Cryogenics

50 K shield IVC / 3 K shield 50 mK shield

cold finger (side probe) 50 K plate

3 K plate

still plate

50 mK plate MC plate

still shield

OVC / 300 K shield vector magnet

side probe main probe

1 m

side slot gate valve

(cooling head) probe pumping port

cold finger (main probe) side magnet

y z

Figure 3.5: Internal construction of the cryostat, with both the main and side probes inserted.

The underlying graphics is adopted from the manual [153]. Details of the dilution unit, mix-ture gas lines, heat exchangers and electric lines are omitted. The vector magnet is illustrated symbolically.

Instead of using those legs, we have mounted it on a custom frame made of stainless steel, and lowered it into a pit below ground level, making the top of the cryostat accessible while standing on the floor.

Two samples can be cooled down in the cryostat at the same time, one in the main probe, and one in the side probe. Both probes are top-loading, and once inserted, heat-anchored to the 4 lowermost plates by a spring mechanism. The structure of the probes are identical, however, with the cold finger attached they have different lengths, tailored to the geometry of each slot. Albeit both probes can be used to carry out experiments at the base temperature of the cryostat, they differ in the magnetic fields which can be applied to the sample.

The cryostat is equipped with 2 superconducting electromagnets: a small one in the side slot, capable of generating 2 T in thez direction, and a 2-axis vector magnet in the main slot, with a maximalB field of 9 T in the principal axisz, and 3 T in the secondary axisy. The vector magnet is composed of two coils, a simple cylindrical solenoid generates the z-field, and a Helmholtz coil generates the y-field. Although the z coil can induce a higher field when operated alone, the maximal B field which can be rotated freely in the z−y plane is 3 T, because of the forces arising between the z and y coils. For the same reason, the small magnet in the side slot and the vector magnet must not be used simultaneously. The vector magnet is mounted on the bottom plate of the 3 K shield, and the side magnet on the still shield. In operation of the dilution unit they are cooled to 3 K and 1 K, respectively.

In addition, samples can be directly mounted on the mixing chamber (MC) plate of the cryostat as well. This option has the advantage of an even better heat anchoring, and more experimental space, e.g. to build a microwave circuit, which usually contains bulky elements and would be hard to fit in the cold-insertable probes. Such high frequency circuits are employed in fast read-out schemes based on reflectometry [155], or can be used to apply pump tones on gate lines [139].

The pressures in the IVC, OVC, and still are measured by vacuum gauges. The 50 K and 3 K plates are equipped with platinum resistance thermometers to monitor the cooldown from room temperature, in the 300–10 K range. Additionally, the 3 K, the still, the 50 mK and the mixing chamber plates are fitted with RuO2 thermometers, which can be used below 10 K. These are measured by a low-signal resistance bridge (PicoWatt AVS-47B), to avoid extensive Joule heating.

Acoustical noise insulation

Although the long pulse tubes allowed us to place the loudest component of the re-frigerator system – the compressor of the cryo-cooler – outside the laboratory, the other units still caused a significant acoustical noise. The expanding helium gas in the pulse tube and the external reservoirs emits a rhythmic, chirping sound. To reduce it, the pulse tubes were wrapped in elastic, rubber-like polymer sheets, branded as Tecsound 70. With its high mass density of 7 kg/m², it adds weight to the tubes and thus damps the vibra-tions. Its high visco-elasticity leads to further noise reduction by absorbing the acoustic power. We applied these sheets to the surfaces of the external helium reservoirs and the remote motor assembly of the cryo-cooler as well. Additionally, we have built wooden boxes around these latter two components, with a wideband absorber foam padding on the inside. Both the wooden sheets and the foam pads are approximately 20 mm thick.

The absorber is an open-celled polyurethane foam branded as Hanno-Protecto 51. With all these efforts we have substantially decreased the chirping of the cryo-cooler. In addi-tion, we have applied Tecsound on the inner side of the rack of the gas handling system and the magnet controller, since the vacuum pumps and cooling fans inside them also produced a considerable noise.

Cold finger

The inner diameter of the tail of the 50 mK shield is 53 mm. The cold finger, designed to fit in such a tight space is shown in Figure 3.6. On the leftmost side we see the gold-plated

clamp, which can be expanded laterally to push against the mixing chamber plate of the cryostat, and create a heat anchor. Three more clamps are found on the probe, anchoring to the 3 K, still and 50 mK plates (not shown). The factory-made probe ends in the mixing chamber heat anchor, all the other parts are homemade. The electrical wiring goes through 3 stages of filtering (detailed in Section 3.3.2): a feedthrough capacitor, a VLFX-80 filter and an RC filter mounted on a printed circuit board (PCB), until it reaches the sample in the chip socket. Because of the size constraints, the 18 pieces of VLFX-80 filters are arranged in two levels, cylindrically. The chip socket (type P2020S-D-Au) hosts a 20-pin leadless chip carrier, fixing it with a locknest mechanism (the chip carrier is released by pushing the upper plate of the socket). After loading the sample chip, a cap is put on the cold finger, protecting the sample and forming a Faraday cage around the filtered lines.

feedthrough capacitor

VLFX-80 filter heat anchor to the

mixing chamber Faraday cap RC filter stage chip socket

thread

Figure 3.6: Cold finger of the top-loading probe of the main slot, with the cap removed, exposing the cryogenic filters.

Gas handling system

Dilution refrigerators use the special properties of the ⁴He-³He mixture to reach tem-peratures of a few millikelvin [156]. Below 0.87 K the liquid separates into two phases, one is rich in ³He, the other one in ⁴He (dilute phase of ³He). In operation there is a flow of ³He from the concentrated into the dilute phase. The enthalpy of ³He in the dilute phase is lower, and thus the temperature is lowered, in analogy to the evaporation of liquids. The low temperature is maintained continuously by circulating ³He in a closed circuit. Unlike the single-shot mode of pure³He refrigerators, dilution refrigerators can op-erate indefinitely long – a capability highly appreciated in the investigation of multi-gated devices.

The gas handling system (GHS) of the cryostat controls the valves of the mixture circuit and other vacuum lines. It hosts the scroll pump and turbo pump which circulate the mixture, a membrane compressor – which facilitates the condensation of the mix-ture initially, but it is bypassed in normal circulation – and a rotary vacuum pump for general purposes. The cabinet itself is the leak-tight container of the ⁴He and ³He gas.

A microcontroller automates the processes of condensation, maintaining the circulation, and mixture recovery. The valves and pumps can also be operated manually on the front panel, where readings of the vacuum gauges are also shown. Liquid nitrogen-cooled cold traps are inserted in the mixture loop to avoid contamination and blockage in the dilution unit.

Cooldown

The cooldown of the cryostat starts with evacuating the OVC and IVC. Then we intro-duce He into the IVC as an exchange gas, and turn on the cryo-cooler.⁴ In approximately 80 hours the temperature saturates at 3 K, a graph of a cooldown as a function of time is shown on Figure A.6. By using ∼150 l liquid nitrogen to precool the system to 77 K one can save ∼ 24 hours. All the materials used for the noise insulation have good temper-ature stability, nevertheless, for the time of the initial cooldown from room tempertemper-ature the wooden boxes are removed, because the components of the cryo-cooler can become quite warm.

Around 40 K the charcoal absorber in the IVC starts to absorb the He exchange gas.

To avoid it, the absorber is heated electrically. After reaching 3 K, to reduce the heat coupling between the different cooling stages, we turn off the heating of the charcoal pump, and the pressure in the IVC drops. Next, we start the mixture condensation using the GHS. First the³He, then the ⁴He gas is condensed, and the GHS switches to normal circulation mode. The condensation takes for ∼ 2 hours, the temperature of the mixing chamber plate saturates at ∼7 mK in ∼4 hours.

The cryostat can be cooled with or without the probes inserted. In the latter case – or when changing samples –, we begin to load a probe into the cold cryostat by mounting it on the gate valve. Following evacuation, we flush it with He gas. Then we open the gate valve and slowly lower the probe into the position depicted in Figure 3.5. By tightening a screw on the top of the probe we expand the four pairs of anchoring clamps. Via these anchors, the dilution unit has∼120 µW cooling power at 100 mK to the probe.

Although the big mass, and accordingly, the high heat capacity of the vector magnet elongates the initial cooldown of the cryostat, it also serves as a heat buffer, facilitating the cooldown of the probe when we insert a sample. Even though the cold finger of the main probe is quite heavy, it is cooled down from RT to 3 K in∼4 hours.