Cryostat
Inside a Multi-Stage Cryostat
A cryostat is built as a set of nested temperature stages, each suspended from the one above it by thin, low-conductivity supports and wrapped in a polished radiation shield. In a dry dilution-refrigerator cryostat, a two-stage pulse-tube cryocooler pre-cools the outer shield to roughly 50 K and an inner plate to about 4 K. Below that, the helium-3 / helium-4 dilution circuit provides the final cooling: the still operates near 0.8 K, an intermediate cold plate sits around 100 mK, and the mixing chamber (MXC) reaches a base temperature of 7 to 15 mK. The entire assembly hangs inside a vacuum can pumped to below 10−5 mbar so that gas conduction and convection are effectively eliminated and only radiation and solid conduction remain.
The reason this staging matters for RF work is that cooling power is scarce and shrinks sharply with temperature. A typical dilution unit delivers several hundred microwatts of cooling at 100 mK but only tens of microwatts near 20 mK, so heat must be intercepted at the warmest stage that can absorb it. This is why attenuators on the qubit drive lines are deliberately split across plates: most of the room-temperature thermal noise is dumped at 4 K, where cooling is plentiful, and only a small residual reaches the mixing chamber. Poor heat sinking of a single coax line or attenuator can raise the device temperature by several millikelvin and degrade qubit coherence.
Mechanical stability is the other constraint. Pulse-tube cryocoolers cycle at 1 to 2 Hz, and the resulting vibration couples into RF cables and the sample mount, modulating phase and adding spurious sidebands. Quantum and astronomy cryostats use flexible thermal links, soft bellows, and remote motor mounts to decouple the pulse tube from the cold finger. Materials are chosen for the regime: oxygen-free copper for thermal links, stainless or NbTi coax for low conduction, and Kevlar or carbon-fiber supports where minimal heat leak with high stiffness is needed.
Heat Leak and Cooling-Power Scaling
Q̇rad = ε × σ × A × (Thot4 − Tcold4)
Conductive heat leak down a support or coax:
Q̇cond = (A / L) × ∫ k(T) dT (from Tcold to Thot)
Dilution-unit cooling power (approximate):
Q̇MXC ≈ 84 × ṅ × (TMXC2 − Tin2) watts
Where ε = effective emissivity, σ ≈ 5.67 × 10−8 W·m−2·K−4, A = area, L = length, k(T) = thermal conductivity, ṅ = helium-3 molar circulation rate (mol/s), and T is in kelvin. Example: at ṅ = 500 μmol/s, TMXC = 20 mK gives roughly 17 μW of cooling power.
Cryostat Types and Operating Ranges
| Cryostat type | Cooling method | Base temperature | Cooling power | Typical RF use |
|---|---|---|---|---|
| LN2 dewar | Liquid nitrogen bath | 77 K | Latent-heat limited | HTS filters, LNA test |
| Liquid-helium cryostat | Helium-4 bath | 4.2 K (1.5 K pumped) | Bath limited | HEMT LNAs, SIS mixers |
| Pulse-tube / GM cryocooler | Closed-cycle gas | 2.8 to 4 K | 0.5 to 2 W at 4 K | Radio-astronomy front ends |
| Adiabatic demagnetization (ADR) | Magnetic salt pill | 50 to 100 mK | Single-shot, hours hold | X-ray microcalorimeters |
| Dilution refrigerator | He-3 / He-4 dilution | 7 to 15 mK | 10 to 25 μW at 20 mK | Superconducting qubits |
Frequently Asked Questions
What base temperature can a dilution-refrigerator cryostat reach, and what limits it?
A modern dry dilution-refrigerator cryostat reaches a mixing-chamber base of roughly 7 to 15 mK unloaded and typically runs at 10 to 20 mK once wiring and devices are installed. The limit is the balance between dilution cooling power and parasitic loads: conduction down coax and supports, blackbody radiation from warmer stages, and residual gas. Cooling power scales as about T2, so a unit giving 400 to 600 μW at 100 mK delivers only 10 to 25 μW near 20 mK. Heat sinking every RF line at each plate is what sets the practical base temperature.
How are RF signal lines wired into a cryostat without ruining the base temperature?
Drive lines use staged cryogenic attenuators, commonly 20 dB at 4 K, 10 dB at the still near 0.8 K, and 20 dB at the mixing chamber, so 300 K Johnson noise is thermalized plate by plate before reaching the qubit. Low-conductivity stainless or NbTi coax carries the signal, heat sunk at every stage. Output lines pass through isolators and a HEMT or parametric amplifier so gain happens before the climb back up the thermal gradient; superconducting NbTi coax is preferred on output because it conducts almost no heat.
What is the difference between a wet cryostat and a dry cryogen-free cryostat?
A wet cryostat is pre-cooled by baths of liquid helium and nitrogen that must be refilled, which sets boiloff cost and hold time. A dry cryostat uses a closed-cycle pulse-tube cryocooler to reach 3 to 4 K, then a dilution circuit takes over for millikelvin operation. Dry systems dominate quantum computing because they need no liquid-helium logistics and run for months, though the pulse tube adds 1 to 2 Hz vibration that must be isolated from sensitive measurements.