The Dilution Refrigerator

Ten Millikelvin

The lowest plate is the mixing chamber plate. It runs below 10 mK, a hundredth of a degree above absolute zero. The quantum processor hangs beneath it in a shielded can.

The cosmic microwave background is 2.725 K. This is two to three hundred times colder.

Mixing chamber ≤ 10 mK · cosmic background 2.725 K

Why So Cold

A superconducting qubit is a superconducting circuit, so first it must be cold enough to superconduct. The harder demand comes from heat: thermal energy is about kT, and the gap between the qubit’s two levels is hf. At 5 GHz, hf/k ≈ 0.24 K.

kT must be far below hf, or heat kicks the qubit into its upper level. At 4 K it would spend almost half its time excited; at 20 mK the chance of a thermal excitation is about six in a million; at 10 mK, about four in a hundred billion.

hf/k = 0.24 K (5 GHz) · excitation ≈ e^(−hf/kT)

Cut Open: Stage by Stage

Outside is the vacuum can; inside it, nested radiation shields, each hanging from a plate. The plates are gold-plated copper, which conducts heat well; between them run thin fibreglass rods, which conduct it badly.

From the top: the room-temperature plate, about 40 K, about 3 K, the still at about 0.8 K, the cold plate at about 0.1 K, and the mixing chamber at about 0.01 K. The upper two are usually called the 50 K and 4 K plates; they run somewhat colder.

300 K → about 40 K → about 3 K → about 0.8 K → about 0.1 K → ≤ 0.01 K

The Pulse Tube: Down to 4 K

The first two stages are cooled by a pulse-tube cooler. A compressor drives helium gas back and forth through the tubes, compressing and expanding it, which carries heat upward. Nothing moves inside at low temperature.

Fridges like this are called “dry”: no liquid helium is poured in. A typical pulse tube removes 1 to 2 W at 4.2 K.

First stage about 40 K · second about 3 K · 1–2 W at 4.2 K

Helium-3 Floats on Helium-4

Further down, the work is done by helium’s two isotopes. Below 0.87 K a mixture of helium-3 and helium-4 separates into two layers: nearly pure helium-3 on top, a dilute phase of mostly helium-4 below.

Even close to absolute zero the dilute phase still holds about 6.5 % helium-3. In the mixing chamber, helium-3 atoms cross the boundary from the upper layer into the dilute phase, and like a liquid evaporating into a gas, they take up heat. That step is the cooling.

Separates below 0.87 K · dilute phase about 6.5 % helium-3

Round the Loop

The dilute phase runs up through heat exchangers to the still. At about 0.8 K, helium-3 evaporates far more readily than helium-4, so more than nine tenths of the gas pumped off is helium-3. As it is pumped away, more helium-3 crosses the boundary in the mixing chamber to replace it.

At room temperature the helium-3 is compressed and sent back down the condensing line: cooled by the pulse tube, liquefied, then through a chain of heat exchangers, where the cold outgoing liquid cools it, into the top of the mixing chamber again. A typical flow is under a millimole a second.

Still pumped → compressed → condensed → heat exchangers → mixing chamber

Lines That Shed Heat

The microwave signals that drive the qubits come down from room temperature. The lines would carry room-temperature thermal noise down with them: at 6 GHz, 300 K means about a thousand thermal photons in each mode.

So each drive line has a 20 dB attenuator at 4 K, at the cold plate and at the mixing chamber. Each one removes 99 % of the noise from above and adds a little of its own stage’s. At the mixing chamber about two thousandths of a photon is left. Readout signals going up pass isolators at the mixing chamber, then a HEMT amplifier on the 4 K plate.

20 + 20 + 20 dB · thermal photons about 1,000 → about 0.002

Taken Apart

The vacuum can and the radiation shields come off downwards, and the plates show. A cooldown starts with pumping out the can; from room temperature to base takes about a day on common systems.

Whichever stage the pointer rests on is lifted out and named.