  406  of the two-stage pulse tube cryocooler may be used as a supplement to provide cooling power at a lower temperature to the 3He supply line  104  through a heat exchanger  408 . Indeed, although a single pulse tube  404  may be used, a second pulse tube  406  can contribute additional cooling power by further lowering the temperature of the 3He supply line  104  beyond 4 K, for example closer to 2 K. 
     The pulse tube cryocooler may be driven by its own compressor  402 . Alternatively, the helium liquefier  108  and the pulse tube cryocooler may share one or more compressor components. If both systems require different pressures, then a booster may be used to raise the pressure in one of the systems. In some embodiments, the compressor  402  for the pulse tube is provided externally to the continuous flow helium refrigerator  106  as part of the gas handling system  105 . 
     Referring to  FIG.  5   , there is shown another embodiment of a dilution refrigerator  100 . In this embodiment, a modified continuous flow helium refrigerator  106  is operable to cool the flange  101 C to temperatures below 4.5 K. A compressor  502  compresses warm helium, which then flows through a series of heat exchangers  206  where the helium is cooled. A portion of the cooled compressed helium gas passes through a first expander  210 A to condense the helium gas into liquid helium, which then accumulates in the liquid helium reservoir  202 . Another portion of the cooled compressed helium gas exiting the heat exchangers  206  is diverted towards an additional heat exchanger  504 , which is cooled by cold liquid helium exiting the liquid helium reservoir  202  and flowing towards the compressor  502 . In other cases, the additional heat exchanger  504  may be disposed within the liquid helium reservoir  202 . The diverted helium gas is then directed through a second expander  210 B to produce liquid helium at temperatures at around just below 2 K. This liquid helium, at temperature T 1 , is directed through first closed loop piping circuit  107  to cool the flange  101 C (via heat exchanger flange  110 ) as well as the 3He supply line  104 . 
     As the helium gas returning from heat exchanger  110  via first closed loop piping circuit  107  has a low density, a compressor  506  is provided to compress this returning helium gas. The helium gas is then passed through at least some of the heat exchangers  206  to provide cooling to the helium gas exiting the compressor  502 , before being compressed by a room temperature vacuum compressor  508  and then being fed to the compressor  502 . As in previous embodiments, gaseous helium at temperature T 2  may be diverted partway through the heat exchangers  206  via second closed loop piping circuit  109  to cool one or more additional flanges, for instance flange  101 B via heat exchanger  112 . 
     The helium liquefier shown in  FIG.  5    therefore includes two interacting closed loops of circulating helium. The first closed loop includes compressor  502 , heat exchangers  206 , expander  210 A and liquid helium reservoir  202 . The second closed loop shares part of the first loop&#39;s path, i.e., the compressor  502  and the heat exchangers  206 , but is then diverted (for example using orifices/valves) through additional heat exchanger  504  and expander  210 B before following through first closed loop piping circuit  107  to the cryostat  101 . Returning helium then passes through compressor  506 , some or all of heat exchangers  206 , and then room temperature vacuum compressor  508  before returning to the compressor  502 . 
     Referring to  FIG.  6   , there is shown another embodiment of a dilution refrigerator  100  with a modified continuous flow helium refrigerator  106  operable to cool the flange  101 C to temperatures below 4.5 K. As in previous embodiments, a compressor  502  compresses warm helium gas, which is then directed through a series of heat exchangers  206  for cooling. The cool compressed helium gas is then directed through expander  210  where it is condensed into liquid before accumulating in liquid helium reservoir  202 . A portion of the liquid helium from the liquid helium reservoir  202  is diverted to a second liquid helium reservoir  602  via piping  604 . Piping  604  includes an impedance to limit the flow of liquid helium towards second liquid helium reservoir  602 . The second liquid helium reservoir  602  is fluidly coupled to a downstream vacuum pump  606  which is operable to lower the pressure of the liquid helium in helium reservoir  602 . As such, the second liquid helium reservoir  602  forms a liquid helium bath at a temperature of about 1 to 2 K. In some cases, a compressor (not shown) may additionally be provided in the cold block  204  between the second liquid helium reservoir  602  and the vacuum pump  606  to assist the vacuum pump  606  in achieving a desired flow rate. As shown in  FIG.  6   , the input and output lines of the second liquid helium reservoir  602  may exchange heat via additional heat exchanger  608 . 
     The second liquid helium reservoir  602 , i.e., the cold helium bath, is operable to cool, via another heat exchanger  610 , the remainder of the liquid helium exiting the liquid helium reservoir  202 . This additionally-cooled liquid helium is then circulated via first closed loop piping circuit  107 , at temperature T 1 , to provide cooling to the flange  101 C (via heat exchanger  110 ) and the 3He supply line  104 . The returning helium from the cryostat is directed through heat exchangers  206  and then back to the compressor  502 . The discharge from the vacuum pump  606  is also directed into the compressor  502 , thereby forming a second pathway to the compressor  502 . Cooling means for flange  101 B are omitted from  FIG.  6    for clarity but may include any of the above-described cooling means for flange  101 B. 
     Referring to  FIG.  7   , in another embodiment of a dilution refrigerator  100 , cooling of the flange  101 C and dilution unit 3He supply line  104  is provided by a continuous flow helium liquefier  108 , as described above, fluidly coupled to the heat exchanger  110 . As was the case in the embodiment shown in  FIG.  6   , cooling means for flange  101 B are omitted from  FIG.  7    for clarity but may include any of the above-described cooling means for flange  101 B. 
     The dilution unit  103 , operable to cool the first group of flanges including innermost flange  101 E, illustratively includes a heat exchanger  702  acting as a condenser, as well as a still, some counter-flow heat exchangers, and a mixing chamber  704 . In this embodiment, the heat exchanger  702 , which is used to condense the 3He from the 3He supply line  104 , is cooled by a liquid 4He bath  706 . 
     As the liquid 4He in the bath is evaporated in order to cool the supply of 3He, the 4He bath  706  employs a continuous supply of liquid 4He. As the helium liquefier  108  is producing liquid helium to cool the flange  101 C and 3He supply line  104 , the supply of liquid 4He used for the 4He bath  706  may be drawn from the first closed loop piping circuit  107 . As such, a supply line  708  is operable to divert a small quantity of liquid 4He from the first closed loop piping circuit  107  towards the liquid 4He bath  706 . In some cases, the supply line  708  may include an impedance tube to limit the flow of 4He towards the liquid 4He bath. While the supply line  708  is shown in  FIG.  7    as branching out from first closed loop piping circuit  107  adjacent the heat exchanger  110 , it is understood that supply line  708  may branch off from the first closed loop piping circuit  107  at any point of the first closed loop piping circuit  107 . In some cases, the supply line  708  may be fluidly connected directly to the liquid helium reservoir  202 . 
     4He evaporated from the liquid 4He bath  706  may be pumped through a return line  710  by a downstream vacuum pump  712  before it returns to the compressor  502 . As such, the evaporated 4He may be liquefied in the helium liquefier  108  in a closed loop. In some cases, to attain specific flow rates, a cryogenic compressor may be provided. In such cases, the cryogenic compressor may be disposed in the outer vacuum can  101 A, within the appropriate flange for the desired operating temperature of the cryogenic compressor, and on the return line  710  between the liquid 4He bath  706  and the vacuum pump  712 . Alternatively, in cases where the return line  710  passes through the cold block  204 , the cryogenic compressor may be located inside the cold block  204 . In such cases, if the return line  710  were coupled to the heat exchangers  206 , the cold helium in the return line  710  may be used to provide cooling to the incoming compressed helium exiting the compressor  502 , thus recuperating cooling power from the return line  710  to improve the efficiency of the helium liquefier  108 . 
     In various embodiments, one or more components of the helium liquefier  108  may be disposed inside the cryostat  101 . For instance,  FIG.  8    shows a dilution refrigerator  100  in which the cold block of the continuous flow helium liquefier is integrated inside the vacuum can  101 A. In  FIG.  8   , the first heat exchanger  206 A, which is at room temperature, is positioned outside the vacuum can  101 A. In other cases, the first heat exchanger  206 A may be positioned inside the vacuum can  101 A. The additional heat exchangers  206 B,  206 C and  206 D, are positioned inside the vacuum can  101 A rather than in a cold block as in the previous embodiments. While four heat exchangers  206  are shown in  FIG.  8   , it is understood that other numbers of heat exchangers may be contemplated. One of these heat exchangers, illustratively the heat exchanger  206 B, may be operable to cool the flange  101 B and the dilution unit 3He supply line  104 . The heat exchangers  206 C and  206 D, which have a lower temperature, are positioned underneath or inside the flange  101 B. They may also be operable to cool the dilution unit 3He supply line  104 , as shown in  FIG.  8   . The expander  210  and the liquid helium reservoir  202  are also inside or within the flange  101 B and provide cold helium that is used to cool the flange  101 C by means of the heat exchanger  110 . 
     The various proposed solutions for providing cooling at the different stages in  FIGS.  1 - 8    may be interchanged. Different solutions can also be combined at any given temperature stage to provide more cooling, or as additional stages to provide cooling at intermediate temperatures. For example, the second closed loop piping circuit  109  may be replaced with a capillary heat pipe and filled with a liquid having a boiling point near the target temperature of the heat exchangers  112 ,  206 A. The combinations shown in the figures are only examples of possible combinations. 
     The above description is meant to be exemplary only, and one skilled in the art will recognize that changes may be made to the embodiments described without departing from the scope of the disclosure. Still other modifications which fall within the scope of the present disclosure will be apparent to those skilled in the art, in light of a review of this disclosure. 
     Various aspects of described herein may be used alone, in combination, or in a variety of arrangements not specifically discussed in the embodiments described in the foregoing and is therefore not limited in its application to the details and arrangement of components set forth in the foregoing description or illustrated in the drawings. For example, aspects described in one embodiment may be combined in any manner with aspects described in other embodiments. The scope of the following claims should not be limited by the embodiments set forth in the examples but should be given the broadest reasonable interpretation consistent with the description as a whole.